NATIONAL BUREAU OF STANDARDS REPORT

10 487

THERMODYNAMIC DATA FOR INDUSTRIAL INCINERATORS

Thermochemistry Section

Physical Chemistry Division

Institute for Materials Research

for Office of Standard Reference Data

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

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2 Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.
NATIONAL BUREAU OF STANDARDS REPORT

MBS PROJECT

3160414 May 1972

NBS REPORT

10 487

THERMODYNAMIC DATA FOR INDUSTRIAL INCINERATORS

with

Guides to the Use of the Tables

By

George T. Armstrong

and

Eugene S. Domalski

Final Technical Report

to American Society of Mechanical Engineers

Research Committee on Industrial Wastes

NATIONAL BUREAU OF STA

for use within the Government. E and review. For this reason, the whole or in part, is not authoriz Bureau of Standards, Washington

the Report has been specifically p

IMPORTANT NOTICE

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 201 5.

; accounting documents intended objected to additional evaluation

listing of this Report, either in

Office of the Director, National

the Government agency for which

pies for its own use.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

Table of Contents

Page

20.0 Preface 1

20.1 Introduction. .................... 1

20.2 Anticipated Needs for Thermodynamic Data. . 3

20.3 Scope and Preparation of Tables 6

20.4 Status of Thermodynamic Data and Auxiliary Aids:

Recommendations for Further Action. ......... 10

20.5 Collaborative Arrangements. ............. 12

21.0 Discussion and Aids for the Use of the Tables ....... 14

21.1 Processes Occurring in Incinerator Combustion .... 14

21.2 Definitions of Thermodynamic Terms. ......... 16

21.2.1 Temperature ........... 16

21.2.2 Energy of a System. 18

21.2.3 State Function. ............... 18

21.2.4 Internal Energy . 19

21.2.5 Enthalpy. ..... 20

21.2.6 Entropy . 22

21.2.7 Free Energy ........ . . 24

21.2.8 Free Energy Function 24

21.2.9 Helmholtz Function. 24

21.2.10 Massieu Function. .... 25

21.2.11 Gibbs Energy. ..... 25

21.2.12 Planck Function 26

21.2.13 Heat Capacity 27
Table of Contents (Cont'd)

Page

21 . 2. 14 Enthalpy of Reaction 27

21.2.15 Enthalpy of Formation. 29

21.2.16 Thermodynamic Standard States and Standard

Reference States 30

21.3 Tabulated Thermal Functions 31

21.3.1 Non-Standard-State vs Standard-State

Functions. ...... 32

21.3.2 Different Temperatures for the Energy Base . . 33

21.4 Calculation of Thermo chemical Quantities 35

21.4.1 Additivity of Chemical Processes . 37

21.4.2 Additivity of Thermodynamic Quantities .... 37

21.5 Enthalpy and Internal Energy of Combustion 38

21.5.1 Calculation of Observed Heat Effects from

Enthalpies of Formation 38

21.5.2 Isothermal Constant-Pressure Combustion. ... 39

21.5.3 Isothermal Constant-Volume Combustion 41

21.5.4 Type Reactions for Combustion of Organic

Compounds - Calculation of Enthalpy of

Combustion for the Isothermal Process 43

21.5.5 Enthalpy of Formation by Estimation 53

21.5.6 Calorific Values or Heating Values of Fuels. . 54

21.6 Reaction Energy and Temperature 60

21.6.1 Effect of Temperature on Enthalpy of Reaction. 60

21.6.2 Relationships between Enthalpies of Isothermal Reaction at Different Temperatures . . 63

21.6.3 Enthalpy Relations when the Temperature of the

System is Allowed to Change 64

21.7 Reaction Equilibrium and Temperature. . . 67

ii
Table of Contents (Cont'd)

Page

22.0 Supplementary Sources of Thermodynamic Data on Chemical

Substances and Materials 78

23.0 Methods of Estimation of Thermodynamic Data 99

24.0 Selected References on Combustion and High Temperature

Reaction Equilibria 108

25.0 Tables of Thermodynamic Data 116

25.1 Description of the Tables 116

25.2 Table I-A, Enthalpies of Formation of Some Organic

and Inorganic Carbon Compounds at 298.15 K 122

25.3 Table I-B, Compound Name - Formula Index 154

25.4 Table II, Enthalpies of Formation of Organic

Polymers at 298.15 K 181

25.5 Table III, Enthalpies of Formation of Inorganic

Oxides at 298.15 K 185

26.0 Appendix 201

26.1 Symbols for Thermodynamic Quantities (IUPAC) 201

26.2 Selected Symbols for Other Quantities Needed in

Thermodynamics 202

26.3 Units of Measurement - International System (SI) . . . 204

26.4 Definitions of the SI Base Units 204

26.5 Prefixes 206

26.6 SI Derived Units (partial listing) 207

26.7 Other Units Exactly Defined in Terms of SI Units

(partial listing) 208

26.8 Physical Constants 209

26.9 Atomic Weights (Relative Atomic Masses) of the

Elements 211

iii

Part II. The Scientific Approach

Thermodynamic Data for Industrial Incinerators

with Guides for the Use of the Tables

20.0 Preface

20 . 1 Introduction

Maintenance of a high-quality clean environment in our current

technological civilization has many facets; however, there is no question

that effective disposal of waste materials is a primary factor in

achieving this desirable goal. The neglect of this perennial, necessary,

housekeeping chore would lead to accumulation of discarded materials in

a way that could not be ignored for reasons of health, safety, efficient

performance of activities, and aesthetic impact. The means of accomplishing the disposal of waste have varied with the state of development of

our civilization and technology and in the most primitive procedures consisted of dumping or dispersal on land, into oceans and lakes, into rivers,

or into the atmosphere.

More sophisticated techniques consist of chemical or physical

processing to modify the form of the wastes and then dumping as before.

Still more sophisticated techniques include chemical or physical processing as before, but modified or selected to achieve a goal of partial

or complete re-use of the waste materials.

The initial cost and effort of devising ways to carry out methods

of disposal increased rapidly with their increasing degree of sophistication. As a result, mostly for economic reasons, the least sophisticated
2

and most direct means are usually used. Satisfactory and optimum technological procedures for the more sophisticated means of disposal have

not been developed yet for many forms of waste.

Among the chemical processing techniques of moderate sophistication

incineration ranks as an important and widely used device for converting

wastes to less undesirable forms before dumping or dispersal. Incineration is applicable to gaseous, liquid, or solid wastes. It reduces the

residual bulk of many solid or liquid wastes, converts most organic

materials into gases which are already part of the natural atmosphere and

can be released directly into it, generates heat which can be used in some

instances, used readily available oxygen or air as its principal chemical

agent, causes chemical processes that are comparatively well understood,

and is readily carried out rapidly on large quantities of materials in

apparatus of comparatively simple design.

Disadvantages of incineration are its generation of some noxious

or toxic gases, smoke, and other atmospheric pollutants unless specially

designed equipment is used, and the low economic value of the products

of combustion. The generation of atmospheric pollutants can be largely

controlled by proper design of the incineration apparatus or by further

processing of the effluent gases before emitting them to the atmosphere.

The ultimate limitation on the usefulness of incineration as a waste

disposal technique (with respect to combustible substances) is probably

going to be the implicit extravagance' of its use.

Nevertheless, because of several advantages listed above, incineration as a waste disposal technique is going to be in use for a long

time into the foreseeable future. As indicated above, the proper design
3

of incinerators is, therefore, environmentally and economically desirable,

and, because of legal specifications on emission, may also be required.

The American Society of Mechanical Engineers (ASME) recognized this

problem as of growing importance in the light of increasing professional

and public awareness of the whole waste-disposal problem and its environmental implications. The ASME Research Committee on Industrial Wastes

undertook to provide a guide to the design of industrial incinerators as

an ASME publication. In collaboration with a task group of his committee,

the National Bureau of Standards through the Office of Standard Reference

Data (OSRD) has prepared this compilation of thermodynamic data on potential

ingredients and products of combustion of industrial wastes. Some guides

to the use of the data for computation of thermodynamic parameters associated with the incineration process are also given. The use of this type

of data is essential in the calculation of incinerator design parameters

for particular disposal problems.

Incineration will undoubtedly assume a well-defined place in the

spectrum of methods available for waste disposal. The field at present

is in a state of considerable innovation and flux; but also includes noncombustion chemical treatments, pyrolysis, and atomization. The data and

the accompanying guides to their use will probably find application in

these areas too because parameters of many of the processes involved can

be calculated using the same input thermodynamic data.

20 . 2 Anticipated Needs for Thermodynamic Data

In the design of industrial waste disposal units, in particular

incinerators, the engineer has two major problems which must be solved
4

in an internally consistent way in order to obtain satisfactory performance. (a) The composition of the mix of input materials, which may

consist in general terms of waste, added fuel, and combustion air or

oxygen, must be understood and adjusted in such a way as to allow the

requisite combustion processes to be carried out leading to known products. (b) The heat balance of the process based on energies of combustion (or other reaction) must be known at various stages of the

process, in order to allow proper temperature control to be maintained.

To meet these requirements there is need for a substantial body of thermochemical data for ingredients of waste, either as enthalpy of combustion

or enthalpy of formation at room temperature, and need for some information

on products of combustion at high temperatures such as their enthalpies

of formation, heat capacities and Gibbs energies. These needs resemble

in many ways those which have been met in the past few years for quantities

of thermodynamic data on rather large numbers of substances as for example

in the rocket propulsion program.

Looking at the waste disposal problem from another point of view

one sees that the use of incinerators has two quite different aspects.

In the first instance, mechanical engineers involved in incinerator design

are faced with the problem of obtaining effective combustion and therefore

must know the combustion performance of the materials they put into the

incinerator in an approximate way. Under many existing circumstances a

high degree of precision in the calculations is not required. However a

secondary problem now is known and is likely to be of considerably more

importance in the future. This is the control of noxious substances
5

emitted by the incinerator which tend to pollute the atmosphere. Because

of the human factors involved in the exposure of the public to the emission

products and because of federal, state, or municipal control mechanisms

which are likely to be specified to limit pollution of the atmosphere,

it will be very important ultimately to know the kind of substances that

will be present in the products of combustion and to guarantee the upper

limits of specified substances. In order to be able to estimate the

combustion product concentrations with assurance we anticipate that considerably more accurate knowledge of the enthalpies of formation of the

ingredients, and the enthalpies of formation and other thermodynamic

properties of a much wider range of products will be required than are

needed in the first instance.

To meet the requirements for thermodynamic data by engineers and

designers, a handbook is needed which will provide (a) tables of thermodynamic data applicable to common problems of waste disposal by incineration and (b) guidance in the use of the tables and in obtaining supplementary information. The handbook may appropriately contain a discussion

of the application of thermodynamic data to calculation of heat balances,

and the effects of the composition of the input materials on the output

composition; also, a discussion of the limitations of accuracy of the

calculations, and the possible need for more elaborate analysis and more

accurate data on input materials if output products must be closely controlled (as for pollution control)

.

The required tables are enthalpies of formation and Gibbs energies

of as large as practical a number of potential input materials at 25°C,
6

and of potential incineration products at 25 Q C and elevated temperatures

ranging to 2000 °C or higher.

An important feature of the presentation of technical data should

be a format suitable for engineering use, and rather detailed guidance

as to use of the data. In additions, as it is not practicable to include

available thermodynamic data on all substances* nor do data exist on

all substances that are potentially of interest, it is important to

provide two specific supplements to the thermodynamic data: (a) bibliographic references to reliable and extensive collections of data on

additional materials, (b) selected lists of methods of estimation of

the properties. A discussion of the merits of these referenced collections and methods of estimation will be helpful to the engineer.

20 . 3 Scope and Preparation of Tables

Following general lines of the discussion presented above, preparation of material for a handbook of thermodynamic data for industrial

incinerator design and operation was undertaken.

As an initial step in limiting the coverage of substances to be

included, a survey was made by Mr. Wayman L. Calhoun (Union Carbide Corp.)

of the ASME Research Committee on Industrial Wastes. The persons queried

were primarily members of 'the Subcommittee on Coordination with Associations and Government. The results of this survey in general indicated

the following points:

(a) A large fraction of the industrial waste to be disposed of

consists of organic materials which fall generally into

three categories:
7

(1) pure substances, well defined

(2) organic materials of variable composition but

resolvable into known components

(3) poorly defined mixtures

(b) A smaller amount consists of inorganic materials. Among

these, ingredients include essentially all the elements

in small amounts and some, such as ferrous and non-ferrous

metals, in relatively large amounts.

On the basis of this survey, the time and effort available, and the desire

to have the tables available in a reasonably short time to enhance their

early usefulness, the final plan for the tables was as follows:

Enthalpies of formation at 25°C (298. 15K) were agreed to be of

primary importance. Tables of thermodynamic functions of temperature

are of less immediate importance as mapy of these are available in the

extensive JANAF Thermo chemical Tables and the computer tapes associated

with them (See source 20, Section 22.0).

The scope of the substance coverage was established as follows:

(a) Organic compounds. All organic substances for which experimental data are available, within the limits of time and

effort available.

(b) Organic materials (not well characterized). Limited to

polymeric substances to which a reasonably good formula

can be attributed.

(c) Inorganic compounds. Inorganic oxides, only.
8

The decision not to list poorly defined materials was made deliberately because of the open-ended nature of the list, the lack of

carefully screened sources of data, and the possibility of approximating

combustion values from data on related pure substances. The alternative

decision was made to include all polymers for which data could be found,

as polymeric substances were prominent among the large volume waste

products

.

For the above three classes of substances enthalpies of formation

at 298. 15K are provided in tables obtained as described below.

To prepare Table I, ’’Enthalpies of Formation of Organic Compounds

at 298.15 K", advantage was taken of the fact that in the Chemical

Thermodynamics Data Center a comprehensive monograph is in preparation

for the OSRD. Files of compounds for which enthalpies of combustion

have been determined now comprise about 4000 compounds. The data on

these have not all been evaluated. The tabulated list, therefore,

comprises the 1000 compounds for which work had been completed. The

selection of these compounds was made on the basis of (a) important

functional groups and, (b) importance of the compound. The selection

of appropriate substances was aided by the fact that a recent previous

review had been made for NASA in which compounds of primary interest in

biology and biochemistry had been selected for early evaluation.

In the selection of values for enthalpies of formation, the data

were derived from measured values of enthalpies of combustion, usually

performed by bomb calorimetry. The measurements had been made, in some

cases, over a period of a hundred years, and hence were of very non-
9

uniform quality. The data for each substance were evaluated and updated

according to uniform criteria, which are described by Domalski (source 4,

Section 22. 0) . They represent the best values that can be derived from

existing data.

Because of the prospective repetition of needs to tabulate organic

compounds with their enthalpies of formation and other data, a permanent,

machine-readable file was organized during the course of this work. The

final listing of compounds which forms Table I was prepared from this

file.

To prepare Table II, "Enthalpies of Formation of Organic Polymers

at 298.15 K", the Chemical Thermodynamics Data Center file of enthalpies

of combustion of organic compounds was combed for relevant substances.

Recent reviews of enthalpies of formation of organic polymers were also

searched. All polymers were included for which reliable enthalpies of

formation could be determined from their enthalpies of combustion.

The final table comprises 39 polymers.

The values listed in Table II were arrived at in the same way as

those in Table I; hence, they represent the best values available on

the basis of existing experimental data.

To prepare Table III, "Enthalpies of Formation of Inorganic Oxides

at 298.15 K", the recent set of NBS compilations of critically evaluated

data on the thermodynamic properties of inorganic substances was the

principal source. These tables (NBS Technical Note 270, D. D. Wagman,

et al., 1965-1971 and continuing) are the most recent comprehensive

critical evaluation on inorganic compounds, and have the title "Selected
.1.0

Values of Chemical Thermodynamic Properties". Oxides for which enthalpies

of formation were known to have been determined, but not yet found in

completed sections of TN 270 were obtained principally from the JANAF

tables. References to the sources of data are given appended to Table III.

Each of the sources listed above is a tabulation of values by

competent reviewers who have devoted years of systematic study to the

selection and evaluation of chemical thermodynamic data. The tabulations

quoted in each case are authoritative and may be said to represent the

best values available on the basis of existing experimental data. Only

one or two estimated values have been included.

The prepared descriptive material consists of:

(a) general background of thermodynamic definitions and formulas

necessary to an understanding of the discussion; (b) detailed discussion

of the calculation of thermodynamic quantities at 298.15 K, using the

material from the tables; (c) a brief general discussion of calculations

involving elevated temperatures; (d) supplementary sources of thermodynamic

data, and methods of estimation, and (e) an appendix giving auxiliary

constants, symbols, and units of measurement.

20.4 Status of Thermodynamic Data and Auxiliary Aids: Recommendations

for Further Action

Listed below are the stronger impressions obtained concerning needs

for information as compared with its availability and completeness. A

few recommendations are made for action to alleviate some deficiencies

or fill certain needs.
11

1. A large category of ingredients for incinerator processes

was found to be "poorly characterized materials": materials which by

dint of some effort could be resolved into well defined substances,

and materials for which this might not even be possible. These materials

are not included in the tables for the handbook. However, the practical

incinerator process manager is going to need information to allow him

to make ad-hoc decisions. This information can take the form of (a)

tables of classes of ingredients of typical poorly characterized

materials, together with appropriate elemental composition and enthalpies

of combustion or a pseudo-enthalpies of formation; (b) tables of enthalpies

of combustion or pseudo-enthalpies of formation of well known classes of

materials for which only average values can be cited. Such materials as

coal, hard-woods, soft-woods, petroleum oils, fall in this category. The

accuracy of the enthalpy values may not be high, but the elemental composition and a pseudo-enthalpy of formation would allow such materials

to be fed into computer programs for calculating high temperature equilibria

as well as any well-defined substance. Only the products of combustion

enter the final equilibria, and their proportions will be fixed by the

proportions of the elements and parameters independent of the nature of

the combustible material.

2. In reviewing the reactions for possible combustion reactions

involving water and various volatile acids, it became apparent that

conditions of operation of an incinerator (for example: using scrubbing

water on effluent gases) can be readily envisioned which will require

vapor-liquid equilibria of a few volatile acid-water solutions. The
12

relevant data include such parameters as partial pressures of HC1 and

H^O as functions of temperature and mole raticfe for solutions of HC1

in water. Other acid gases such as HF, SO^, SO^, N 2^5 a-*- so enter

such equilibria. Satisfactory data for these equilibria probably exist,

but could not be organized within the scope of this project.

The number of organic substances for which enthalpies of combustion

are known is much larger than those tabulated. The critical review of

the data is proceeding rapidly, and a much longer list will be available

in perhaps two years. The list given as Table I could then be augmented.

A serious deficiency exists in the availability of experimental

enthalpies of combustion (and formation) of organic polymers. This

is made quite obvious by the availability of reliable combustion data

for only 39 out of the multitude of polymers in large scale industrial

use. More experimental values are needed on these large-volume chemicals,

to provide additional data for an augmented Table II. There are also

other important uses for such data.

20 . 5 Collaborative Arrangements

As the administrators of the National Standard Reference Data

System (NSRDS) , the Office of Standard Reference Data (OSRD) at NBS

(Dr. D. R. Lide, Director) agreed to provide the handbook materials to

ASME for its Research Committee on Industrial Wastes (E. S. Monroe,

Chairman) . The working organization within NBS which was assigned by

OSRD to carry out the project was the Thermochemistry Section of the

Physical Chemistry Division, Institute for Materials Research. Dr.

George T. Armstrong and Dr. Eugene S. Domalski carried out the work.
13

using the resources of the Chemical Thermodynamics Data Center (Mr. D. D.

Wagman, Manager), which is organizationally located in the Thermochemistry

Section.

The organization of the work was planned by Mr. E. S. Monroe

(E. I. du Pont de Nemours and Company, Inc.), Mr. R. A. Conway (Union

Carbide Corp.), Mr. W. L. Calhoun (Union Carbide Corp.) and Dr. S. R.

Beitler (Director of Research, A.S.M.E.) all representing the A.S.M.E.,

and by Dr. H. J. White, (OSRD) , Dr. George T. Armstrong, Chief, Thermochemistry Section, Dr. C. W. Beckett, Physical Chemistry Division Office,

and Dr. David Garvin, Coordinator of Data Programs for the Physical

Chemistry Division Office. During the early part of 1971, after the

project was started, Mr. F. H. Small (Union Carbide Corp.) replaced

Mr. Conway.

During the course of the work, continuing guidance was received

from the ASME Research Committee on Industrial Wastes. Assistance from

the staff of the Chemical Thermodynamics Data Center, in particular

Mrs. J. J. Grimes and Miss B. Beckwith is acknowledged, in setting up

a mechanism for information storage and retrieval of enthalpies of

formation of organic compounds, and from Mr. J. I. Minor of the Thermochemistry Section in processing the data files.
14

2 1 . 0 Discussion and Aids for the Use of the Tables

21.1 Processes Occurring in Incinerator Combustion

Thermochemical and thermodynamic data have well defined applications in the analysis of incinerator processes

and in the design of incinerators. The energy released

during the combustion process appears as heat. This heat

causes the gases formed in the reaction to be hot, and the

non-volatile materials to form hot ash, cinders, or molten

refractory materials. It may be carried away in hot effluent

gases or by conduction through the walls. The heat must be

under control in that the incinerator must be designed to

withstand it, and possibly, by heat exchangers, to make use

of it in an auxiliary operation. This heat may be used to

volatilize non-combustible substances in the ingredients,

such as water, which needs only to be volatilized in order

to make it an acceptable effluent into the atmosphere. Under

any circumstances the heat will be carried away from the

reaction zone; and the mechanism by which this is to be done

is an important part of the incinerator design. The reaction

processes may require supplementary heat or possibly damping

in order to make the combustion complete or to provide gaseous

or solid products as appropriate at the end of the process.

Information required for the calculation of these processes

are the nature of the ingredients and products, and the

values of 'cheir enthalpies of formation, heat capacities

or enthalpies of the products as functions of temperature.
15

The heat of the reaction may cause some of the products

formed to be partially or completely dissociated. The temperature to which the effluent gases and the residues are

heated, and the nature of the products found in them are

determined to a large extent by the dissociation equilibria

and other equilibria that can occur as a result of interactions between the products of combustion. The proportions

of materials present in the products are strongly dependent

upon the equilibrium constants of the various possible reactions. The important thermodynamic data here are the Gibbs

(free) energies of formation and the equilibrium constants

of formation of the products of reaction at the possible

temperatures. The occurrence of spontaneous reactions in a

constant pressure system is governed by a decrease in Gibbs

energy; and the equilibrium proportions of substances present

are determined (as the equilibrium constant) from sums of

the Gibbs energies of formation from the elements. Available

data may be the Gibbs energy or it may be enthalpy and entropy data from which the Gibbs energy may be calculated.

The equilibria are strongly temperature dependent; hence

there are strong connections among the enthalpy of reaction,

the heat capacities of the substances, heat retention in the

incinerator, and the proportions of products that will be

present following the reaction.
16

A third area of importance of the thermodynamic data

is in the possible interaction of ingredients or products

of combustion with the materials of construction of the incinerator. Here much more flexibility occurs. The materials

to be burned may be relatively fixed before incinerator design is attempted, or on the other hand the variety of materials may be very great. The selection of materials of

construction may depend upon knowledge of volatility or refractoriness of substances possibly to be formed by interaction of the hot incinerator gases with the walls.

Thermodynamic data applicable to the solution of some

of these problems are discussed in the following parts of

Section 21. This presentation and some general principles of

their use is not an attempt to recommend methods for calculation of specific incinerator design parameters, but rather

to provide a ready reference to the meaning and typical applications of thermodynamic data of special value in such

applications.

21.2 Definitions of Thermodynamic Terms

21.2.1 Ternp erature . Temperature is a measure of the hotness

of a system. Notes A system may be a given quantity of a single substance, or it may be a complex mixture or aggregate

of material.

When analyzed in terras of the motions of the acorns or molecules

constituting a material, the temperature is a measure of the
17

average kinetic energies of their random movement. Substances in a system and all parts of a system tend to approach the same temperature, and will attain the same temperature if disturbing processes are absent.

The temperature occurs as a parameter of importance in

all heat transfer processes, in chemical reaction processes,

and in the properties of materials and chemical substances.

All thermodynamic formulas and laws involving temperature with a basis in theory require temperature to be

expressed in terms of the thermodynamic or absolute temperature scale. The internationally agreed version of the thermodynamic temperature scale is the International Practical

Temperature Scale. The kelvin (symbol K) is the unit of temperature and the size of the kelvin is determined by defining

the temperature of the triple point of water as 273.16 K.

The freezing point of water (melting point under 1 atm pressure

of air) is defined as 0.01 K below the triple point, hence

the normal ice point is 273.15 K.

The ice point temperature is 0°C on the frequently

used Celsius (centigrade) temperature scale. The size of

the temperature units is the same on the Celsius and the

thermodynamic scales. The relationship between the scales

is expressed by the equation

t = T -273.15

where t is the temperature (°C) on the Celsius scale, and T is

the temperature (K) on the thermodynamic scale.
18

21 „2„2 Energy of a System

Every physical system has associated with it a certain amount of energy which is variously described in terms

of several state functi ons-- internal energy, enthalpy, Gibbs

energy, or Helmholtz energy- -depending upon the use to which

the information is to be put*

The energy of a system is an extensive parameter; that

is, the amount of energy is proportional to the mass (kilograms) or the amount (moles) of each substance present.

Note: The unit of energy is the joule (symbol J)

,

though values are commonly given also in

calories (symbol cal) and, in engineering

practice are sometimes given in British

thermal units (symbol Btu) . The amount of

substance referred to in an equation is in

terms of moles (symbol mol). In this handbook, unless otherwise specified, a tabulated

enthalpy, or other thermodynamic quantity

attributed to a particular substance is for

a mole of that substance as described by its

formula. The mass corresponding to a mole

is found by taking the molecular weight is

grams. The engineering unit pound mole

(symbol lb -mol) is not used in this handbook.

See Appendix section 25 for definitions of

the units of measure and for relationships

between the units.

21.2.3 State Function

State functions are any of several extensive thermodynamic functions, relating to the energy of a system, of which

the values are uniquely defined for a given system when its

state is defined. These include internal energy , enthalpy , Gibbs energy, Helmholz energy , entropy , and some functions

derived from them. The state of a system is defined when
19

it is at equilibrium in a given physical state at a given

temperature, and under a given set of external stresses,

such as a given pressure. The important feature of a state

function is that the value does not depend upon the path

by which the specified state of the system is reached. Put

in another way, the difference in value of a state function

in two states of a system is independent of the path by

which the system is changed from one state to the other.

It should be noted that all the state functions defined below are not required for direct use in incineration

design. However, they need to be defined here, because of

their uses in tabulation of thermal data (see Sec. 21. 3) in

some of the auxiliary reference sources to be cited later.

21.2.4 Internal Energy

A system is said to have internal energy (symbol U)

which changes as heat is added or removed, and work is done

on or by the system. While the absolute value of the internal energy of a system is arbitrary, and unimportant for

the purposes of thermodynamics, changes in internal energy

can be measured. The equivalence of heat and work in their

influence on the internal energy of a system is expressed by

the equation

AU = q + w

In the above equation, AU represents a change in internal

energy. An increase AU in the internal energy of a system
20

may be caused by supplying an amount of heat, q, to the

system and doing an amount of work, w, on the system. The

two quantities, w and q, are not state functions, but depend

on the path followed. They have the same energy units,

may be applied simultaneously or sequentially, and may have

any values relative to one another. The direction of heat

and work transfer as denoted by their signs must be chosen

in a consistent manner. There is no universally accepted

convention as to the signs of heat and work energy supplied

to a system, so care should be taken to note the convention

used in any particular presentation.

The internal energy is a function of temperature, pressure, and other parameters, which has a characteristic value

for a fixed amount of a particular substance in a defined

state. Another common symbol for internal energy is E.

In a reaction carried out at constant volume the heat

effect of the process measures a change AU (or AE) in the substances. If heat is produced by the reaction (exothermic

reaction) the change AU is negative. An engineer examining

combustion measurements made in a bomb calorimeter may find

the data expressed as AU or AE as this is a constant volume

process.

2 1,2.5 Enthalpy

The enthalpy, sometimes called heat content, (symbol H)

,

of a system is a measure of its energy which differs from the
21

internal energy by the amount of work done by the system

against the pressure of the surrounding medium. The enthalpy

is defined by the following relationship

H = U + pV

in which U is the internal energy, p is the pressure of the

surrounding medium, and V is the volume of the system. The

enthalpy and the internal energy of a system are the same

when the pV term is zero. This occurs only when (1) the

system is a condensed phase and the external pressure is zero,

or (2) when the system is an ideal gas at the absolute zero

of temperature.

In a constant pressure process, (i.e. a process in

which initial and final pressure are the same) the change

in enthalpy is given by the following equation

AH = AU + pAV

The change in enthalpy associated with a process is equal to

the change in internal energy only when (1) the pV terms are

all zero as above, or (2) when the volume of the products is

the same as the volume of the reactants.

As in the case of internal energy, the absolute value

of the enthalpy is arbitrary and only changes in enthalpy

can be measured.

For processes occurring at constant pressure, such as

combustion at normal atmospheric pressure, if the products are

cooled to the starting temperature, the heat effect observed
22

is the enthalpy change AH. For an exothermic reaction AH

is negative. See Section 21.5 for illustrations of calculations of AU and AH.

When two molecular species in a system react to form

another molecular species, such as

H-H(g) + Cl-Cl(g) -* 2H-C1 (g)

and the reaction is exothermic (AH is negative) we can

say that the molecular arrangement of the products is more

stable, or gives stronger bonds than those of the reactants.

This excess energy released by forming the stronger bonds

becomes available and may be released as heat. A decrease

in internal energy, or enthalpy is a driving force which

tends to cause a process to occur spontaneously (in order

to arrive at a more stable state), but though it is a dominant

effect, it is not sufficient in itself®

The entropy (symbol S) is a measure of the disorder

or randomness in a system. Another way of putting it is

that the entropy of a system is directly related to the

number of states of existence available to it. If the

number of states of existence for a collection of atoms is

greater in one molecular configuration than in another configuration the entropy will also be greater. The difference

in the entropy of liquid water and gaseous water may be used

as an example. When water is condensed to liquid its
23

molecules have much less freedom of movement than when the

water is a gas. The gas molecules have many more configurations available to them, and so at a given temperature

the entropy of a given amount of water vapor is much greater

than that of the same amount of water liquid.

Heating a body reversibly increases its entropy by

an amount equal to the quantity of heat divided by the

absolute temperature. Thus an infinitesimal amount of

heat, 6q, supplied reversibly increases the entropy of a body by d6 where

For a given substance the kinetic, rotational, and

vibrational movement of the molecules increases with temperature. The amount of disorder therefore increases with

temperature and the entropy of a substance is greater at

a high temperature than at a low temperature.

The tendency for entropy to increase is a driving force

which causes processes to occur spontaneously, but is not

sufficient in itself. It is usually not sufficient to overcome an opposing energy change and where it is sufficient we

will have a spontaneous endothermic process. The entropy in

any closed system tends to increase with time, with an ultimate maximum when equilibrium has been reached.

When reactions are carried out rapidly and under nonequilibrium conditions, hence irreversibly, as is the common

practice in rapid combustion, the increase in entropy of the
24

whole system is always greater than that calculated for

the reversible reaction.

21.2.7 Free Energy

See Gibbs Energy; see also Helmholtz Energy.

21.2.8 Free Energy Function

See Planck Function; see also Massieu Function

21.2.9 Helmholtz energy

The Helmholtz energy (symbol A) is a measure of the

maximum work that can be done by a system. It is defined by

the equation

A = U - TS

The change in Helmholtz energy that occurs in a process at

constant temperature is given by the equation

AA = AU - TAS

In an isothermal process, the maximum amount of work that can

be done by a system is -AA, the decrease in Helmholtz energy.

The Helmholtz energy is a valid measure of the tendency

for a process to occur spontaneously. For a process occurring

at constant temper a ture and constant volume, the necessary

condition for the process to occur spontaneously is a decrease in the Helmholtz energy.

AA < 0

For an isothermal process occurring at constant volume the

necessary condition for equilibrium is that
25

dA = 0

The Helmholtz energy may be found referred to as Helmholtz

free energy or Helmholtz function . It should not be confused with the Gibbs energy discussed below.

21.2.10 Massieu Function

The Massieu function (symbol J) is the negative of

Helmholtz energy divided by temperature (J = -A/T) . The

Massieu function does not contain any new information not

found in the Helmholtz energy; but it is a useful form for

calculation of equilibrium processes at constant volume. The

Massieu function is found less commonly tabulated than its

Gibbs energy analog, the Planck function.

21.2.11 Gibbs Energy

The Gibbs energy (symbol G) is a measure of the maximum work that can be done by a system. It is defined by the

equations

:

G = U + pV - TS = H - TS

The change in Gibbs energy that occurs in an isothermal process

at constant pressure is:

AG = AU + pAV - TAS = AH - TAS

For the isothermal process, the maximum work other than

expansion work that can be performed by a system is -AG, the

decrease in Gibbs energy.

The Gibbs energy is also a valid measure of the tendency

for a reaction to occur spontaneously. For an isothermal
26

process subject to a constant pressure, the necessary condition for the process to occur spontaneously is a decrease

in the Gibbs energy

AG < 0

For an isothermal process subject to a constant pressure,

the necessary condition for equilibrium is that

dG = 0

An important consequence of this condition is that the

Gibbs energy provides one criterion for the maximum temperature

reached in a c embus t ion zone. At the temperature of the

combustion zone the proportions of substances present will

be governed by the fact that this isothermal Gibbs energy

change will be zero for each possible reaction. That is

each reaction will establish an equilibrium at that temperature

See Section 21.7 for discussion and an example.

The Gibbs energy is frequently found referred to as

merely free energy , and any references to free energy without

qualifying adjectives should be taken to mean Gibbs energy.

It is also called Gibbs free energy or Gibbs func t i on by some

users.

21. 2 . 12 Planck Function

The Planck function (symbol Y) is the negative of Gibbs

energy divided by temperature (-G/T). The Planck function

does not contain any new information not found in the Gibbs

energy; but it is a very useful form for calculation of
27

equilibrium processes at constant pressure. (See Section

23.3.2). The Planck function is more commonly referred

to as free energy function . The terms fef or Gibbs energy

function are also sometimes found referring to this function.

21.2.13 Heat Capacity

The heat capacity is the ratio of the energy supplied to

the temperature change of a body. It may be an average heat

capacity over a temperature range or the limiting ratio over

an infinitesimal temperature change. If the system is maintained at constant pressure, the heat capacity, Cp, is the

rate of change of enthalpy with temperature.

If the system is maintained at constant volume, the heat

capacity, Cv, is the rate of change of internal energy with

temperature

(6 q\ = Cv = [bv\

VST/v \6T/v

The heat capacity allows one to calculate temperature changes

to be expected from liberation of specified amounts of heat,

or the amount of heat needed to create a given temperature

change.

21.2.14 Enthalpy of Reaction (Heat of Reaction)

For a reaction that goes to completion, the enthalpy

of reaction at constant temperature is the negative of the

observed calorimetric heat when carried out at constant
28

pressure and with the products brought to the same temperature as the reactants. It could be logically considered to be the sum of the enthalpies of the products

of reaction minus the sum of the enthalpies of the reactants.

This concept, however, leads to a practical difficulty. The enthalpies of individual substances are based

on arbitrary scales and cannot be added or subtracted

without adjustment. This adjustment is made by relating

the enthalpy scales of various substances through their

enthalpies of formation (heats of formation) (See Section

21.2.15 . On this basis the enthalpy of reaction is the

sum of the enthalpies of formation of the products minus the

sum of the enthalpies of formation of the reactants. If the

sum of the enthalpies of formation at the temperature of

interest is less after the reaction than before, then the

enthalpy of the system has been reduced and the excess

enthalpy will have appeared as heat.

For reaction (1)

A + B -> C + D

AHr = AHf [C]+AHf [D] - AHf [A] - AHf [ B ] (1)

In the example, AHr is the enthalpy of reaction, and the

other enthalpy terms are the enthalpies of formation of the

substances contained in the brackets. A negative enthalpy

of reaction means that the reaction is exothermic while a
29

positive enthalpy of reaction means that the reaction is

endothermic

.

21.2.15 Enthalpy of Formation (Heat of Formation)

For the special case in which a single product is

formed and the reactants are the elements in a standard

reference state defined for each element, the enthalpy of

reaction is called the enthalpy of formation, and has the

symbol AHf.

For reaction (2)

H

2 (g) + = H

2 0(liq) (2)

AHr = AHf[H

2 0(liq)]

AHf, which has a characteristic set of values for any substance is a very important thermodynamic function. The enthalpy change occurring in any reaction can be calculated if

the enthalpies of formation are known for all the substances

participating as reactants or products. By convention the

enthalpies of formation of the elements in their standard

reference states are zero, at any temperature (see Section

21.2.16 . An element not in its standard reference will,

in general, have a non-zero enthalpy of formation. The standard reference state for hydrogen is the gas composed of

molecules, H

2 (g). On the other hand the gas consisting of

hydrogen atoms H(g) is not the standard reference state for

hydrogen. Thus AHf°[H(g)] at 298K = 52.04 kcal mol ^ while

AHf ° [

H

2

( g ) ] =0, at all temperatures.
30

21.2.16 Thermodynamic Standard States and Standard Reference

States

The molal values of the internal energy, enthalpy,

Gibbs energy, Helmholtz energy, entropy, heat capacity and

enthalpy of formation are functions of the temperature. For

simplicity and convenience the values that these thermodynamic properties have for particular substances are usually

tabulated for the substances in their standard states (indicated by a superscript zero on the thermodynamic symbol as

in AHf ° , Cp° , etc. The standard states are defined as follows

For a pure solid or liquid the standard state is the substance

in the condensed phase under a pressure of one atmosphere.

For a gas the standard state is the ideal gas at a pressure

of one atmosphere. For the functions AHf, AGf, and log Kf

the values tabulated usually represent the quantities appropriate for the reaction by which the substance is formed in

its standard state from the elements in their standard

reference states. The conventional notations in this case are

AHf°, AGf ° , log Kf°. For this purpose, in the usual case,

the standard reference states of the elements are taken to be

the molecular form and phase that are stable at one atm pressure at 25°C (298.15 K) . A few of the elements, oxygen,

nitrogen, hydrogen, fluorine, and chlorine, are diatomic gases

under these conditions. The inert gases (He, Ne, etc.) are

monatomic gases. Bromine and mercury are liquids. For the

solid elements the stable crystal phase at 298.15 K is the
31

standard reference state. The single exception to this

is phosphorus, for which white crystal phosphorus is used

because the more stable forms have not been well characterized

thermochemically. In the use of any tables other than those

in this handbook, care should be taken to understand the

standard states used for the elements, as there is some

non-uniformity in this, particularly at temperatures different

from 25°C.

21.3 Tabulated Thermal Functions

Tabulated values for the thermodynamic functions are

given in terms of carefully defined observables that can be

evaluated by experimental means or derived easily by unambiguous calculation from experimental and theoretical relationships. The functions discussed up to this point such

as internal energy, enthalpy, Gibbs energy, Helmholtz energy,

and entropy suffer from vagueness, particularly with respect

to the energy base to which they are referred, but also in

other ways. The tabulated thermal functions found in this

handbook and in the references given in Section 22.0 are designed to avoid such vagueness. The same criteria are not

used in every tabulation, however. It is important to note

certain descriptive features of the terminology in order to

distinguish the basis of the values in a particular set of

tables. When differences in the function descriptions are
32

noted, in some cases they are unimportant for many calculations, but in other cases are very important. The principal

distinctions that may be observed are given below, with

some notes as to their importance in particular applications,,

Because changes to achieve international uniformity

have been made just recently, many tables which had been

published present the thermal functions in terms of an older

and still widely used system of notation. The principal

identities are

E = U ; F = G

The symbols E and F represent the Lewis and Randall (Reference

14, Section 22,0) notations. IJ and G represent the IUPAC

or IUPAP notation. Practically all earlier tables for Gibbs

energy and various derivative functions of it published in

the United States use the symbol F and the term free energy

for Gibbs energy. The same tables usually use E for internal

energy.

21.3.1 Non-Standard -State vs. Standard-S ta te Functions

The superscript zero is placed by a function to indicate

that the substance is in the standard state. The presence

of a superscript zero by a standard ~s tate function and its

absence by a non -s tan d ard- state function should be deliberate

distinctions, though this is not always made clear in the

presentation of a table. U as compared to U° , H vs H° , G vs

G° , Cp vs Gp° differ by amounts that are usually small for
33

liquids and solids near 1 atm pressure, because of their

low compressibility. They become important at high pressures and in the region of the critical temperature. For

gases the differences should not be ignored. In this case,

the distinction is between the real gas and the ideal gas.

For detailed energy balances the real gas state is preferable.

Unfortunately real gas functions are unavailable for large

numbers of substances. However, the steam tables (Section

22.0, References 2, 7, 8, 13), and the NBS Tables (Section

22.0, Reference 5) apply to real gases.

21.3.2 Different Tempera tures for the Energy Base

Internal energy, enthalpy, Gibbs energy, Helmholtz

energy, entropy, and certain derived functions are cumulative

functions of temperature; and the numerical value given to

them, therefore, represents an increment as the temperature

of the substance is changed from some reference temperature.

The commonly used reference temperatures are 0 K and 298.15 K

(The subscript 298 is often used in referring to 298.15 K)

.

(a) The quantity tabulated for internal energy may be

U° - U°

Q

or U° - U° 9g

depending on the base of temperature used. These two quantities differ by a constant term:

(U° - u° 3 - (U° - U°u ) = (U° - U°) 298 ; ^298 0

' The quantity (^98 - Uq) may be found tabulated occasionally.
34

(b) The quantity tabulated for the enthalpy may be

H° - Hg or H° - H| 98

depending on the base of the temperature used. These two

quantities differ by a constant term:

<H° - Hg) - CH° - H» 98 ) = H» 98 - Hg

The quantity (H°gg - Hg) may be found in many tables.

(c) The quantity tabulated for entropy is usually

S ° or S

° - S298

The quantity S° , rather than S° - Sg is usually tabulated on

the assumption that Sg can be exactly determined. It is

usually zero, but may be a constant non- zero quantity. The

difference between the above terms is Sg 98 ; and this is

found in many tables.

(d) The quantity tabulated for Gibbs energy is usually

G ° - H

0

or G

° - H

298

The base Hg instead of Gg is chosen because the relationship

G° = Hg, - TSg, gives us Gg = Hg when T = 0.

The terns differ by the constant term (Hg

9 g

- Hg) , which as

mentioned above, may be found in some tables.

(e) The quantities usually tabulated for the Planck

function C-G/T) are

- (G° - Hg)/T or -(G° - Hg 98 )/T

These quantities differ by the amount

-< H

298 “ H

8 )/T

which is not a constant, since T is in the denominator.
35

Despite its anomalous character the function -(G° - H^g)/!

is very useful, because it allows calculations to be made

involving processes for which AH° 98

is known. These include

enthalpies of reaction, enthalpies of phase transition, and

so on. Such calculations are quite practical with this

function even if the quantity H°gg - H° may never have been

measured, as would be necessary to obtain -(G° - H°)/T. The

negative function is used for the Planck function because most

table entries then become positive.

(f) The quantities tabulated for enthalpy of formation

( AH^ ) are

AHf ° (at 0 K) and AHf°(at 298.15 K)

These quantities differ by the amount

AHf ° (at 298.15 K) - AHf°(at 0 K) = £pi(H° 98 - H°)i

where the sum of enthalpy increments (H^gg - H°) is taken over

all the i products and reactants, with the number of moles

of each given by pi, where pi is positive for the products

and negative for the reactants. The quantity AHf 0 (at T) is

also frequently given at a series of temperatures.

21.4 Calculation of Thermochemical Quantities

21.4.1 Additivity of Chemical Processes

Any chemical process can be conceived as occurring in

stages, for each of which a chemical reaction can be written.

These processes are additive in effect, and the overall reaction is the sum of the reactions into which it has been
36

resolved. As an example, we give the combustion of carbon

to form carbon monoxide (equation 21.1) followed by the

combustion of carbon monoxide to form carbon dioxide (equation

21.2). Energies are in kcal mol

C (graph! te) + Jo2 (g) - CO(g) AK»98 = -26.416 (21.1)

CO(g) + £02 (g) - co

2 (g) AH»98 = -67.635 (21.2)

C (graphite) + 0

2 (g) - co2 (g) AH°98 = -94.051 (21.3)

The sum of the reactions is the appropriate reaction for the

complete combustion of carbon directly to form carbon dioxide

(equation 21.3). In summing such a sequence of reactions the

same substance is not ordinarily shown on both sides of the

final reaction, but only the excess on one side or the other.

As ano tiler illustration we give the combustion of an

organic substance (for example, cellulose for which the repeating

unit is to form carbon dioxide and gaseous water

(equation 21.4), followed by condensation of the water to

liquid (equation 21.5). The overall reaction may be written

as the combustion of the organic substance to form gaseous

carbon dioxide and liquid water (equation 21.6).

C

6

H10°5 (solid) + 6°

2 (g) - 6C0

2 (g) + 5H2 0(g) (21.4)

5H

2 0(g) -> 5H

2 0(liq) (21.5)

G

6

H10°5 (solid) + 60

2

( S } - 6C0

2

( S ) + 5H

2 0(liq) (21.6)
37

21.4.2 Additivity of Thermodynamic Quantities (Law of Hess ) When a sequence of chemical processes is carried out,

as illustrated in Section 21.4.1, the thermodynamic quantities associated with the reaction are additive in the same

way as the chemical reactions. The overall thermodynamic change

of the final process is the sum of the thermodynamic changes

of the intermediate or postulated processes into which it

has been resolved.

Changes of enthalpy, internal energy, Gibbs energy,

Helmholtz energy, and entropy are additive in this way. The

enthalpy changes associated with reactions (21.1), (21.2),

and (21.3) are given beside the equations for illustration.

A sequence of processes of any desired length can be added

this way.
38

21.5 Enthalpy and Internal Energy of Combustion

21.5.1 Calculation of Observed Heat Effects from Enthalpies of

Formation

Combustion processes can be carried out practically in a

variety of ways. Commercially , for example, combustion is often

carried out as a flowing, nearly adiabatic process operated at constant

pressure. The heat of reaction is dissipated through insulated walls,

to heat exchange surfaces, and in heating quench water, or is carried

up the stack in the products of combustion. Adiabatic cons tant- volume

calculations are also useful in a practical way to determine pressure

and temperature build-up from explosive combustions which might occur

in incinerators.

In order to calculate the enthalpy of combustion (AHc) or

internal energy of combustion (AUc) of a substance, it is essential

to know the products of combustion and their proportions. The products

and their proportions depend, first of all, on the composition of the

substances burned and the oxidizer used. In addition, however, they

depend upon the conditions of the combustion process. Factors involved

include the pressure of the oxidizing air, the temperature and pressure

reached by the reacting system, the relative proportions of elements

present, and the rates at which substances pass through various reaction

zones

In this space it is impossible to give a complete analysis of

the factors involved and methods for making calculations. However, the

processes involved can be resolved into idealized simpler processes; the
39

isothermal process and the adiabatic process. A brief discussion of

some of the factors involved in adiabatic processes and other processes,

in which the reaction products are hot, is given in Sections 21.6 and

21.7. In the following two sections (21.5.2 and 21.5.3) we limit ourselves to enthalpy and internal energy changes and the related heat

effects for some isothermal processes representing the combustion of

substances as determined under idealized conditions. In Section 21.5.4

we extend the discussion to the combustion of several types of organic

compounds, and in Section 21.5.5 discuss some other formalized fuel

combustion reactions. We shall restrict our discussion to combustion

in which oxygen (or air) is the oxidizer.

The isothermal process is a convenient form for presenting

carefully defined thermodynamic information in a standard way, in which

the heat observed can be expressed in terms of enthalpies of formation

listed in tables of this handbook. Isothermal combustion can be carried

out at constant pressure or at constant volume. These two processes

are discussed below.

21.5.2 Isothermal Constant-Pressure Combustion

Combustion can be carried out in an open burner as a constantpressure process with all reactants and products at the same initial

and final temperature and pressure. The heat effect observed, Qp(obs),

in which the subscript p represents the constant-pressure process is

a measure of the enthalpy change.

In a constant-pressure process, typically though not necessarily,

water and any other appreciably volatile substance among the products
40

remain in the gas phase, and oxygen is present in excess. In this

case the observed heat effect which we shall calculate is closely

related but not identical to the quantity, net heat of combustion, used

in fuel technology (See Section 21.5.6).

For the purpose of this illustration we shall presume that AH

and AH° do not differ significantly. Hence we may write:

Qp(obs) = -fflc(at T K) * -/Hc°(at T K)

For a typical reaction, the combustion of polyethylene, equation (21 . 7)

represents the process per mole of monomer unit.

C

2

H

4 (solid polymer) + 30

2 (g) -* 2C02 (g) + 2H20(g) (21.7)

The enthalpy change for reaction (21.7) can be calculated from data in

Tables I, II, and III.

fflc°(at 298 K) = 2fflf°[C0

2 (g)] + 2 fflf

0 [H

2 0 (g) ] - ZHftC H (solid polymer)]

= 2(-393.509) + 2 (-241. 818) -(-56.48) kJ mol" 1

= -1214.17 kJ mol" 1

Qp(obs) ~ AHc'Ut 298 K) =-1214.17 kJ mol”1

As the molecular weight of polyethylene (monomer unit) is 28.0542 g

(0.0280542 kg) the specific net heat of combustion of polyethylene is

-1214.17 . , 0Q MT/ , 28.0542

During the reaction an increase in volume occurs, representing

principally the increase in number of moles of gas, An. The increase in

the amount of gas is 1 mole of gas per mole of reactant (4 moles of gas

formed minus 3 moles of gas reacted) . On the basis that the volume of
41

solid reactant is small compared to the increase in volume of the gases,

and that the gases follow the ideal gas law, the work term p AV is

expressible as

p AV c ZnRT

At 298.15 K, RT has the value 2.479 kJ mol \ As An=l, pAV=2.48kJ

mol "*.

If for any reason one wishes to calculate the internal energy

change, AU° (at 298 K) for reaction (21.7) it may now be done

ZUc° (at 298 K) = fflc°(at 298 K) - pAV

= -1214.17 - 2.48 kJ mol"

1

- -1216.65 kJ mol"

1

= -43.37 MJ kg"

1

21.5.3 Isothermal Cons tant-Volume Combustion

Combustion can be carried out in a closed burner as a constantvolume process with all reactants and products contained in the same

volume and at the same temperature at beginning and end of the reaction.

In a constant-volume process, it is customary to achieve complete combustion by using oxygen in excess and under a pressure of 20 to 30

atmospheres. In this case the heat effect, Qv, to which the subscript

v has been added to represent the cons tan t-volume process, is a measure

of the internal energy change.

Qv(obs) - - BJc * &Jc°

If it is possible to devise a system in which all the products

of reaction (21.7) remain in the gaseous state, then -ZDc°(at 298 K)

would be as we have calculated it before and Qv(obs) would be 1216.65

kJ mol" 1

(43.37 MJ kg" 1

).
42

A more usual circumstance for a constant-volume process is for

the condensable products of combustion to be condensed to the liquid

state. In this case, the observed heat effect which we shall calculate

is closely related, though not identical, to the gross heat of combustion

(see Section 21.5.6) used in fuel technology. In this case, the observed

reaction would be given by equation (21.8).

C

2H4

(solid polymer) + 30

2 (g) 2C02 (g) + 2H20(liq) ( 21 . 8 )

The enthalpy change again can be computed using data from Tables I, II,

and III

ffl°(at 298 K) = 2 4Hf°[C0

2 (g)] + 2 /Hf 0 [H

20 (liq) ] - ZHf 0 [C (solid polymer)]

= 2 (-393. 509) + 2 (-285 . 830) - (-56.99) kJ mol"1

= -1302.20 kJ mol" 1

= -46.42 MJ kg"

1

As before, we can now calculate the internal energy change. In

this case, because the water was condensed, the number of moles of gas

is reduced; An = -1 mole per mole of reactant.

pAV s An RT = -2.48 kJ mol" 1

ZUc°(at 298 K) = AHc° (at 298 K) - p AV

= -1302.20 - (-2.48) kJ mol

= -1299.72 kJ mol" 1

= -46.33 MJ kg"1

Thus for this constant volume process

Qv(obs) * -&J°(at 298 K) = 1299.72 kJ mol

-1

-1

= 46.33 MJ kg

-1
43

Note that both AUc°(at 298 K) and /Hc°(at 298 K) are more negative

for reaction (21.8) than the corresponding values for reaction (21.7),

and the reaction is, therefore, more exothermic. The extra heat comes

from the condensation of the water.

21.5.4 Type Reactions for Combustion of Organic CompoundsCalculation of Enthalpy of Combustion for the Isothermal Process

The substances present in the combustion products depend first

upon the elements present. The phases of the products (gas, liquid, or

solid) depend upon the temperatures and partial pressures of the substances at the conclusion of the process.

Calculations of /He or /He (at 298 K) such as are shown in the

preceding section can be made for any given process, provided the

equation can be written for the process, and provided the enthalpies

of formation of reactants and products are known.

To assist in the calculation of the energy changes, equations

are given in Table 21.1 and Table 21.3 for a standard type reaction

for each of several classes of organic compounds.

The classes of compounds are based on the elements present in

an empirical formula, and are not functional classes. Compound classes

containing various typical combinations of the elements C, H, N, 0, P,

S, F, Cl, Br, and I are given. Not all possible combinations are given.

However, the pattern of the reactions should be clear from the table,

and it should be possible for the user to extend the table to include

all the information required for other combinations of the same elements.
44

The products of combustion that will be encountered are different,

depending upon whether the process is carried out at constant volume or

at constant pressure, and the product in which a given element is found

depends to some extent upon other elements present.

For the combustion processes, we make the following somewhat

arbitrary presumptions. Some water will have been supplied in the

constant-volume process to dissolve the soluble acids formed.

The product of combustion of carbon is CO^Cg).

The product of combustion of hydrogen is H^QCg) in the constantpressure process, and 1^0 (liq) in the constant-volume process. If the

halogens F or Cl are present, some of the hydrogen may be present as

HF(g) or HCl(g) in the constant-pressure process in which water is

formed as a gas, or as HF(aq) or HCl(aq) in the constant-volume process

in which condensables are condensed. If sulfur or phosphorus is present,

some of the hydrogen may be present as H^SO^Caq) or H^PQ^aq) in the

constant-volume process, in which water and other condensables have

condensed.

The product of combustion of organic nitrogen is taken to be

the gaseous element, N^Cg). Some oxides of nitrogen may be formed in

the constant-pressure process, and some HNO^(aq) may be formed in the

constant-volume process. A correction to the enthalpy change of the

type process may be required, to obtain the observed heat, if appreciable

quantities of either are formed. Some oxides of nitrogen or nitric acid

may also be formed, even if the element is absent in the combustible

substance, because nitrogen from the combustion air may combine with
oxygen at the temperature and pressure of the combustion reaction. The

occurrenceof nitrogen-oxygen compounds may be expected to be much more

pronounced in the cons tant-volume process than in the constant-pressure

process, because of the higher temperatures usually reached in the

constant-volume process, and possibly also because of the reduction in

number of moles of gas caused by formation of the compounds.

The product of combustion of organic phosphorus is taken here

to be p

4°10 (§) in the constant-pressure process and H^PO^(aq) in the

cons tant-volume process. The presumed concentration of H^PO^ is one

mole in 40 moles of H^O. If the resulting concentration in an actual

combustion differs appreciably from this, a dilution correction may be

required in order to calculate Qv(obs) . Note that some compilations

of enthalpies of combustion of phosphorus compounds presume the final

form of the phosphorus to be H^PO^(c), and hence care must be taken

when comparing enthalpies of combustion from various sources.

The product of combustion of organic sulfur is taken to be

SC^Cg) in the constant-pressure process and H^SO^Caq) in the constantvolume process. The conversion to the higher oxidation state is

catalyzed by oxides of nitrogen, and the conversion may be expected to

be nearly complete if appreciably high pressures and temperatures are

developed. The presumed concentration of one m°i e in H5 moles

of H^O. If the resulting concentration in an actual combustion differs

appreciably from this, a dilution correction may be required in order

to calculate Qv(obs).
46

The product of combustion of organic fluorine is taken to be

HF(g) in the constant-pressure process, and HF(aq) in the constantvolume process. The presumed concentration of HF is one mole in 20 moles

of H,

? Q. If the resulting concentration in an actual combustion differs

from this by an appreciable amount, a dilution correction may be required

in order to calculate Qv(obs). The formation of HF by burning an organic

compound in oxygen depends upon the presence of hydrogen in the combustion

material. If hydrogen is not present in sufficient quantity to combine

with all the fluorine, the balance of the fluorine will appear as CF^, or

possibly COF^, unless other elements (such as metals) are present. If not

wanted, this contingency can be avoided by adding an auxiliary combustible

xtfhich contains enough hydrogen to combine with the fluorine. The equation

for this alternate process is given (Equation 9, Table 21.3). If CF^ or

COF^ are formed and their avoidance is not deemed necessary, the calculation

of Qv(obs) will be affected by the proportions present, which may be determined by analysis or by calculation from equilibria.

The product of combustion of organic chlorine is taken to be

HCl(g) in the constant-pressure process, and HCl(aq) in the constantvolume process. The presumed concentration of HC1 is one mole of HC1

in 600 moles of H^O. If the resulting concentration differs appreciably

from this, a dilution correction may be required in order to calculate

Qv(obs) accurately. Because oxygen and chlorine are of comparable

electronegativity, the possibility of forming elemental chlorine, 012 (g),

exists. If its presence is objectionable, it may be possible to remove

it by use of a reducing agent, such as As

20

3

(aq), outside the combustion
47

zone. A correction must be applied to Qv(obs) for the reduction process.

If the presence of must be allowed, the calculation of Qv(obs) is

affected, and the proportions of Cl^ and HC1 may have to be determined

by analysis or from equilibrium calculations in order to determine Qv(obs)

.

Experience indicates that 15 to 20% of the chlorine is formed as Cl^ and

80 to 85% as HC1 in the constant-volume process.

The product of combustion of organic bromine is taken to be

elemental bromine, as the gas in the constant-pressure process and as

the liquid in the constant-volume process. The form of the bromine in

a given reaction system should be determined by analysis. In calculating

Qv(obs) or Qp(obs), a correction can be applied to AU or AH for any

deviation from the equation given. Experience indicates that 90 to 97%

of the bromine is formed as in the constant-volume process.

The product of combustion of organic iodine is taken to be

elemental iodine, as the gas in the constant-pressure process. For a

given reaction system, the form of the iodine should be determined by

actual analysis. In calculating Qv(obs) or Qp(obs) a correction can

be applied to ZSJ or /5H for any deviation from the equation.

Table 21.1 presents type equations for combustion reactions of

organic compounds burning at constant pressure in an atmosphere of

oxygen. The equations are balanced with generalized letter coefficients

derived from the letter subscripts of the elements in the formula. The

stoichiometric amount of oxygen and the amounts of the type reaction

products are given. Table 21.1 is supplemented by Table 21.2 which

gives for the reactions the elements present, the increase in quantity

of gas, An, calculated from the amounts of gaseous products and reactants
48 oo

Pt-I PCoo

V 00 + '—

CM /rs o 00 -—

CO sx oo

d -TV o w

Cl) 4-! 00 CM i—

00 PC

u

j?

00 + p*-l

X -—

PC \ -—

o X"^ o 00 —

00| CM

X 00 x^N 00 00 1—

•—

00 00 '—

00

0-1 'w-' •-X o CM •w/ 1 + CM 'wX

C) CM CMd- O CM + Vi CNJ 2 PC PC c/j 2 '.d| X"N PQ t-H

(1) /—\X|<N 00

Vl

a | cm U| CM <o|<r 4-1

O j CM 00 •^x •Hi CM 12

(11 + o + + + + + o +

-42|CM CM 4- 1 u CM PC

t.0 x-n x^. /*( x-\ r\ PC x^. o 00 00 00 00 00 00 00 X"s oo 00

pi (0 V_X *•

—

>—S—s—

•-X + h 2 V—

4-0 4-) o o o o o o o 00) CM o o

CJ CM CM CM CM CM CM CM X~\ i CM CM d PC PC PC X PC PC PC 1 00 PC PC

d d)

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•-x -40|CM

d o -Q|c^J

Vi -o|M rQ | CM Xl|CM »J2 1 CM -Q|CM 40 |CM CM o

six -Q|CM

d

•rl PC + + + + + + + + CJ + + +

X*N

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s V

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x\ x-s x^

Q) oo 00 OO OO 00 OO 00 00 \ d 00 OO 00

Vt V-X '—

•w- >-/

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d CM CM CM CM CM CM CM CM CM CM CM

CO o O

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to cjO cj cj cj cj CJ CJ CJ CJ

u

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Vo P i d

d

d

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d

d

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d >»xd

d

d

4-1 d to

c) 0)

J-* (0 t t 1 f f f f i f f t f

to

d -—\ < i o 00 o ^x

CJ CO CM 1—

d x-\ O • 4J 00 1—

d T3 d V—

- N -- n

CNJ <D 0) CM 00 00 ocj<f OO 4-1 00 o vx •—

<D

d -u £

CM CM i i—

•T-l -H -—

/—y rv o o r-v

r-Q

d

a o 00 oo a) 00 vol 00

cti Vi

W -—

V-( /~

' M|<t vx

H

d

a CM CM ml^r 4-1 4-1 CM CM

di co •H o O

O + O x^

x—

4J Vi 00 00 + + + 00 oo

CO o •M - X ~*~s x-N X-N r\

b 4 -—

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b 4 ' 03 X-N X-N n. pu

rl rd

b 4 -a|<r

b 4 b 4 b 4 -Q 1 Mf

b 4 X

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•rl

m N.X N*x s»x 'w' Nw/

dd

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4-1

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•rl ^ 03

4-1 CJ Od XN X

0)

pr\ cr

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x—

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cr c

cr i—/—N X-'S

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o •K cr CJ* i—

rH rH CJ a* O'4 •H •H cr

•rl

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x /""“S •H •H #%

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4-1 0) cr4 «—

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CJ

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CO o •H * v-/ •-/ V—

CO #-Oa as

d

d i—

a CJ nj a» MH d)

aU v-x o

•d6 d ** s-/ 'w'

O PV COO s-/ J2 •H

•u

O CJ ~o CJ -o X)

a 00 00 i—1 U •T—

o co & o o o PC Ph pH CJ PQ M

cj -ad pcf0

p/1 pd" p/3 Pd° pd^ pi0

pd° p/1

C) C/D o3

d o3 cO

d cti cdd

d 03 03

d

Cu

K.> CJ cj CJ CJ o CJ CJ CJ CJ CJ CJ CJ H X \ X—

/-\ x-«- X>—N —s r-N x—\

X—

1—1 CM CO -d- LO vO 00 o rH CNJ N_x V-/ N-r sx rH i—1 r~J s-x

'V-X N«X (*)

(c,liq)

indicates

that

the

equations

are

valid

for

either

solid

or

liquid

substance

(g)

indicates

that

the

equations

are

valid

for

gaseous

substance.
Table

21.2,

Enthalpy

Changes

for

Table

21. Iii

03 r—,

i—l f 1 1—1 i—r

——j O 3 CD a) 49 & 3 3 c CJ CJ o 3 a

cO 3 3 3 3 (—1 3 3

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03 3 3 3 6C|CM 33

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u CJ cj CJ 1 XXX

XX

X 3 4-1 4-1 3

rH1 a

03 3cO 3

CO s

cfl 3S

X

<3 'X|W|CM

XX

rH cn CO •—

5

<1 i—1 u 4-J

x •U i | CM | 1 • X i i o U) 03 03 03 3 1 <f + 92 *t—4 CM 3 s X rO X X X X CM r—i

•h|cm

X 3 3 3 3 CM cn X 1 X|<M at i i X

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X JO [cm J3|OvI X|CN Xl CM

X[cmX 1 CM

w 1 00

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ON ON ON 0^ ON ON Os as ON ON ON ON o 00 J 8 3 3 •rH 3 X v—1

4J 3 o 00

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<1 + + + + + + 4- + + 1 + 3 cn y~N x|mi- 3 3 •H 3

x|mt Xf-tf X| -0"

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•H >i

X •H

cd 44 on 3 s 3 cd 3 cn X a. X O X C/3 o cd 3 4-J S 3 #4 St #v rH X 3 <3 o 0) X o z o o Z fH CJ « M 4-i 3 CJ e c» «N •4 •N r\ »N FN CJ cn O

01

X

X

X

X

X

X

X

X

XX

X

X 3 3 3 i—1

cn CN C4 #» #» r» •H

a

H *H

w cJ o CJ C_) o CJ CJ CJ CJO

X CJ 3 X 3 3 XJ X H 3 3 3 u cn 4-J o s CJ •H cn 3 II 3

4-J /^S

y

\ y-s y*"N yrs y'-'s y“N y—N y~i y*N •Hu i—4 u f—1

CM cO "d- X

X r^. 00 ON o rH CNJ 44 > 00

to 'w' W' N»y N/ 'w' '—c i—1 i—1

rH 6, •iH <1 3

<u sy vy v-y <1 CJ a- 3

pi *
Table

21.3

Type

Combustion

Reactions

of

Organic

Compounds

Burning

at

Constant

Volume

in

an

Atmosphere

of

Oxygen

(Excess

Water

Present)

Products

are

Formed

as

Gases

and

Aqueous

Solutions

50

O a

ol CM

CM a o

Xj CM G

m / V •H c G ©

Sj + a T-l F—

CM 2* sf cr a CO />-N o c! c1 /“* G cr a ©

Pm 4-1 © CM 60 •H cO F—

o CNJ cn w a! w V-' CM a a

a cr- CM CM cr fn O © ^-s

as a in as CO a CM G a o cr

fll W i-«i a •H o 4-1 /-N 4-1 r-i o cm 60 a a a

oo 60 4 >5f cr '—

o

v-< + C! + o + 60j«M c0 + CM V«F CM CM •r-1 C/D '*—> CM z Z cr /'“N CM 1 a a M

4-1 cr cr cr a cr a cr OiCM U|CM iH 4-t C0 44 4-1 ''a| •H •H | CM •r-)J CM

r-l a 4-1 rH X j CM 60 a

cn + + o s_x N»/ + +

a CM o O o + + ©

o /-s /s a CM CM CM CM /—

/-s 3 cr cr cr cr a a a a|n* a cr cr

-a •H ft •H •H 4-1 4-1 o .H a?

/“V T—

r—

u v-x w w> CO j CM «w CM cxicm *4° a|<N ' ' a O © o Q o . o

CM CM CM CM ! I | ! •s i CM a a a a 5© a a

^10 j CM a1 CM 43|CM 0\ CM 0|N

4S|CM a|«N X»|CM JQ|CM sL/ vt/ O’

/«i a|«n a|«M

4- + + + + + + +

u

u + + +

/*

/>, /-N 6

69 60 60 60 60 60 60 N €0 60 60 60 v/ w X V

»«

CM CM CM CM CM CM CM CM CM CM CM o o o o o © © © + © o O

u u u © © © © © (KfJ © © U

(0 « a) «d SO c0 c0 «0 e0 «0 C0

4 4 4 4 4 4 4 4 4 4 4 4

ft

/-\60CM © <F-"\ 60 60 60 VF 4/ —

PGl'O' e CM CM CM

(0 O © © 1 60 «i fn 60 s~-. <F-N 0© a 60 X m 4-1 1 4-1 1 x|<r o C4 CM mf<r <n|cM cnjcM % CS8 CM

/F-s O o o + © /—

o 60 60 + + + 60 60

•H w w /“S /-N a|-r F—

«w> vy M CM CM T3|CS| ajcM *t3j CM a|cM ajcM ttDj^ a|<r CM CM

•u

0> o o 1

| |

I 1 + o o

Q /->

0 0 1 ^ C0

1 /—

o ajcM a|-r a|<r a a!<r aK-r a|<r a|-cf X aj-r a|<r a|<r

•s + + + + + + + + + 4- + +

4H cO 10 «d CO cO cO cO cO «0 cfl cO 0) o V-/ W w v_/ V-/ Va/ W

U

00 + + + + + + + + + + + +
51

COi—i

CM

a) rHPP

cO HHO

44

ooG

cO p3

cj>v

a.

rH

4-1 gZ

CM

II H

Pi <5>

<3a ,—, ,—, ,—,

I—1 G 00| CM ,—, ,—, G G G G rH G G

CJO

OO 00 <—« 44 i—i44

r » oo t—t 1 i—i

Pi r—

r

CJ CJ

C

GG

G . G rH

G

r

—1 G

m 0)

G CM

G

GG

G

G

GG 00 CJ 00

O 00 CJ ON G\ jd CJ NO

U

GG

4-1 4-> 4-1 4-1 CO

G • G « G c tt|CMC • C 4-1 4-1 cn cn cn cn CM G r— G n- G o G G NO G cn CO pp pp pp pp r—1

4P 00 4-1 00 4-1 CM

H + 4-J NO 4-1 pp pp

rH

GG

GG 1 cn oo CO 00 CO CO CO CO rH CO

G

G 1 cn cn CO cn pp l PP 1 PP 1 PP PP|CM PP 1 pp cn CO rH >—

>—

*—

r

*—

G

G

GG

w

GG <—> 1 • O *H 44 44 44 G | CO /~N CO r-—s

CO

N CO CO cn /“N CO 44 44

a 5 5

CO [ CM >—44 CM

44

L. 1 MH

44 | CM

C . i 44

OOjCM 44 00

44

PP | CM I. * 44 98 Z<3 1 1 1 1 1 5 1 Z

<1 1 3 1 m

00 1 33 1 1 PP|<N PP| CM P3|CM i-O | CM —O | CM 1 PP | CM 1 P3|CN| 1 PPjjM 1 CM 1 PP|CM 1 PP | CM PP|CN * 1 x

00

On

CM5 a

cO

CJ PiX

00

ON

CM

K

<8c

a)£G

rHwco

•HUO

COG

Pi

co

00m

00

CMI

cO i—I m

cn

oom

oo

CMI

cO i—I m

cn

00m

oo

CMl

cO rHm

CO

00m

oo

CMI

cO iHm

CO

oom

oo

CMl

cO rHm

CO

oo

in

oo

CM

cO rHm

co

00m

oo

CMI

cO i—I m

CO co

ON ON co co i i

<D

CJG

co

4-1 CO "3

CO

CDaG

co u

CD PPG

CO

I——I 44Z

CO

ONCOIgaG

cO

4-1 CD3

CO

CO

ONCOI

<D

CJGG

4-1 CO 'g

CO

CO

ON

COI

a) CMCOO

00oCO

COON

COI

CMON

CM

co

ONCOI

CMONr—I

CM

CO no co cn cn

oo /^\

m 00 00 00 • N G ON • • • m X • in m m

OP o 00 00 00

CM + CM CM CM CM

ll

G

co1 1 1 1 G V—" G G G

rH rH rH rH 1 1 m m m m m

co co CO CO co

ON ON ON ON ON

cn cn cn co CO «— —• cu f

lt-4 IW COfJCM I I JOjCM -O 1 CM m m

cm co cm l 3 , ~N CO /"N 44 1 CM >— 44 | CM

44 I Z I

<D

CJCG

4-1 CO §

CO i—i

4-1 Z

<1

00 rH

NOI /—\

O0( CM

0£j CM '

1 I <Doi'pdI G X j cm G

4-1 +

CO PP PP|<N G

CO P3

CO

CM

00ON

COI O| CM jDjCM | po|<N | po|CM I ml—I

CO

00

NO

CDoGG

4-1 CO PPG

CO

CDuGG

4-1 CD3

co

m

m inm

CO -G CM

PP 4- G I G

CD <

*—1 PP CM | «H M-' 5 m

PP|<N m

m0

ON1 < rH rH 1 1 rH rH rH /*N 1 rH rH i CO co CO CO CO co N G CO CO • • • • • • W 00 • • O | CM oo 00 00 00 00 00 «H CO 00 1 NO1 NO1 NO1 NO1 NOi NO1 +G

r^>• NO

NO1 NO1 G G G G G G G n- G G

rH 1—1

rH rH rH rH «—1

rH l rH rH

mmm

m LO

m

m

m

mm o O o o o o o o o o

<r <r

ON ON ON ON ON ON ON ON ON ON

CD

CJCGH

CO PPG

COI pp|cni m

rH

CO

00NOI mo

<rONI

-o|mt i

pol'd- I I I I I U|CM n3|CM CJ | CM T3|CM 'O j CM

44 1 CO| CM 1

441 CO | CM 1 pp|-d- l /TS

'PP| X\<t 1 >r\ pp|<r T3|CM PP|<J- PP|-d- pol'd- i + 1 1 1 ZjCM CJ| CM

'w'

00|<3- VwX

dol'd- w pGl-d- W

pp|<r

ro|'d- i i

CO o P4 CO o »» 0% 0S *N rH rH z o z o o z P4 CJ CJ Z M

r\ 0S 0% 0k 0\ 0k 0k #> 0k

W 33 33 z z z z z z Z z

r» 01 0k 0k 0k 0k 0k 0k CJ CJ CJ o CJ CJ CJ CJ CJ CJ CJ CJ

co

m NO oo ON

GG

C/3

footnote

Table

21.
52

Table 21.5 Auxiliary Data for Determining Enthalpies

of Combustion of Organic Compounds

Subs tance

(state)

AHf °

kcal mol ^

AHf 0

kJ mol

P Reference

co

2

( g ) -94.051 -393.51 [1]

H

20(g) -57.796 -241.82 [1]

H

20(liq) -68.315 -285.83 [1]

HF(g) -65.14 -272.55 [2]

HF (aq) (20 H

2 0) -76.71 -320.95 [3]

HCl(g) -22.062 -92.31 [1]

HCl(aq) (600 HO) -39.823 -166.62 [1]

HBr(g) -8.70 -36.40 [1]

HBr(aq) (600 HO) -28.935 -121.06 [1]

HI (g) +6.33 +26.48 [1]

HI (aq) (600 H

2 0) -13.088 -54.76 [1]

h

3

po

4 (40 h

2o) -308.032 -1288.81 [1]

P 4°10 (' S ^ -677.4 -2834.2 [2] so

2

( g ) -70.944 -296.83 [1]

H

2S0

4

(115 H

20) -212.192 -887.81 [1]

H r

2

( g ) +7.387 +30.91 [1]

I

9 (g) +14.923 +62.44 [1]

I 2

( c ) 0.0 0.0 [1]

Br

2 (liq) 0.0 0.0 [1]

[1] Wagman, D. D., Evans, W.H., Parker, V. B., Harlow, I., Bailey, S. M.,

and Schumm, R. H., Nat. Bur. Standards Technical Note 270-3, January 1968.

[2] Stull, D. R., and Prophet, H., JANAF Thermo chemical Tables, 2nd Edition,

National Standard Reference Data System, NSRDS-NBS-37 , 1141 pp . (June 1971)

(U.S. Government Printing Office, Washington, D. C. 20402).

L 3 j Domalski, E. S. and Armstrong, G. T., J. Research NBS 71A , 105-118

(1967)

.
53

determined from the stoichiometry, and expressions for calculating

ffl°(at 298 K) in kcal mol ^ and kJ mol ^ from the enthalpies of formation

of products and reactants given in Tables I, II, and III and Table 21.5.

Table 21.3 presents type reactions for combustion reactions of

organic compounds burning at constant volume in an atmosphere of oxygen,

with water added to dissolve product acids, and all water formed condensed to the liquid state. In other respects Tables 21.3 and 21.4 are

similar to Tables 21.1 and 21.2, respectively.

Table 21.5 gives the values of AHf°(at 298 K) in kcal mol ^ and

in kJ mol ^ for products found in Tables 21.1 and 21.3 These data were

used in deriving the equations of Tables 21.2 and 21.4. They can be

used to calculate the enthalpy and internal energy changes for combustion

of particular substances, and for other reactions, following the procedures

described in this and the preceding sections.

21.5.5 Enthalpies of Formation by Estimation

Supplementary sources of enthalpies of formation, many of which

are not found in Tables I, II, or III may be found in monographs listed

in Section 22.0.

If the value of the enthalpy of formation (or enthalpy of combustion) is not found in any available reference source, it is possible

to estimate a value which is reasonably accurate. Monographs, chapters

of books, and review articles giving methods for estimating various

thermodynamic quantities are given in Section 23.0. Values of enthalpies

of formation estimated using these methods may be in error by one to

five kcal mol ^ (4 to 20 kJ mol .
54

21.5.6 Calorific Values or Heating Values of Fuels

The terminology of heating values used in the fuel industries

and applied to coal, coke, petroleum products, and natural or manufactured gas, refers to quantities closely related to the enthalpy

and internal, energy of combustion as discussed in this book. The terms

given below may be found in use. The following definitions are quoted

from ASTM methods referenced.

Standard Definition of the Terms Gross Calorific Value and Net

Calorific Value of Solid and Liquid Fuels (Definitions (1) and (2) are

found in Reference (1) below).

(1) gross calorific value (gross heat of combustion) , Qg in the

case of solid fuels and liquid fuels of low volatility, the heat produced

by combustion of unit quantity, at constant volume, in an oxygen bomb

calorimeter, under specified conditions.

Note - The conditions are initial oxygen pressure of 20 to 40 atm, final

temperature of 68 to 95 F (20 to 35 C) , products in form of ash, liquid

water, and gaseous CO^s SO^, and nitrogen. This definition is not applied

to gaseous or highly volatile liquid fuels.

(2) net calorific value, (net heat of combustion) , Qn in the case

of solid fuels and liquid fuels of low volatility, a lower value calculated

from the gross calorific value as the heat produced by combustion of unit

quantity, at constant atmospheric pressure, under conditions such that all

water in the products remains in the form of vapor.

Note - The net calorific value (net heat of combustion) is calculated from

the gross calorific value (gross heat of combustion) at 68°F (20°C) by

making a deduction of 1030 Btu/lb. (572 cal/g) of water derived from unit
55

quantity of fuel, including both the water originally present as moisture

and that formed by combustion. The deduction is not equal to the latent

heat of vaporization of water (1055 Btu/lb. at 68 F (20 C) because the

calculation is made to reduce from gross value at constant volume to net

value at constant pressure, for which the appropriate factor under these

conditions is 1030 Btu/lb.

Definitions (1) and (2) are found in Reference (1) below. The quantities

Hi and Hs found in Reference (1) are respectively Qg and Qn above.

Slightly variant definitions can be found in other places. Also, in

different ASTM methods different base temperatures are found. The

quantities gross and net heat of combustion are therefore not very

explicitly defined.

For the conversion from gross to net heat of combustion, several

nearly equivalent formulas are found in the standard test literature.

These take into account the per cent hydrogen in the sample.

Relation (at 25°C) Units ASTM Method Fuel Type

(1) Qn Qg - 10 . 30 (Hx9) Btu/lb D271-70;D2015-66 Coal, coke

(2) Qn Qg - 5 . 72(Hx9) cal/

g

D271-70 Coal, coke

(3) Qp (net)

Qv(gross) - 91.23(H) Btu/lb D240-64 ;D2382-65 Petroleum

Products

(4) Qp (net) = 0.7195 Qv(gross) + 4310 Btu/lb D 240- 64 ;D 2382-6

5

Petroleum

Products

In the above equations H is per cent hydrogen by weight.

Qg is found referred to in the methods as Hs, Hg, Qg (gross at 25 C, or the

letters B and C.

Qn is found referred to in the methods as Hi, Hn or Qn (net at 25 C) or the

letters N and N '

.
56

The terminology Qp (net, at 25°C) and Qv (gross, at 25°C) is due to

Jessup (Reference (3)). It uses Q for heat in a positive sense, uses

subscript p to indicate the constant pressure process and v to indicate

the constant volume process, and in parentheses states whether the net

or gross heating value is referred to and the temperature to which the

heat effect refers. It is a more explicit statement of the conditions

for which the heat effect is valid than are the other samples in use.

The slight discrepancy between formula (1) and formula (3)

should not be of concern. While formula (3) is probably based on a

more accurate analysis of the thermal effects involved, the inaccuracy

with which H is known and the variations from sample to sample in

measuring the heating value probably introduce larger uncertainties

than the differences.

To convert Qg to On the hydrogen content of the fuel must be

known. This is preferably determined by analysis. In the absence of

a measured value an estimate of the difference (Qg-Qn) for petroleum

fuels can be made. Equation (4) is a relationship based on an experimental correlation between Qg and per cent hydrogen for liquid hydrocarbons and hydrocarbon mixtures. It is not as accurate as equations

(1) or (3).

Equation (2) differs from equation (1) only in the factor

1.8 Btu/lb = 1.0 cal/g

.

Definitions of Terms for Gaseous Fuels (Reference (1c), (Id) below).

(3) total calorific value , the total calorific value of a gas

is the number of British thermal units evolved by the complete combustion,

at constant pressure, of one standard cubic foot of gas with air, the
57

temperature of the gas, air, and products of combustion being 60 °F, and

all the water formed by the combustion reaction being condensed to the

liquid state.

(4) net calorific value , the net calorific value of a gas is the

number of British thermal units evolved by the complete combustion, at

constant pressure, of one standard cubic foot of gas with air, the

temperature of the gas, air, and products of combustion being 60 °F and

all of the water formed by the combustion reaction remaining in the

vapor state.

Note 1 - The net calorific value of a gas is its total calorific value

minus the latent heat of evaporation at standard temperature of the

water formed by the combustion reaction.

Note 2 - The definitions given [Terms (3) and (4)] are for total and net

calorific values per standard cubic foot of gas. The definitions corresponding to any other unit quantity of gas are obtained by substituting

the name of the desired unit in place of the term "standard cubic foot"

in the definitions. Methods of calculating calorific values per cubic

foot of gas under any desired conditions of pressure, temperature, and

water vapor content are specified [in the ASTM method].

Definitions (3) and (4) are found in

ASTM Designation D900-55

Standard Method of Test for Calorific Value of Gaseous Fuels

by the Water Flow Calorimeter. See Reference (1) below.
58

Definition (3) is also found ini

ASTM Designation D1826-64

Standard Method of Test for Calorific Value of Gases in Natural

Gas Range by Continuous Recording Calorimeter. See Reference

(1) below.

The British thermal unit used in the gas industry and the standard

cubic foot of gas are also defined in these methods.

The gross heat of combustion at constant volume, Qv(gross) approximates — fU 9 the change in internal energy of the combustion process with

water formed in the liquid state. The negative sign appears because

Qv(gross) is positive for an exothermic reaction, while ZD is negative.

The net heat of combustion at constant pressure, Qp(net), approximates -ZH, the change in enthalpy of the combustion process with water

formed in the gaseous state. The negative sign appears as above.

In ASTM Method D-2382 (See reference (2) below), the following

caution is noted: Users of this method desiring to calculate Adc° at

298 K for a pure compound should note that corrections must be applied

to the value of Qv (gross) for buoyancy of air, heat capacities of

reaction components, reduction to a constant-pressure process, and

deviation of the reaction from the thermodynamic standard state.

The total calorific value and the net calorific value of a gas

differ only in that the water formed is condensed to determine the

former and not the latter. Thus the value of the net heating value of

a gas approximates the net heat of combustion at constant pressure but

on a volumetric basis rather than a mass basis. The total calorific
59

value of a gas could be given the name gross heat of combustion at

constant pressure, a term which is rarely if ever used.

References to Section 21.5

(1) 1971 Annual Book of ASTM Standards, Part 19. Gaseous Fuels; Coal

and Coke. (American Society for Testing and Materials, Philadelphia,

Pa., 191032.

(a) D 271-70 Standard Method of Test for Analysis of Coal and Coke.

(b) D 407-44 Standard Definitions of the Term Gross Calorific

Value and Net Calorific Value of Solid and Liquid Fuels.

(c) D 900-35 Standard Method of Test for Calorific Value of

Gases by the Water Flow Calorimeter.

(d) D 1826-64 Standard Method of Test for Calorific Value of Gases

in Natural Gas Range by Continuous Recording Calorimeter.

(e) D 2015-66 Standard Method of Test for Calorific Value by

Adiabatic Bomb Calorimeter.

(2) 1971 Annual Book of ASTM Standards, Part 17, Petroleum ProductsFuels-Solvents ; Burner Fuel Oils; Lubricating Oils; Cutting Oils;

Lubricating Greases; Hydraulic Fluids. (American Society for

Testing and Materials, Philadelphia, Pa. 19103).

(a) D 240-64 Heat of Combustion of Liquid Hydrocarbon Fuels by

Bomb Calorimeter;

(b) D 2382-65 Heat of Combustion of Hydrocarbon Fuels by Bomb

Calorimeter (High-Precision Method)

.

(3) R. S. Jessup, Precise Determination of Heat of Combustion by Bomb

Calorimeter, Nat'l Bur. Standards Monograph 7, 1960. (U. S.

Government Printing Office, Washington, D. C.).
60

21.6 Reaction Energy and Temperature

21.6.1 Effect of Temperature on Enthalpy of Reaction

The enthalpy change in a reaction (for instance, the

enthalpy of combiistion) is a function of the temperature at

which the reaction occurs, and of the nature of the reacting

substances. We may illustrate the relationships involved

by reference to Figure 21.1. Figure 21.1 is a schematic

diagram of enthalpy states of a system in which a reaction

can occur and the temperature can change.

At T

^ the sum of the enthalpies of formation of the

reactants may be represented as point A; the sum of the

enthalpies of formation of the products by point B. The

enthalpy change of the isothermal reaction, reactants -

products, at T^ is

AH(B - A) = AH(reaction, at T^)

= fAHf (products , at T^) - EAHf (reac tants , at T^) (1)
61

A, B, C, D, are points on the state diagram for enthalpy

of a system in which a reaction can occur and the temperature can change. An observed process, the transition from state A to state D can be resolved into two

components as shown. In one component the enthalpy

changes with composition, and in the other component the

enthalpy changes with temperature.
62

At T

2

the sum of the total enthalpies of formation of

the reactants may be represented by point C; the sum of

the enthalpies of formation of the products, by point D.

The enthalpy change of the isothermal reaction, Reactants -*

Products, at

AH(D - C) - AH( reaction, at T^)

= fAHf (products, at T£) - £AHf (reactants , at T

2

) (2)

To heat the reactants from T^ (point A) to T

2 (point C)

requires that an enthalpy equal to the difference between C

and A be added to the reactants. This enthalpy is mathematically given by the relationship:

T

AH(C - A) = J* 2 £Cp( reactants )dT (3)

i l

or equally well 2(H - (reactants, at T 0 ) - (3’)

£(H - Hq)

(

reactants , at T^)

= E(H - H

2 gg) (reactants, at - (3")

S(H - H298^ (reactants, at T )

Depending upon the availability of data, AH(C - A) may be

evaluated by summing the enthalpy terms H - Hgor H - H^gg or

by summing and integrating the heat capacity terns. The term

J T

2 ECp(reac tants)dT may be approximated over small temperature

ranges by ECp(reac tants) (T

2 - T^) ; that is, by assuming the

Cp's are constant. (The abbreviation ZCp(reactants) should be

understood to mean the total heat capacity of all the reactants,

and so the individual heat capacities must be weighed according

to the amounts of substance involved.)
63

To heat the products from T^ (point B) to (point D)

requires that an enthalpy equal to the difference between D

and B be added to the products. This enthalpy is mathematically exactly given by the relationship:

AH(D - B) = J

T

2 £Cp(products)dT (4)

or equally well = S(fe - Hq)

(

products, at T£) -

£(H - Hq)

(

produc ts , at T^) (4*)

or = E(H - ^298^ (Products > at T

2

) ~

£(H - (products, at T^) (4")

pT The term J 2£Cp (produc ts)dT may be approximated over small

T

1 temperature ranges by ECp (produc ts)(T

2

- T^) that is, by

assuming the Cp’s are constant.

21.6.2 Relationships between Enthalpies of Isothermal Reactions

at Different Temperatures

The difference in enthalpy between points D and A (Figure

21.1) is constant for a given reaction. Advantage may be

taken of this fact to demonstrate a method of calculating

the relationship between AH( reaction, at T^) and AH (reaction,

at T

2

). The energy difference is independent of the path

followed. Thus a path A -> C -* D may be followed or a path

A -» B -> D may equally well be followed. An arbitrary path

A -» D, represented by the diagonal may also be followed.

Mathematically: AH(D - A) = AH(D - C) + AH(C - A) (5)

= AH(D - B) + AH(B - A) (6)
64

Substituting quantities from the above discussion we have

T

AH(D - A) - AH (reaction, at TJ + J FCp(reac tants) dT

Zrp = J

^ ECp(products ) dT + AH(reaction,

at T

l

) (7)

In the simple case where Cp’s are independent of the

above relationship is sometimes simplified to the following:

AH(reaction at T

2

) = AH(reaction at T^) + ACp(T -T^) (8)

in which ACp is the difference: heat capacity of products minus

heat capacity of reactants.

21.6.3 Enthalpy Relations When the Temperature of the System

is Allowed to Change (at Constant Pressure)

The enthalpy difference between point D and point A,

AH(D - A) is a function only of the ingredients of the system

and the temperatures T

2

and T^. Pressure effects are negligible

except in unusual cases. We shall consider only the isobaric

k

process. For a given system, the difference, AH(D - A), is

dependent on T

2

and T^. For a given system, if T

2

and are

fixed, then AH(D - A) is also fixed. The relevant relationships

are given by equation (7). If a reaction occurs in which the

reactants are at T^ (point A) and the products are at temperature T

2 (point D) , the enthalpy change is AH( observed)

.

This appears or is evident as heat, Q

= - AH(observed)

.

Two extreme cases can be recognized.

The only work done is presumed to be pressure-volume work.
65

(a) The adiabatic process . No heat transfer between

the system and the external world occurs in the adiabatic process.

Mathematically this is equivalent to saying

Q

= -AH( observed) = 0

T

Since AH(observed) = AH(reaction, at Tj + Jb, l Cp(produc ts) dT

1

this means that for the adiabatic process, -AH(reac tion, at TJ = T

L

p 2

J T

£ Cp(products)dT. This is a mathematical way of saying

1

the enthalpy of reaction, being retained in the system, if

exothermic causes the temperature of the products to rise

an amount determined by their specific heat.

The temperature rise that will occur is often determined

by a method of successive approximation. An estimate is made

of the temperature rise. The specific heats are used to calculate the necessary -AH( reaction at T^). If the value for

-AH (reaction, at T^) calculated in this way is less than the

true value obtained from the Tables, the estimated temperature

is increased, and the process repeated. If the value calculated for -AH( reaction, at 1 ) is larger than the true value,

the estimated temperature is decreased. The iteration is repeated until the calculated and tabular values of -AH( reaction,

at T^) are as close to one another as desired.

(b) The isothermal process . Heat transfer between the

system and the external world is complete in the isothermal

process, so that the temperature of the system always remains

at T^. No practical system is completely adiabatic, and more
66

or less heat transfer will be encountered in any real reaction process. At the other extreme, the amount of heat

transferred equals the negative of the enthalpy of the

isothermal process,

T

-Q = AH(observed) = AH(reaction at T, ) + L Cp (products)dT

t ±1

Since = T

^ the second term of the right hand side is zero,

and

Q

= -AH (reaction, at T^)

The temperature rise of the products of reaction can be

regulated by allowing the transfer of varying amounts of heat.

The maximum possible temperature rise is, of course, the

adiabatic temperature rise. This maximum temperature can be

regulated to some extent by varying the composition of the

sy s tem

.
67

21. 7 Reaction Equilibrium and Temperature

Data in the tables of this monograph and in additional tables of

thermal functions referred to in Section 22.0 are suitable for calculations

of thermodynamic equilibria at the final temperature in reactions involving

a few or many species. We limit ourselves here to a very brief outline

of the procedures and refer the reader to other sources for detailed

procedures. Several references to more detailed presentations of the

general problems of handling high temperature equilibria of multicomponent

systems are found in Section 24.0. Because several parameters must be

adjusted simultaneously or at least in a mutually consistent way and

because many variables are present in a multicomponent system, the solution

of such problems may be very time consuming and arduous unless assisted

by rapid machine calculation. The techniques for using such aids change

rather rapidly and the user may find being developed from time to time

procedures that are more efficient in the use of machine time. All discussion presented here is based on an assumption of equilibrium in the

gaseous state. Equilibrium may be quite closely reached in hot reacting

systems; but even in the absence of equilibrium the results of equilibrium

calculations may provide a useful approximation to the real situation.

There is currently much work being done on the application of thermodynamics

and kinetics to estimate dynamic non- equilibrium performance. Some such

work is described in references in Section 24.0 (see, for example,

references [5, 8, 29]).

When a complex mixture is allowed to react until it comes to equilibrium, two general limiting cases can be readily identified and

described. (1) The resulting temperature is determined by the energy
68

of reaction—no energy losses being allowed. (2) Energy exchange is

allowed, and the combustion products are brought to the same final temperature as the initial temperature. These two situations represent the

adiabatic and isothermal process, respectively. The real situation lies

somewhere in between. There are always some heat losses to the surroundings.

The equilibrium thermodynamic state of the system comprising the products of combustion can be completely described by specifying the composition and enthalpies of the initial materials that have been burned and

the final pressure at which the products will be present. The final

temperature and product composition will then be given in terms of four

sets of simultaneous equations giving; (a) mass balance; (b) enthalpy

balance; (c) pressure balance; and (d) chemical equilibria.

(a) The equations for the conservation of mass are summarized as

equations (1A) and (IB)

.

a = E a^ for the reactants (1A)

k=l

As an initial step the number of gram- a toms, a^, of the i ' th element, which

we shall identify as A^, introduced into the reaction zone is calculated

from equation (1A) ; is the sum of the number of gram-atoms of A^ in

the substances introduced. There are a different substances introduced,

which we shall identify as and these are enumerated from k = 1 to k = a.

The number of moles B,^ is n^ and the subscript of A^ in the chemical formula

of B^ is a^» If there are N elements present, i will range from 1 to N

and there will be N such equations.

As an example let us consider a combustion mix introduced into the

furnace and consisting of one kilogram of cellulose (monomer formula.
69

C r HinO,-; molecular weight, 242), one kilogram of benzene (formula, C,H,

;

o ID D bo

molecular weight, 80), and thirty kilograms of combustion air (approximate

formula, 78% N^; 20% 0^1 2% H

20 ; molecular weights, N^, 28; 0 2> 32;

H

20, 18).

The numbers of moles of the various substances are calculated

as follows [for simplicity approximate atomic weights are used]

n

l

(cellulose) = 1000/242 = 4.13 moles

n

2 (benzene) = 1000/80 = 12.50 moles

n

3

(o

2

) = (0.20) (30000/32) = 187.50 moles

n

4

(n

2

) = (0.78) (30000/28) = 835.71 moles

n

5

(h

20) = (0.02) (30000/18) = 33.33 moles

The numbers of gram atoms, o^, of the various elements are calculated as follows:

O-^ (carbon) * 6(4.13) + 6(12.50) = 99.78 gram atoms

a

2 (hydrogen) = 10(4.13) + 6(12.50) + 2(33.33) = 182.96 gram atoms

(oxygen) = 5(4.13) + 2(187.50) + 33.33 = 428.98 gram atoms

(nitrogen) = 2(835.71) = 1671.42 gram atoms

For this example N is 4 and a is 5.

Having established the composition of the combustion mix a necessary

step in the calculation of the mass balance is to list the presumed reaction

products to be considered. This is a critical step, depending upon the

judgement of the individual; there being no way a priori to establish

definitively what products will be formed.

Referring to the above example we shall expect to find CC^, H^O, C^,

and N

2 as major components of the combustion products. However, if care

is to be used in controlling effluent gases we must also take into account
70

the possibility of formation of GO, NO, N0^ s and HNO^. As a matter of procedure we shall also consider the gaseous monatomic elements, 0,0, N,H,

as being present. If the amount of oxygen is limited, one must also

consider such possibilities as unburned or partially burned ingredients

such as gaseous CFh , CH, C„, C^H^, and HCO. There are a very large

number of potential components resulting from incomplete combustion.

The variety of potential products of combustion will increase rapidly as

additional elements are included in the combustion mixture.

When this has been done, the number of gram-atoms of the elements

can be expressed as the sum of their presence in the products of combustion

by equation (IB)

.

a

.

i

3Z for the combustion products (IB)

In equation (IB), is the same series of quantities calculated by

equation (1A) . There are 3 presumed products of combustion, and there

are moles of product B^ in the formula in which the subscript of the

element A. is a. .

.

i ij

Equations (IB)

(carbon)

a

^ (hydrogen)

a 0 (oxygen)

(nitrogen)

become:

= - n„^ 4- n_„ + n^„ 4 2n„ + 2n

CO CO CH, CH '2 C

2H2 + ^CO

"H + 2d11 + 2 ”h„o

+ 4n„„ + n„„ 4 2n

CH CH

1 C

2

H

2 +"HCO + n

HNO,

= n^ + 2n^ 4

0 0 o +

°K0 + 2n

N0 o + n

H o0 + 3nHN0^ + n

C0 + 2n

C0 *

4 4 nNQ + n^

Q ^+

The values assigned to the n's cannot be made final without solving the

equilibrium equations.

nHC0
71

(b) Equation (2) is the equation for the conservation of energy

in the case where all energy of reaction goes to heating the products

of combustion.

I \

[Zilf 298

° f B

k + (H

T

” H

298'

k=l 1

) ° f V

= I n.mq9s

of B. + (H - H

298) of Bj ] (2)

J ^ As before there are a ingredient substances (or reactants) in the

combustion mix, and these are enumerated from k = 1 to k = a . The enthalpy

contribution of each ingredient is given by a term on the left hand side

of the equation and consists of the number of moles times its enthalpy

of formation at 298 K plus an enthalpy increment if the initial temperature

of the ingredients differs from 298 K.

The enthalpy requirements to form the products of combustion and

bring them to the final temperature T^ are given by the right hand side

of the equation. There are 8 combustion products B and these are

enumerated from j =1 to j =8. The enthalpy requirement for each combustion product is given by a term which consists of the number of moles

n times its enthalpy of formation at 298 K plus an enthalpy increment to

bring its final temperature to T^.

Note that the number of moles of each substance formed in the products

will depend upon the temperature of the products, and this dependence will

be particularly pronounced if some comparatively unstable combustion products

can be formed. Therefore the quantities n. must be made consistent with

1 the requirements of the possible equilibria at the final temperature. The

quantities rL , on the other hand, depend only on the mixture burned.
72

Note also that if energy losses occur, such as losses through the

furnace walls, the final temperature will not be as high as if there

were no such losses.

(c) Equation (3) is the pressure balance equation.

3 P = E P. (3)

C j=l J

In equation (3) P^_ is the total pressure in the chamber where the

combustion products are present, and P^ is the partial pressure of the

j

1 th product, B^ . The partial pressures are given in terms of the number

of moles and the total pressure by equation (3'), assuming the fugacities

P.

P

t Z n

.

3 j-1

(3’)

are all proportional to the pressures. Note that the partial pressures

can be calculated only after the mole ratios are known.

(d) Equations (4) and (4*) are the equations for the reaction

equilibria involved. There are various ways in which the equilibria

may be specified. An unambiguous way which assures that all possible

equilibria are implicitly included is to give the equilibrium constant

of formation of each substance from the atoms of the elements present.

N

RT In K. = RT In f. -E a. . In f

.

i=l ij (4)

N

RT In K = (-AHf°) - (Of - H«) + 2 a. ,[(AHf°). + (G° - H°).] (4')

J o j

i o j xj o i i ox

The constant K. is the equilibrium constant of formation of B.. the i

' th

3 3 constituent of the products, from the atoms of the elements. There are
73

N elements present, and so for each substance present the elements in it

are enumerated from i = 1 to i = N. The coefficient a. . represents the

ij

subscript of element i in the formula for the substance . The equilibrium

constant can be expressed in two ways represented by equations (4) and (4')

respectively. Equation (4) represents the definition of the equilibrium

constant of formation from the gaseous monatomic elements in terms of the

fugacities of the elements and of the combustion products, f ^ and f ,

respectively. Equation (4') represents the equilibrium constant in terms

of the Gibbs energies of the substance and of the elements respectively,

and the enthalpy of reaction, which can be derived from the enthalpies of

formation of the substance and the elements respectively. The reader

should note that the elements as used in the equations (4) and (4

1 ) are not

in their standard reference states, but are in the form of the gaseous

monatomic species. The elimination of RT In from equations (4) and (4')

allows a single equation to represent the equilibrium for each reaction.

For gases at not too high pressures the fugacity equals the pressure

(i.e., f = Pj)* For gases to which this equality does not apply, a

correction term may have to be applied. For condensed phase products

formed f. is considered to be unity.

J We may illustrate the equilibria involved in the previous example

in the following way:

2H(g) t H

2 (g)

20(g) t 0

2 (g)

2N(g) t N

2 (g)

2H(g) + 0(g) t H

20(g)
74

C(g) + 0(g) ? co(g)

C(g) + 20(g)? C0

2 (g)

N(g) + 0(g) ? NO (g)

N(g) + 20(g)? N0

2 C(g) + 4H(g)? CH

4 (g)

C (g) + H(g) ? CH(g)

2C(g) ? C

2 (g)

2C(g) + 2H(g) ? C

2

H

2 (g)

H (g) + C(g) + 0(g) ? HCO(g)

H(g) + N(g) + 30(g) ? HN0

3 (g)

This sequence of reaction is sufficient to specify the equilibria involving

the formation of the substances specifically listed above. It will be

apparent from the above sequence of reactions that a number of the proposed

species will be found on3y in extremely small quantities and a way can

probably be found to reduce the number of equations by eliminating these

species. In addition, it can easily become apparent that one or more

additional species are important enough for inclusion. The criteria for

inclusion will differ for different species depending upon contribution

to the mass or pressure balance, toxicity, corrosiveness or other factors.

The equilibria shown were chosen as a systematic way of identifying

unambiguously a sufficient number of non-redundant equations including

all the substances under consideration. An attempt to write down directly

the equilibria that are of real importance may lead to problems because

of redundancies or because they form an insufficient set. Provided that

all substances of importance have been listed a set involving formation

of a substance from the gaseous atoms such as those given above, includes

implicitly or explicitly all equilibria of importance.
75

The mass balance equations for the combustion products can now

be listed.

(carbon) = n(C) + n(CO) + n(C0

2

> + n(CH

4

> + n(CH) + 2n(C

2

)

+ 2n(C

2 H2

) + n(HCO)

a

2 (hydrogen) = n(H) + 2n(H

2

) + 2n(H

20) + n(HNC>3

) + 4n(CH

4

) + n(CH)

+ 2n(C

2H2

) + n(HCO)

a

3

(oxygen) = n(0) + 2n(0

2

) + n(H

20) + n(CO) + 2n(CC>

2

) + n(NO)

+ 2n(N0

2

) + n(HCO)

a

4

(nitrogen) = n(N) + 2n(N

2

) + n(NO) + n(NC>

2

) = n(HN0

3

)

The pressure balance equation can be written:

P

t = p(c) + p(co) + P(co

2

) + p(ch

4

) + p (ch) + p(c

2

) + p(c

2 h2

)

+ P(HCO) + P(H) + P(H ) + P(H

20) + P(0) + P(0

2

) + P (NO)

+ P(N0

2

) + P(HN0

3

) + P (N) + P(N ).

An iterative procedure for calculating equilibrium compositions and

energies is as follows

(1) Prepare equations for reactions that may participate in equilibria

at the resulting temperature.

(2) Write mass balance equations for each element in terms of molecular

species present based on combustion ingredients introduced.

(3) Write expressions for equilibrium constants.

(4) Assume a temperature T

2 and a number of moles for each product

and try the consistency of the equations. Calculate the number of moles

of gas and test the material balance. If material imbalances result

adjust n. When n has been adjusted to balance, the temperature, T

2 and
76

moles of products n . are consistent. This gives a product profile for

1 a given T^. However, T

2 may be incorrect for the enthalpy. Calculate

the enthalpies of the products at (including enthalpies of formation

and enthalpy increments to T^)

.

(5) Then repeat determinations of product profiles until enthalpies

of products and of reactants are equal. This gives the correct T^,

and the remaining quantities, moles of each product, partial pressures,

etc., are then correct.

A different approach is to find the composition of the combustion

which minimizes Gibbs energy of the system. This approach is discussed

in References [33] and [34] of Section 24.0. Only the principle of this

method will be mentioned here. The procedures for carrying out a calculation may be found in reference [33].

The condition for a minimum (or a maximum) in a mathematical function

is that the derivative or differential be zero. The condition for thermochemical equilibrium is that the Gibbs energy, dG, be a minimum for the

system. This is expressed by the statement which sets the differential

equal to zero (equation (5))

dG = 0 (5)

At a fixed temperature and pressure and for a specified set of combustion

products B. the differential dG is given by equation (6).

dG

j=l

y . dn

.

3 J

( 6 )

Here dn. is a differential change in the number of moles n. of component

B_., and

y^

is the chemical potential of the species B^ . The chemical
77

potential of is the differential rate of change of the Gibbs energy

of the system per mole of B. added to the system (equation (7)).

For an ideal gas :

(7)

y . = G! + RT In P,

3 3 3 This system is subject to the same constraints as before, that the mass

balance must be maintained and that the energy balance must be maintained.

By consideration of all of the possible chemical products and maintaining the mass balance of the elements present, a set of mole numbers

for the combustion products can be calculated which leads to a minimum

Gibbs energy and equilibrium temperatures for the whole system by an

iterative process.
78

22.0 Supplementary Sources of Thermo dynamic Data

on Chemical Substances and Materials

The following monographs are collections of thermodynamic data

compiled from the original literature by competent thermo ch emis ts and

presented in a well organized way. These sources have been selected

to provide reasonably comprehensive coverage but are by no means a

complete list of compilations of thermodynamic data. Except for the

Landolt-Borns tein tables, foreign language compilations have not been

included because of their limited accessibility. The extensive Russian

compilations of thermodynamic tables are essentially very similar to

some of the more comprehensive compilations listed here. Two general

texts on thermodynamics and thermochemistry are also included.

1. Ashcroft, S. J., and Mortimer, C. T.

Thermochemistry of Transition Metal Complexes

(Academic Press, London, New York, 1970).

This book surveys the literature to 1968 on energy processes involving

transition metal complexes including both organic and inorganic ligands.

A critical review of the thermochemical data for over 1500 systems of complexes is given. Comparable data from various sources are shown in juxtaposition. Values of Ai, ZG, and AS for various stages of complex formation

are usually listed for processes in aqueous solution. ZHf°, AGf °

, ZSf° for

crystalline complex substances are given where available. In many instances

correlations of the data for various metals with a single ligand, and for

various related complexes of a given metal, are given graphically or by means of bond-energy estimates based on the data.
79

2. Bain, R. W.

National Engineering Laboratory (NEL) Steam Tables, 1964

Physical Properties of Water and Steam 0-800°C, 0-1000 Bars

(Her Majesty's Stationary Office, Edinburgh)

These are typical steam tables, with data tabulated in SI units,

except that pressure is in bars and temperature in °C. The tables

were ratified by the Sixth International Conference on the Properties

of Steam. An introduction to the tables is given. See also sources

(8, 13).

3. Cox, J. D., and Pilcher, G.

Thermochemistry of Organic and Organometallic Compounds

(Academic Press, London, New York, 1970)

This monograph is a critcal compilation of thermo chemical data

published since 1930. The heats of formation of some 3000 substances

are listed, with estimates of error. Where enthalpies of vaporization

are known or can be reliably estimated these are listed and in these

cases the enthalpies of formation of both gaseous and condensed phases

are given. Extensive introductory material presents experimental procedures and procedures for reduction of experimental data of the type

found in the book. Applications of thermochemical data are given, and

there is a section on methods of estimating enthalpies of formation of

organic compounds.
80

4. Domalski, E. S.

Selected Values of Heats of Combustion and Heats of Formation

of Organic Compounds Containing the Elements C, H, N, 0, P, and S.

(Journal of Physical and Chemical Reference Data _1, 221-277 (1972))

Selected values of the enthalpies of combustion and enthalpies of

formation of 719 organic compounds are reported. These are essentially

the same as in the present compilation, but the selected values are

augmented by commentary and original source references. The Wiswesser

Line Notation is also given for each compound. The methods used in

updating older work are described.

5. Hilsenrath, J., Beckett, C. W., Benedict, W. S., Fano, L.,

Hoge, H. S., Masi, J. F., Nuttall, R. L., Touloukian, Y. S.,

and Woolley, H. W.

Tables of Thermal Properties of Gases

National Bureau of Standards Circular 564, (1955)

(U. S. Government Printing Office, Washington, D. C. 20402)

This monograph gives tables of compressibility factor, density,

entropy, enthalpy, specific heat, specific-heat ratio, and sound velocity

for the real gases: air, argon, C0

2

, CO, H

2

, N , 0

2

, and steam over

the range 0.01 to 100 atm and to 3000 K (in most cases). It also gives

ideal-gas thermodynamic functions to 5000 K. Vapor pressures, thermal

conductivity, viscosity and Prandtl number are given over the range of

available experimental data. Critical commentaries and descriptions

of the analyses of the data are provided.
6. Hultgren, R., Orr, R. L., Anderson, P. D., and Kelley, K. K.

Selected Values of Thermodynamic Properties of Metals and Alloys

(John Wiley and Sons, Inc., New York, London, 1963).

This volume gives the results of critical evaluations of the thermodynamic properties of the 63 metallic elements and 168 alloy systems.

Self-consistency of the data, consistency with known thermodynamic

relationships, consistency with known phase diagrams, and agreement

between similar measurements, formed the bases for selection of the

values. Heat capacities (Cp) at low and high temperatures and vapor

pressure data are reviewed and references are given. Values are tabulated for Cp, H - H , and -(G^ - H )/T, for condensed and gas phases

with T as the principal variable; and values of P, AG, and ZH of the

vaporization process are given. Values for H_. 0 - H^, S ono , T , ZH and

Z9 8 u zyo m m

AS^, and analytical expressions for - H^gg as functions of T are given

A supplement containing information on three additional elements and

4 alloy systems was issued in 1966.

7. Joshi, R. M. , and Zwolinski, B. J.

Vinyl Polymerization, Volume 1, Part I, edited by G. E. Ham

(Marcel Dekker, Inc., New York, 1967)

Chapter 8: Heats of Polymerization and their Structural and

Mechanistic Implications

The authors discuss experimental methods used to measure and derive

heats of polymerization. A listing of experimental data on heats of
82

polymerization is provided for 81 organic polymerization reactions

.

Other tables give heats of formation, heats of vaporization, entropies,

Gibbs' energies, equilibrium constants, rate constants and activation

energies at 25°C for a variety of polymerization processes. A discussion

of the structural influence upon the heat of polymerization is also given.

At the end of the chapter, 164 references are cited.

8(a). Keenan, H. J., Keyes, F. G., Hill, P. G., and Moore, J. G.

Steam Tables

Thermodynamic Properties of Water, including Vapor, Liquid, and

Solid Phases (International Edition, Metric Units)

(John Wiley and Sons, Inc., New York, London, Sydney, Toronto, 1969)

This book presents the results of a new and independent correlation

of all the new thermodynamic data and all previously existing data. It

constitutes a complete revision of the Keenan and Keyes Tables of 1936 and

an extension of range to 1000 bars and about 1300°C.

Values of the thermodynamic properties specific volume, internal

energy, enthalpy, and entropy are tabulated with pressure and temperature

as parameters, for vapor-liquid equilibrium, vapor-solid equilibrium,

superheated vapors, and compressed liquid. Mollier and temperature-entropy

charts are included along with charts of heat capacity of liquid and vapor,

Prandtl number, and isentropic expansion coefficient. A detailed table

for the critical region shows volume and temperatures as parameters.

The present tables are in no sense a formulation of the International

Skeleton Tables (1963) . In general they are in good accord with, and their

values fall within the tolerance of the International Skeleton Tables.
83

Exceptions are discussed. Extensive, tables of viscosity and thermal

conductivity are reproduced from the documents of the Sixth International

Conference on the Properties of Steam.

Energy units are joules, temperatures are K or °C, pressures are in

3 bars, volumes in cm and masses in grams. The data and tables are discussed in an appendix of 25 pages; and a list of 37 references is given.

The introduction is in English, French, German, Italian, Japanese, Russian,

and Spanish. See also sources (2, 13).

8(b). Keenan, J. H., Keyes, F. G., Hill, P.G., and Moore, J. G.

Steam Tables

Thermodynamic Properties of Water, including Vapor, Liquid,

and Solid Phases (English Units)

(John Wiley and Sons, Inc., New York, London, Sydney, Toronto,

1969)

.

This edition of the Steam Tables supplies the same basic information

as source (8a) except that English units are used.

A review of the sources of data and comparison of derived tabulated

values with experiment, and a summary of the equations used in deriving

the tabulated data are given in an appendix of 29 pages. Tables for the

vapor give specific volume, specific internal energy, specific enthalpy,

and specific entropy at temperatures from 32° to 2400°F, and at pressure

2 intervals from 0.2 to 15,000 lb/in ; as well as several properties of the

very low pressure gas. Similar tables are given for the liquid, covering

somewhat different ranges. See also sources (2, 13).
84

9. Kelley, K. K.

Contributions to the Data on Theoretical Metallurgy

XV. A Reprint of Bulletins 383, 384, 393, and 406

Bureau of Mines Bulletin 601 (1962)

(U. S. Government Printing Office, Washington, D. C.)

This monograph is a reprint collection of previous monographs having

the same principal title. The subtitles of these are listed below.

III. The Free Energies of Vaporization and Vapor Pressures of

Inorgnic Substances. Bureau of Mines Bulletin 383 (1933).

IV. Metal Carbonates— Correlations and Applications of Thermodynamic

Properties. Bureau of Mines Bulletin 384 (1935).

V. Heats of Fusion of Inorganic Substances. Bureau of Mines

Bulletin 393 (1936) .

VII. The Thermodynamic Properties of Sulfur and Its Inorganic

Compounds. Bureau of Mines Bulletin 406 (1937).

This volume together with Bureau of Mines Bulletins 542, 584, and 592

constitute a complete set of the thermodynamic data series.

A typical presentation of the selected data for vaporization gives

Cp(g), Cp(liq), Cp(c), Z!Cp, AH^^, as analytical equations in

temperature, and values of AH 9 gg, S

? ^g, and T^ „ The monograph on metal

carbonates gives selected values and equations for Cp , S, ZGf ° , AHf°

for CO, C0

?

, H

? 0, carbonate(aq) and bicarbonate(aq) ions, and 25 metal

carbonates or bicarbonates. A table of dissociation pressures is given.

The monograph on enthalpies of fusion gives selected values of AHm for
85

63 elements and many of their compounds. The monograph on sulfur

compounds gives similar information for elemental sulfur, a few gaseous

non-metallic compounds, and for the sulfides and sulfates. Illustrations

of the uses of thermo chemical data, critical discussions of the source

data, and bibliographies are given in each monograph.

10. Kelley, K. K.

Contributions to the Data on Theoretical Mettalurgy

XIII. High-Temperature Heat-Content, Heat-Capacity, and Entropy

Data for the Elements and Inorganic Compounds

.

Bureau of Mines Bulletin 584, (1960).

(U. S. Government Printing Office, Washington, D. C.)

This comprehensive monograph gives procedures used in the correlations,

and gives selected values, tables, and analytical functions in temperature

for the subject thermodynamic data of several hundred substances. A

bibliography of sources is provided. The breadth of coverage is very

great. Substances for which data are provided include the first 92

elements and many of their acids, oxides, carbides, nitrides, hydrides,

hydroxides, halides, carbonates, nitrates, phosphates, sulfates, borates,

cyanides, mixed oxides and intermetallic compounds.
86

11. Kubaschewski , 0., Evans, E. LI., and Alcock, C. B.

Metallurgical Thermochemistry, 4th Edition

(Pergamon Press, Oxford, New York, and other cities, 1967)

This monograph is a standard reference work for metallurgists, and

deals with the thermochemistry in a rather broad way with special emphasis

on inorganic compounds and alloys. About 140 pages of tables of thermochemical data are given in which are presented AHf^^g, S°^g, T

trans’

Tm

’

T. , structural information, ZH , /Si , and ZH , , for elements and

b m vap subl

compounds

.

Constants of analytical expressions for Cp, the vapor pressure, and

ZGf° or ZG for a reaction, with temperature as the variable, together

with the temperature range of applicability, are given for many substances.

A separate table gives the thermodynamic properties of mixing for alloys.

The tabulated data are derived from other compilations and the original

literature

.

The accompanying text, comprising some 300 pages, gives the theoretical

basis of the deviation and application of thermo chemical data, a discussion

of the estimation of thermo chemical data, and examples of thermochemical

treatment of metallurgical problems.

12. Merrill, A. L., and Watt, B. K.

(a) Energy Value of Foods; Basis and Derivation

Agriculture Handbook No. 74, 1955.

(b) Watt, B. K., and Merrill, A. L.

Composition of Foogs; Raw, Processed, Prepared

Agriculture Handbook No. 8, revised, 1963

(U. S. Government Printing Office, Washington, D. C. 20402)
87

This pair of monographs provides numerous composition and energy

values for food and foodstuff ingredients. It should be noted, of

course, that the Calorie used in food energy values is 1 kcal as used

in this handbook. In Agriculture Handbook No. 74, Part I gives a

discussion of the sources of food energy in terms of organic compound

class, and of the experimental determination of heats of combustion.

Parts II, III, and IV apply the data to physiological processes. An

appendix gives composition and heat of combustion of foods. Tables 1-5

and table 24 give heats of combustion of specific food items or component

substances. Care should be used in taking values from the numerous tables,

as correction factors have sometimes been applied to adjust for physiological processes. These adjustments are indicated by footnotes. In

Agriculture Handbook No. 8, Appendix A is of particular interest as it

gives notes on energy values and nutrients, including (adjusted) heats

of combustion of many foods and food ingredients.

13. Meyer, C. S ., McClintock, R. B., Silvestri, G. J., and Spencer,

R. C. , Jr

.

ASME Steam Tables 1967

Thermodynamic and Transport Properties of Steam; comprising Tables

and Charts for Steam and Water

(American Society of Mechanical Engineers, New York, N.Y., 10017)

These tables give an introductory discussion of their source. Nine

tables and thirteen charts of thermodynamic properties are given. The

data were computed from equations adopted in the IFC*, Formulation for

^International Formulation Committee of the Sixth International Conference

on the Properties of Steam.
88

Industrial Use, which is reproduced. Reference is made to computer

procedures for handling the source equations. Three tables of transport

properties are given, based on the skeleton tables and empirical equations

developed by the Sixth International Conference. The principal tables

are in U. S. Customary units. See also sources (2, 8).

14. Pitzer, K. S., and Brewer, L.

Thermodynamics: Gilbert N. Lewis and Merle Randall (Second edition)

(McGraw Hill Book Company, Inc., New York, Toronto, London, 1961)

This monograph on thermodynamics and its application to physics and

chemistry is a revision and updating of the classical work by Lewis and

Randall, that did much to shape the development of thermodynamics in the

20th century. It provides a reasonably complete presentation of the

principal subjects of thermodynamics. In addition it provides in the

appendices (among other subjects) tables and discussions of (1) properties

of normal solutions, (2) properties of gaseous solutions, (3) a tabular

summary of thermodynamic formulas, (4) tables of thermodynamic properties.

The latter tables include AIf° 0 and ~(G° - H° 0 )/T for halides, oxides,

sulfides and related compounds, carbides, and nitrides, at 298, 500, 1000,

1500, and 2000 K. Values of -(G - H°)/T at the same temperatures,

- H°, and AHf ° are given for some of the elements. Also, - (G - H°)/T

at the same temperatures, AHf°

9g , /Hf°, and H"

9g - H° are given for some

gaseous carbon compounds, halides, oxides, hydrides, and related compounds.

Sources of data are given.
89

15. Rossini, F. D., Pitzer, K. S., Taylor, W. J., Ebert, J. P.,

Kilpatrick, J. E., Beckett, C. W., Williams, M. D., and Werner, H. G.

Selected Values of Properties of Hydrocarbons

National Bureau of Standards Circular C461, (1947).

(U. S. Government Printing Office, Washington, D. C.)

This monograph was prepared as part of the work of the American

Petroleum Institute (API) Research Project 44. Values are given for

some 36 physical and thermodynamic properties of several hundred

hydrocarbons in metric and in U. S. Customary units. The data in most

instances represent values found from careful studies, many of which

were done in connection with the same API Research Project. Experimental

data are supplemented by theoretical calculations or empirical correlations. References to the source data and a bibliography are given.

The data in many instances are identical to those in the Carnegie Press

publication by the same name listed below. See also source (16).

16. Rossini, F. D., Pitzer, K. S., Arnett, R. L., Brown, R. M. , and

Primentel, G. C.

Selected Values of Physical and Thermodynamic Properties of

. Hydrocarbons and Related Compounds

(Carnegie Press, Pittsburgh, Pennsylvania, 1953)

This monograph resulted from the work of American Petroleum Institute

(API) Research Project 44. Values are given for 40-odd physical and

thermodynamic properties of several hundred hydrocarbons in metric and U. S.

Customary units. The data in most instances represent selected values from
90

careful studies, many of which were done in connection with the same API

Research Project. Experimental data are supplemented by theoretical

calculations or empirical correlations. References to the source data

and a bibliography are given. The data in many instances are identical

to those in NBS Circular C461, listed above. See also source (15).

17. Rossini, F. D., Wagman, D. D., Evans, W. H., Levine, S., and Jaffe, I.

Selected Values of Chemical Thermodynamic Properties

National Bureau of Standards Circular 500 (1952)

(U. S. Government Printing Office, Washington, D. C. 20402)

This was for many years the most comprehensive authoritative compilation of thermo chemical data at 298.15 K for inorganic substances. All

inorganic substances and organic substances containing two carbon atoms

or fewer per molecule are included if thermodynamic data exist for calculating one of the properties tabulated. Properties tabulated in Part I

are ZHf ° , /Hf° 9g , AGf°

9g , log Kf , S°9g , and Cp° 9g

. Properties tabulated

in Part II are temperature, pressure, enthalpy change, entropy change

and heat capacity change for the phase changes: transition, fusion, and

vaporization. The data from original sources were critically evaluated

by competent thermochemis ts and best values selected for the functions

tabulated, maintaining internal consistency by the relationship: AGf° = 470

AHf°

9g - TA3°

9g

. The sources of data for each data item are listed and

a bibliography is included. Some information in this book can still

not be found readily elsewhere as the revision is not yet complete.

See Wagman, et al, (source [24]) below.
91

18. Schafer, D., and Lax, E. (editors)

Landol t-Bo rns tein

Zahlenwerte und Fuctionen aus Physik, Chemie, Astronomie,

A Geophysik, und Technik, Sechste Auflage

Eigenschaf ten der Materie in Ihren Aggregatzus t'anden

4 Teil, Kalorische Zus tandgrossen

(Springer-Verlag , Berlin, Gottingen, Heidelberg, 1961)

This most recent issue of thermodynamic information of the famous

Landolt-Bornstein series gives thermal properties: molar heat capacity,

entropy, enthalpy, enthalpy of formation, Gibbs energy of formation,

in the standard state, and enthalpies of phase changes for many organic

and inorganic substances in SI units. The dependence of thermal functions and heat capacity upon temperature is given for many substances.

Some other thermodynamic quantities are given. Extensive tables are

given of group contributions to enthalpy of formation and the Gibbs

energy of formation of organic substances (gases) in kcal mol

X and

kJ mol . Many of the heat capacity data are presented in diagrams.

19. Stern, K. H., and Weise, E. L.

High Temperature Properties and Decomposition of Inorganic Salts

Part 1. Sulfates - NSRDS-NBS-7 (1966)

Part 2. Carbonates - NSRDS-NBS-30 (1969)

(U. S. Government Printing Office, Washington, D. C.)
92

These two monographs treat the thermodynamics and kinetics of decomposition of sulfates of over 60 metals, and carbonates of over 21 metals

in a systematic way. The general features of the decomposition chemistry,

phase transition temperatures, densities, and decomposition equilibria

as functions of temperature are discussed. Also the mechanism of endothermic solid state decomposition, kinetic equations, and surface area

changes during decomposition, and several parameters affecting rate of

decomposition are discussed. These parameters include pressure, activation energy, method of preparation, heat transfer and crystal imperfections

Data given for each of the substances involved include density, thermal

expansion coefficient, transition temperatures, entropy at 298 K, enthalpy

of formation at 298 K, as well as the following functions of temperature:

Gibbs energy of decomposition, equilibrium constant K and Log K of decomposition, and the Gibbs energy functions -(G° - H°gg)/T. The coverage is

not uniform as all the data have not been measured for all the compounds.

The substances involved are SO^, SO.,, °2’ C°2 S C0 ’ carbonates > the

sulfates, and the oxides. The values obtained are the results of a

critical review of the original literature sources.

20. Stull, D. R., and Prophet, H., editors

JANAF Thermo chemical Tables, 2nd Edition, 1971

National Standard Reference Data Series NSRDS-NBS 37, (1971)

(U . S. Government Printing Office, Washington, D. C. 20402)

This work appeared first as a series of loose-leaf data sheets,

revised at intervals as new information became available. Each sheet
93

was dated. The first bound edition of the work (1965-1966) was issued

by the Clearinghouse for Federal Scientific and Technical Information

(since changed to: National Technical Information Service) as Document

PB-168370 and supplements. This has been somewhat revised for the second

edition. Approximately 1000 compounds, elemental molecules, and atomic

species, including a few gaseous ions, are included in this work. The

elements included were selected for relevance in rocket propellant

ingredients or products of combustion, and hence the elements of lower

atomic weight and substances formed from them predominate. However a

few heavier elements such as Pb , Hg, and W are included. Thermal functions

Cp°, S°, - (G° - H’ )/T, H°-H° Q , /Hf °

, IG f°, and Log Kp are tabulated

from 0 to 6000 K or to a lower temperature limit of meaningful data.

AHf° at 0 K and 298 K, S° os AH and T as well as spectroscopic informa298 m m

tion needed for statistical mechanical computation of thermodynamic

properties are listed. The sources of data are listed and briefly

discussed. A lengthy introduction discusses sources, methods of treatment,

and methods of application of the tables.

21. Stull, D. R., and Sinke, G. H.

Thermodynamic Properties of the Elements

Advances in Chemistry Series, Number 18

(American Chemical Society, Washington, D. C., 1956)

Tabulated values of Cp°, H° - H° S°, -(G° - H° )/T, AHf ° , 2Gf°,

Zy O Zy O and log Kf are given for the solid, liquid, and gas states of the first

92 elements over the temperature range 298 to 3000 K. Also given, where
94

available, are H° Q - H®, temperatures of phase changes and the associated

zy o o enthalpy changes, and critical constants. The source data for each element

are cited and briefly discussed. While now 15 years old, this book is

still the most convenient reference for high temperature properties of

some of the heavier elements.

22. Stull, D. R., Westrum, E. F., and Sinke, G. H.

The Chemical Thermodynamics of Organic Compounds

(John Wiley and Sons, Inc., New York, London, Sydney, Toronto, 1969)

This monograph is divided into three parts. The first part gives

theoretical basis and principles of thermodynamics and thermochemistry,

some experimental and computational methods used, and some applications

to industrial problems. The second part gives thermal and thermo chemical

properties in the ideal gas state from 298 to 1000 K. In this section,

the sources of data are listed and discussed and standardized tables are

presented for 918 organic compounds. Values of Cp° , S°, -(G - H° C )/T,

zy o H° - AHf ° , AHf ° , AGf°, and log Kp are given at 100 K intervals.

In the third section are listed selected values of enthalpy of formation,

entropy, and consistent values of AGf° and log Kp of organic compounds

at 298 K. In excess of 4000 compounds are listed. A very few inorganic

compounds are also found in this book. A chapter very briefly discusses

methods of estimating thermodynamic quantities.
95

23. Touloukian, Y. S.

Retrieval Guide to Thermo phys ical Properties Research Literature

(McGraw Hill Book Co . , New York, 1960- )

These volumes, which are a continuing series, contain thoroughly

cross-indexed references to the source literature for bulk transport

and thermodynamic properties. The properties first covered are:

thermal conductivity, specific heat, viscosity, thermal radiative

properties, thermal diffusivity, diffusivity, diffusion coefficient,

and Prandtl number. A limited but continually increasing number of

data sheets are available on materials and pure substances, giving

charts and tabulated values based on a critical evaluation, analysis,

and correlation of existing data. These are separately supplied by

the Thermophysical Properties Research Center (Purdue University) on

a subscription basis. These comprise the Data Book: Volume I,

Metallic Elements and Their Alloys; Vol. II, Non-metallic Elements,

Compounds, and Mixtures (in Liquid and Gaseous States at Normal

Temperature and Pressure); and Vol. III. Non-metallic Elements,

Compounds, and Mixtures (in the Solid State at Normal Temperature

and Pressure)

.

24. Wagman, D. D., Evans, W. H., Parker, V. B., and (in various individual

parts) Halow, I., Bailey, S. M., Schumm, R. H., Churney, K. L.

Selected Values of Chemical Thermodynamic Properties

National Bureau of Standards Technical Note 270, October 1965

(and continuing)

(U. S. Government Printing Office, Washington, D. C. 20402)
96

This technical note is a revision of NBS Circular 500 Part I (see

above) and is issued in parts as segments of the work relating to selected

sequences of elements are completed. The following parts had been issued

as of 1971.

270-1 Tables for the first twnety- three elements in the standard

order of arrangement

270-2 Tables for elements 24-32 — elements in the standard order

of arrangement

270-3 Tables for the first thirty-four elements in the standard

order of arrangement

270-4 Tables for elements 35-53 in the standard order of arrangement

270-5 Tables for elements 54-61 in the standard order of arrangement

270-6 Tables for the alkaline earth elements, elements 92-97 in

the standard order of arrangement.

The remaining elements will be covered in two or three additional parts to

appear over a period of about two years. Documentation and references have

not yet been issued.

This is the most comprehensive recent compilation in English of critically evaluated thermo chemical data at 298.15 K for inorganic substances.

All inorganic substances and organic substances containing two carbon atoms

or fewer per molecule are include if thermodynamic data exist for calculating any of the properties tabulated. The coverage when complete will

be approximately 12,000 substances. Properties tabulated are AHf° AHf° _, 0 2. 7 0

AGf°

9g , ^298 15

" H

o

s ^298 5 ^993 15

* T^ e ^ata f rom original sources have

been ciritically evaluated by competent thermo chemis ts and best values

selected for the functions tabulated, maintaining internal consistency by

the relationships AGf°

9g = ZHf°

9g - TAS°

9g , and AHf°

9g = Mf

= Z (H° 9g - H°)
97

25. Watt, B. K. and Merrill, A. L. (see Merrill, A. L. and Watt, B. K.,

source 12)

.

26. Wicks, C. E., and Block, F. E.

Thermodynamic Properties of 65 Elements - Their Oxides, Halides,

Carbides, and Nitrides

Bureau of Mines Bulletin 605, (1963)

.

(U . S. Government Printing Office, Washington, D. C.)

Part I of this monograph is a seven page introduction to the application of thermodynamic functions, with particular reference to metallurgical process. Part II gives tabular data and graphs of enthalpy, enthalpy

of formation, and Gibbs energy, for the substances listed in the title.

Also listed are T , /Ti , T, , ZH , and analytic expressions for Cp

,

298 m m b v

r

H - H , and G - H Q

. The units are the calorie, the mole, and the

1 Zy o 1 Zy o kelvin. References to sources of information are given. The sources

included original sources, reviews by other groups, and estimates. The

data are, therefore, of very non-uniform reliability.

27. Wilhoit, R. C., and Zwolinski, B. J.

Handbook on Vapor Pressures and Heats of Vaporization

of Hydrocarbons and Related Compounds (API 44 - TRC)

(Thermodynamics Research Center, Texas A and M Research Foundation,

College Station, Texas, 1971)
98

This handbook gives subject data on 680 hydrocarbons, 95 sulfur

compounds, and water from 0 to 150°C. It is indexed by compound name,

and by boiling point.

28. Zemansky, M. W.

Heat and Thermodynamics, 5th edition

(McGraw Hill Book Company, New York, Etc., 1968)

This well known textbook provides a clear pedagogical presentation

of the principal subjects of thermodynamics.
99

23 . 0 Methods of Estimation of Thermodynamic Data

Because of the essentially unlimited number of possible organic compounds, and the very large number of inorganic compounds, the probability

of encountering a substance or material for which the thermodynamic properties have not been measured is quite large. Methods of estimation

are, therefore, essential to supplement tabulated values of thermodynamic

properties based on experimental studies. Some guides to the more commonly used methods are listed below. This is by no means a complete

list, as there have been some hundreds of studies of methods of correlation or estimation.

1. American Society for Testing and Materials

Estimation of Net Heat of Combustion of Aviation Fuels

ASTM Method of Test D-l405

ASTM Standards, Part IT, Petroleum Products

(American Society for Testing and Materials, Philadelphia, Penn;

annual

)

This method of test allows an estimate accurate to about 0.5 percent

to be made of net heat of combustion of petroleum fuels having well defined characteristics. Fuels included are certain classes of aviation

gasoline, jet engine fuels and kerosines. The required measurements are

aniline point and API gravity, which are routine laboratory tests applied

to most batches of petroleum products. The estimates have reduced validity if applied to fuels not meeting the specifications for which the

method was developed. The experimental studies and the correlations

were performed at the National Bureau of Standards.
100

2. American Society for Testing and Materials

(1) Proposed Method for Estimation of Net and Gross Heat of

Combustion of Burner and Diesel Fuels

ASTM Standards, Part IT, Petroleum Products, January 19&9,

Appendix XI , D-2-19&8

(2) Proposed Method of Test for Estimation of Net Heat of

Combustion of Distillate and Residual Fuels

ASTM Standards on Petroleum Products, December 1962, Vol. I,

Appendix XII, D-2-19&2, pp. 12^7-1299.

(American Society for Testing and Materials, Philadelphia, Penna)

These tables, relating net and gross heat of combustion to API gravity of

diesel and burner fuels and distilled and residual fuels were published

for information by ASTM Committee D-2 on Petroleum Products and Lubricants, but failed of acceptance as a standard method of test. The deviations of individual actual fuels from the correlation and the disagreement

between these two sets of tables occurs principally in the very low APIgravity range. The estimate of net heat of combustion may still be

expected to be valid to within a few percent. It Is necessary to measure

API gravity in order to use this method for a particular batch of fuel.

3. Benson, S. W.

Thermochemical Kinetics

Methods for the Estimation of Thermochemical Data and Rate Parameters

(John Wiley and Sons, Inc., New York, London, Sydney, 1968)

This monograph gives tables of necessary data and descriptions of methods

of their use for calculating AHf, Cp, and S, at 25°C for gas phase mole-
101

cules and. radicals and for extrapolating them to higher temperatures. The

procedures can be applied to hydrocarbons, oxygen-containing compounds,

nitrogen-containing compounds , haloalkanes , organo-sulfur compounds , and

organo-metallic compounds; and deal principally with organic compounds.

U. Benson, S. W. , Cruickshank, F. R., Golden, D. M. , Haugen, G. R.,

O'Neal, H. E. , Rogers, A. S., Shaw, R., and Walsh, R.

Additivity rules for the estimation of thermochemical properties

.

Chem. Rev. 69 , 279-32U (1969)

This lengthy technical article gives procedures for calculating the properties AHf0

, S° , Cp° , for organic compounds in the gas phase. Parameters

for calculating Cp are given for temperatures from 300 to 1500 K at intervals. The availability of Cp at T allows calculation of AHf° and S° at

the same temperatures. The necessary constants for making the calculations

are given for individual chemical groupings in some 38 tables. Many

classes of functional groups and molecular conformations are included.

Examples are given comparing calculated and observed values. Agreements

of 1 kcal mol ^ or less in AHf° and 1 cal mol ^ K or less in Cp° and S°

are generally found.

5. Bondi, A.

Physical Properties of Molecular Crystals, Liquids, and Glasses

(John Wiley and Sons, Inc., New York, London, Sydney, 1968)

This monograph is designed for the use of chemical engineers to estimate

physical properties needed in design calculations, as well as of physical

chemists and synthetic chemists who need to understand the relationship

between structure and physical properties. Correlations of several kinds
102

are described in the text. These are then restated as methods for estimation of the properties.

Substances considered include non-polar and polar gases , non-polar and

polar liquids, associated liquids, crystalline solids, glasses, polymers,

and polymer melts, as well as others. Procedures given include many

variants, depending upon the properties given as initial information.

Among the properties for which procedures are given are: density, heat

capacity, enthalpy, entropy, enthalpy and entropy of fusion, enthalpy of

sublimation and vapor pressure, cubical thermal expansion coefficient,

bulk modulus, Young r s modulus, compressibility, thermal conductivity,

rotational diffusion constant, relaxation times, mass diffusion, viscosity, and others.

6. Cox, J. D., and Pilcher, G.

Thermochemistry of Organic and Organometallic Compounds

(Academic Press, London, New York, 1970)

In this monograph, Chapter 7, "Sbme Theoretical Applications of

Thermochemical Data" , gives a discussion of the application of schemes

for calculating AHf (or equally well, AHo).

The group-contribution method of Benson and Buss is discussed and tables

of group contributions are given. The bond-energy schemes (by which

Ah (atomization) and hence AHf or AHc can be calculated) developed by

Laidler, and by Allen, are discussed and tables of contributing terms

are given. Other schemes developed by Tatevskii, Platt, GreenshieldsRossini, and Somayajuiu-Zwolinski , are briefly described. Special factors affecting these methods are discussed and Illustrated including
103

steric effects, ring strain, and resonance. The accuracy of the estimates is discussed and examples of the use of the methods are given.

7. Janz, G. J.

Thermodynamic Properties of Organic Compounds

Estimation methods, principles and practice (revised edition)

(Academic Press, Inc., New York, London, 1967

)

This well established monograph discusses computation of thermodynamic

properties such as heat capacities, entropies, enthalpies and Gibbs energies by statistical mechanical methods , by methods of structural similarity, by methods of group contributions, by methods of group equations,

and by methods of generalized vibrational assignments. The chemical

properties: enthalpy of formation, and enthalpy of combustion are treated

in terms of bond energies and group increments. Some j8 tables are given

of increments, group contributions, and bond contributions as specifically

needed for estimation of particular properties.

8. Joshi, R. M. , and Zwolinski, B. J.

Vinyl Polymerization, Volume 1, Part I, edited by G. E. Ihm

(Marcel Dekker, Inc., New York, 1967 )

Chapter 8: Heats of Polymerization and their Structural and

Mechanistic Implications

The application of various semi-empirical bond-energy schemes to the calculation of heats of polymerization are discussed.

9. Kubaschewskl , 0., Evans, E. LI., and Alcock, C. B.

Metallurgical Thermochemistry, Uth edition

(Pergamon Press, Oxford, New York, and other cities, 19&7 )
104

This hook contains a chapter of 35 pages on estimation of thermochemical

data. Methods are given for calculation of heat capacities (Cp ) of

gases, solids, and liquids, and constants are given for estimating ACp

for some reactions involving gases. Estimation of entropies and enthalpies of evaporation and fusion is briefly treated. Tables and charts are

given for estimating entropies of solids and gases. Charts are given

illustrating regularities in enthalpies of formation of compounds, and

special attention is given to estimating enthalpies of formation of

inter-metallic compounds and sulfides, selenides, and tellurides.

10. Mason, D. M. , and Eakin, B. E.

Calculation of Heating Value and Specific Gravity of Fuel Gases

Institute of Gas Technology Research Bulletin 32 , (1961), 18 pp.

(institute of Gas Technology, Chicago, Illinois)

This pamphlet gives procedures for calculating heating value and specific

gravity of a gaseous fuel from an analysis of its component substances.

It is applicable to commercial fuel gases. Compressibility factors are

taken into account. The heating value calculation has errors less than

1%.

11. Pauling, L.

The Nature of the Chemical Bond, 3rd edition

(Cornell University Press, Ithaca, New York, i960)

This well established monograph provides general information about the

nature of chemical binding In (principally) inorganic compounds which is

fundamentally very important for the estimation of enthalpies of formation, but not always easily applied.
105

12. Pitzer, K. S. , and Brewer, L.

Thermodynamics: Gilbert N. Lewis and Merle Randall, 2nd edition

(McGraw Kill Book Co., New York, etc., 1961 )

Chapter 32 of this book describes methods for estimating entropies and

other thermodynamic properties. The emphasis is on entropy, but energies of inorganic substances are also briefly treated showing the use

of a Born- Haber cycle. Ad hoc procedures are suggested for estimating

enthalpies of formation of inorganic compounds for which data are not

available

.

13. Reid, Robert C., and Sherwood, T. K.

The Properties of Gases and Liquids, their Estimation and

Correlation, 2nd edition.

(McGraw Hill Book Co., New York, etc., 1966 )

This lengthy monograph follows the procedure of discussing various methods

available for calculating or estimating particular properties of particular materials, and then provides recommendations for action with respect

to each kind of property. Included in the book are procedures for making

estimates of critical constants, normal boiling temperatures, LennardJones-potential parameters, compressibility factors and equations of

state, liquid molal volumes and densities, and vapor pressures. Estimates

of enthalpies of vaporization, and of ideal-gas heat capacities, enthalpies and Gibbs energies of formation are treated. For real fluids variations of enthalpy, entropy, internal energy, and heat capacity with

pressure are treated. Some methods are given for estimating the properties of fluid mixtures. Surface tension and the transport properties
106

—viscosity, diffusion coefficient and thermal conductivity—are discussed. Numerous tables present comparisons of observed and calculated

properties

.

lU . Schafer, K., and Lax, E. (editors }

Landolt-Bornstein

Eigenschaften der Materie in Ihren Aggregatzustanden

b Teil. Kalorische Zustandgrossen, pp. 18-32

( Sprlnger-Verlag , Berlin, Gottingen, Heidelberg, 196l )

Extensive tables are given of group contributions to enthalpy of formation

and Gibbs energy of formation of organic substances (gases ) in kcal mol ^

and kJ mol \ They form a suitable basis for estimating properties of

gases

.

15. Tatevskii, V. M., Benderskii, V. A., and Yarovoi, S. S.

Rules and Methods for Calculating the Physico-chemical Properties

of Paraffinic Hydrocarbons

(Translated from the Russian by M. F. Mullins and edited by B. P.

Mullins )

(Pergamon Press, New York, Oxford, London, Paris, 1961

)

This monograph is a summary and a consolidation of the results of some

years of work by Tatevskii and others, extending and elaborating some

procedures introduced by Rossini and others. It suffers from ambiguity

of statement which is somewhat distracting, but the methods presented in

it have been attracting increasing attention recently. Properties calculated include: molar volume, molar refraction, vapor pressure, enthalpy

of formation from atoms or elements, Gibbs energy of formation, and
enthalpy of combustion. Three different methods are used. Tables of

constants and illustrations of the accuracy of the methods are given.
108

24.0 Selected References on Combustion and High

Temperature Reaction Equilibria

1. Bahn, Gilbert S., and Zukoski, Edward S., editors

Kinetics, Equilibria, and Performance of High Temperature Systems.

(Proceedings of the First Conference, 2-5 Nov. , 1959)

(Butterworths , Washington, D. C., 1960)

This conference proceedings is directed primarily to rocket propulsion systems and to chemical and phsycial processes occurring in

propulsion systems. There are several papers describing procedures

for calculating equilibria and temperatures of complex reacting systems.

Several of these use digital computer programs which are described.

See also proceedings of the second conference by the same title.

2. Berenblut, I. I., and Downes, A. B.

Tables for Petroleum Gas - Oxygen Flames: Combustion Products and

Thermodynamic Properties.

(Oxford Press, New York and Oxford, 1960).

3. Bradley, J. N.

Flame and Combustion Phenomena

(Menthuen, Barnes & Noble, New York, 1969) .

4.

Combustion (Serial)

(Combustion Publishing Co., Inc. New York, N. Y.)
109

5.

Combustion and Flame (The Journal of the Combustion Institute)

(Butterworths , London, 1957- )

This journal publishes experimental and theoretical investigations

dealing with combustion, detonation, and explosion, including such topics

as: combustion in practical systems, fires, fluid dynamics, heat transfer and radiation; heterogeneous combustion; ignition; instability; mechanisms and kinetics; phase changes; thermal decomposition; thermochemistry

and thermodynamics; and other topics.

6. Combustion Science and Technology (Serial)

(Gordon and Breach, London, 1959- )

.

7. Corey, Richard C.

Principles and Practice of Incineration

(John Wiley and Sons, New York, N. Y., 1969).

8. Ducarme, J., Gerstein, M. , and LeFebre, A. H. , editors (Serial)

Progress in Combustion Science and Technology

(Pergamon Press, New York, 1961- ).

9. Fleming, Donald K.

Aero thermo chemis try

(First Biennial Gas Dynamics Symposium, 1956)

(Northwestern University Press, Evanston, 111.).

10.

Fristrom, R. M. and Westenberg, A. A.

Flame Structure

(McGraw-Hill Book Co., Inc., New York, N.Y., 1965).
110

11. Gaydon, A. G., and Wolfhard, H. G.

Flames, Their Structure, Radiation and Temperature

(Chapman and Hall, Ltd., Londor\ 1970).

12. Hougen, Olaf A., Watson, Kenneth M. , and Ragatz, Roland R.

Chemical Process Principles, Part II Thermodynamics

(John Wiley and Sons, Inc., New York, N.Y.; Chapman & Hall,

Ltd, London, 2nd ed. 1959)

.

Chapter 25, "Chemical Equilibrium Constants, Chapter 26, "Equilibria

in Chemical Reactions," and Chapter 27, "Equilibria in Complex Reactions",

are of particular relevance to the determination of temperatures and

products of combustion resulting from combustion processes. Charts and

illustrative problems are given.

13. Jost, Wilhelm (H. 0. Croft, translator)

Explosion and Combustion Processes in Gases

(McGraw-Hill Book Co., Inc., New York, N.Y., 1946).

14. Lewis, B., Pease, R. N., and Taylor, H. S. (editors)

Combustion Processes

(High Speed Aerodynamics and Jet Propulsion, Volume 2)

(Princeton University Press, Princeton, N. J., 1956)

In this large volume there are numerous chapters on the combustion

of solids, liquids, and gases, the kinetics of combustion reactions

and on detonation process by various authors. Chapter A by Carter and

Altman discusses reaction equilibrium and the temperatures obtained by

the combustion energy. Chapter C by S. R. Brinkley, Jr., discusses

computational methods for complex reacting systems.
Ill

15. Lewis, Bernard, and Von Elbe, G.

Combustion, Flames and Explosions of Gases, 2nd ed

.

(Academic Press, New York, N. Y., 1961)

16. Minkoff, G. J. and Tippen, C.F.H.

Chemistry of Combustion Reactions

(Butterworths , London, 1962).

17. Mullins, B. P.

Combustion Researches and Reviews, 1955

(Pergamon Press, New York, 1955)

18. Mullins, B.P., and Fabri, J.

Combustion Researches and Reviews, 1957

(Pergamon Press, New York, N.Y., 1957)

19. Mullins, B. P., and Penner, S. S.

Explosions, Detonations, Flammability and Ignition

(Pergamon Press, New York, N.Y., 1962)

20. Penner, S. S.

Chemistry Problems in Jet Propulsion

(Pergamon Press, New York, N.Y., 1958)

21. Penner, S. S.

Chemical Rocket Propulsion and Combustion Research

(Gordon and Breach, New York, London, 1962)
112

22. Penner, S. S., and Ducarme, J.

Combustion and Propulsion Researches and Reviews, 1959

The Chemistry of Propellants

(Pergamon Press, New York, 1960)

23. Pugh, Brinley

Fuel Calorimetry

(Plenum Press, New York, N. Y., 1966)

24. Smith, Marion L., and Stinson, K. W.

Fuels and Combustion

(McGraw-Hill Book Company, New York, N. Y., 1952)

25. Spalding, D. B.

Some Fundamentals of Combustion

(Academic Press, Inc., New York, N.Y., 1955)

26. Starkman, Ernest S. (editor)

Combustion Generated Air Pollution

(Plenum Press, New York, London, 1971)

27. Strehlow, Roger A.

Fundamentals of Combustion

(International Textbook Company, Scranton, Pa., 1968)

28. Surugue, J. N.

Experimental Methods in Combustion Research

(Pergamon Press, New York, N.Y., 1960).
29.

113

Symposium (international) on Combustion

1st - 1928 to 12th - 1969

(The Combustion Institute, Pittsburgh, Pa.)

30. Thring, M. W.

Selected Combustion Problems

(Pergamon Press, New York, N.Y.)

31. Thring, M. W.

The Science of Flames and Furnaces

(John Wiley & Sons, Inc., New York, 1952)

32. Thring, M. W., Fabri, J., Lutz, 0., and Lefebre, A. H.

Combustion and Propulsion - Third AGARD Colloquium

(Pergamon Press, New York, N.Y., 1958)

33. Vulvis , L. A. (M. D. Friedman, translator)

Thermal Regimes of Combustion

(McGraw-Hill Book Co., Inc., New York, N.Y., 1961)

34. White, W. B., Johnson, S. M., and Dantzig, G. B.

Chemical Equilibrium in Complex Mixtures

J. Chem. Phys. 28, 751-755 (1958).

35. Wilkins, R. L.

Theoretical Evaluation of Chemical Propellants

(Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963).
114

36. Williams, Forman A.

Combustion Theory: The Fundamental Theory of Chemically

Reacting Flow Systems

(Addison-Wesley Publishing Co., Inc., Reading, Mass., Palo

Alto, Calif., London, 1965).

This is "an advanced graduate text or reference for workers in the

field of combustion." Some sections deal specifically with processes

occurring in rocket motors, but most of the text is so generally oriented

that it is applicable to combustion problems in other areas. The titles

of major sections are: Summary of basic fluid dynamics and chemical

kinetics; Rankine-Hugoniot relations; Diffusion flames and droplet burning;

Reactions in nozzle flow and in sound waves; Laminar flame theory; Gaseous

detonations; Turbulent flames; Ignition, quenching, and flammability limits

Solid propellant deflagration; Combustion instability in solid and liquid

propellant rockets; Monopropellant droplet burning; Spray combustion;

Chemical reactions in boundary layers; Appendix A. Summary of applicable

results of thermodynamics and statistical mechanics; Appendix B. Review

of chemical kinetics; Appendix C. Continuum derivation of the conservation

equations; Appendix D. Molecular derivation of the continuum equations;

Appendix E. Transport properties.

37. Wolfhard, H. G., Classman, I., and Green, L., Jr. (editors)

Heterogeneous Combustion

(Progress in Astronautics and Aeronautics, Vol. 15)

(Academic Press, Inc., New York, N.Y., 1965).
115

38. Zabetakis, M. G.

Flammability Characteristics of Combustible Gases and Vapors

(Bureau of Mines Bulletin 627, 1965).

39. Zeleznik, F. J., and Gordon, S.

A General IBM 704 or 7090 Computer Program for Computation

of Chemical Equilibrium Compositions, Rocket Performance,

and Chapman-Jouguet Detonations

NASA TN D-1454 (October 1962)

.

See also NASA TN D-132 (October, 1959)

and NASA TN D-1737 (October, 1963).
116

25.0 Tables of Thermodynamic Data

25.1 Description of the Tables

Table I-A Enthalpies of Formation of Some Organic Compounds

and Inorganic Carbon Compounds at 298.15 K.

Content . Table I-A is a list of about 1000 carbon compounds

(989 compounds, some differing in physical state or stereochemical

configuration gave a total of 1093 entries) in which the information

given in columns, left to right, is: molecular formula, formula

weight, name (physical state), enthalpy (heat) of formation in kcal

mol \ enthalpy (heat) of formation in kJ mol ^

, references for

enthalpy data.

Formula format . A molecular formula (for substances consisting

of discrete molecules) is given in which the elements are listed in a

partially alphabetical order with the numbers of atoms as subscripts.

Carbon is always the first element. Hydrogen, if present, is always

the second element. The remaining elements follow in the alphabetical

order of their chemical symbols. Empirical formulas are given for

ionic solids.

Arrangement of compounds . The formulas are listed in alphabetical

order following the arrangement of the Chemical Abstracts Formula Index

(Hill arrangement, E. A. Hill, J. Am. Chem. Soc. _22, 478-494 (1900)).

The compounds are also in numerical order of the number of atoms per

molecule. Beginning with the element on the left, the lowest subscripts

are listed first and increase to higher numbers only when all elements
117

to the right have been listed from the lowest to the highest number.

Thus, all compounds with are listed before any with C^; all compounds

with C^A^ before any x^ith C^A^, and so on. The arrangement is illustrated

in figure 25.1.

C

1

A

1

C

1

A

1

B

1

C

1 A2

Figure 25.1

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1

A

2

B

1

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2 ClVl

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c

i

z i

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1

Z

2

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2

A

1

Compound name (and physical state). A well known name for each

compound is given to make a positive identification of the substance

and remove any ambiguity resulting from the possibility of several

isomeric forms having the same composition and molecular weight. The

physical state of the compound is listed: gas (g) , Liquid (liq), or

crystal (c)

.
118

Enthalpy of formation . (Sometimes called heat of formation) . The

enthalpy of formation of the compound from the elements is given in two

columns, respectively in kilocalories per mole and in kilojoules per

mole. In the table of data the uncertainties are not given explicitly.

The values in general are accurate to between one and 10 parts in the

last figure given. A negative enthalpy of formation means the reaction

of formation from the elements is exothermic.

Reference . The values of enthalpies of formation were taken from

a few collections of carefully evaluated data and represent the best

current appraisal of the available experimental data. The source

references are listed at the end of the table.

Table I-B Compound Name-Formula Index (of Carbon Compounds)

Content . Table I-B is a name-formula index of all the compounds

in Table I-A arranged alphabetically in order of the name. For some

compounds, an alternative name is listed with a cross reference to the

name found in Table I-A.

Use of Table I - To find the enthalpy (heat) of formation of a compound .

Write the molecular formula of the compound in the format given in paragraph 2 above, and then look for the formula in Table I-A following the

arrangement listed in paragraph 3 above. Some formulas represent more

than one substance. Distinguish between them by the name and physical

s tate

.

If the formula is not known, look up the name in the alphabetical

listing in Table I-B to find the formula, and then proceed as before.

Failure to find the name in the alphabetical listing does not mean for
119

sure that the compound is not listed, as it has been impossible to list

all the names that may be used for the compounds. In event the compound

is not found in the alphabetical name index, look for alternate names,

or determine the formula and proceed as above.

Table II - Enthalpies of Formation of Organic Polymers at 298.15 K .

Conten t . Table II is a list of 39 organic polymers, in which the information given in columns, left to right is: chemical formula of the

repeating unit, formula weight of the repeating unit, name (and physical

state), enthalpy (heat) of formation in kcal mol \ enthalpy (heat) of

formation in kJ mol \ references for enthalpy data.

Formula format . Same as Table I-A.

Arrangement of Compounds . Same as Table I-A.

Compound name, (and physical state) . A name based on the monomer

is frequently given. A few common names and trade names are used.

Enthalpy (heat) of formation . The value cited represents the

enthalpy of formation of the repeating unit from the elements.

Uncertainties are not explicitly given. The values, in general, are

accurate to between one and ten parts in the last figure given.

Reference . The original source of the heat of combustion data

is given. A list of references is found at the end of the table.

Table III - Enthalpies of Formation of Inorganic Oxides at 298.15 K .

Content . Table III is a list of 285 inorganic oxides, in which

the information given in columns, left to right is: empirical or

molecular formula (and physical state), formula weight, name, enthalpy
120

(heat) of formation in kcal mol \ enthalpy (heat) of formation in

kJ mol \ reference for enthalpy data.

Formula format . Solids forming continuous covalent or ionic

lattices have the empirical formula given. Gases, liquids, or solids

having molecules (as for instance As^O^(c)) are represented as the

molecular formula. Oxygen is listed last in the formula. The state:

gas (g) s liquid (liq), or solid (c) is listed in parenthesis following

the formula. When more than one crystal form is known, the crystal

form is listed. Non-crystalline solids are listed as amorphous

(amorph)

.

Arrangement of compounds . The formulas are listed in alphabetical

order of the symbol of the first element and in order of increasing

numbers of atoms of each element in the formula. Phases of the same

compound are listed in the order (g) , (liq), (c) .

Compound name . A descriptive chemical name is given. In a few

cases a common synonym or a mineral name is given.

Enthalpy of formation . (Sometimes called heat of formation).

The enthalpy of formation from the elements is given in two columns,

respectively in kilocalories per mole, and kilojoules per mole. In

the table the uncertainties are not given explicitly. The values in

general are accurate to between one and ten parts in the last figure

given. A negative enthalpy of formation means the reaction of formation

from the elements is exothermic.
121

Reference . Numerical references refer to the source of the data

in the list of references at the end of the table. All data were taken

from reliable collections of carefully evaluated data and represent the

best current appraisal of the available experimental data.
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N

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1 64

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Z“B

C0MP0UND

NAME-F0

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1 65

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I—B

COMPOUND

NAME-FORMULA

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| 66

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X

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TABLE

I-B

COMPOUND

NAME-P0RMULA

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1 67

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e. Q

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COMPOUND

NAME-FORMULA

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168

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TABLE

I-B

COMPOUND

NAME-FORMULA

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1 69

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TABLE

I-B

C3MPHUND

NAMF.-F0

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1 70

0

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thyl

heptane

-Me

thylhexane
TABLE

I-B

CtfMPtfUND

NAME-FORMULA

INDEX

1 7 1

(\j cvj a ^ ^ T) C/5 OJ OJ <* z 2 2 2

vO CO vO*-^ 0s ®* a: k a ns &

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thylthlophene

Methyl

tridecylate
TABLE

I-B

COMPOUND

NAME-FORMULA

INDEX

1 72

©

c

asa

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S~B

COMPOUND

NAME-FORMULA

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1 73

9)er

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o <t cm a cmc m

roc >. O C Z © n N

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I

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CtfWPtfUND

N

A

MEFtf

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I 74

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TABLE

t-B

COMPOUND

MA.ME-F0

KMULA

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1 75

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n © 8

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I-B

COMPOUND

NAME-Pfl

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176 I

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TABLE

i-B

COMPOUND

NAME-FORMULA

INDEX

1 77

g -O' <

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acid
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I-B

COMPOUND

NAMP-FflRMULA

INDEX

n

i

pi

<t Kl O

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T-B

COMPOUND

NAME-FORMULA

INDEX

1 79

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COMPOUND

NAME-FORMULA

INDEX

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1

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rvj C

a. cm n

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c

ev

X

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co cm inz c cm z ^ cm o ro or

co ft- o ~ ~ ~ ~ — — cm cm c\j z Cvj cm n

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n

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ip in m in in ® h — — rn 0 UOOUUUUUUO IP

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fa «-* - <* X O Z CO Z O

m m n o —

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u o u u u u

in r

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c c

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x x in u u u

c

in cs

1 r <* or c

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bs a » 0 a 9 d *0 c c d d C « G 9 4- X IT e o ® 9 C >» d d "4 « o •ad 4» d

4«* 0 H 9 £ f-» C 0 9 0 r *0 d d fa •o •H XJ 9 d 9 fj

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a 6 E a a i i fa >» G C 0 E c d d o d 0 > d >. X >> •0 0 >» >* •H >* >» X X 8 0 y u u

ro *. •«< r* ~d "at H H P D *0 d p 0 9 9 9 -si > crm* 1 > p»> w «=i p-> fa fa c c > c a X X X O G c c c

a (. fa fa fa fa fa 8 a 8 8 C fa 1 fa fa fa fa fa 9 d J 1 d c d d 0 9 »a4 1 »*d d 8 8 1 X 1 «=i C=t CM H H b b H H P hJ G -* P P — p P P P p C > o > > > > > > > > CM > X e 0 a X 9 N N M

R

I

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R
25.4

Table

II.

Enthalpies

of

Formation

of

Organic

Polymers

at

298.15

K

181

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1 1 i G i G 1—1 G G G 1 1 CO CO cn CO G CO in

ft -H cn G r—

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O -G oo 1——1 i o Ih O Fh PC i 2 i o i i 1 O o o o o 1 o o 4-4 cd •

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pff CO , qj r**5 CM CM PC PC PC CM CM o PC pg PC pa PC pa pa pa PC pa pa

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Enthalpies

of

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of

Organic

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at

298.15 K

(Cont'd)

182

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a

aO Po 3 3 3 3 1—

rH CD a) *h 3 3 a J3 •H 3 •H 3 •H rH

CO 0) rH

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3 3 03 •u 3 3 3 3 rH >>» 3 3 0 0) O CD r-H 3 3 | 3 3 3 3 3 3 3 M3 0 0 3 3 3 3 3 M3 CO a rH N rH N X 4-J

>-) 0 4-) to 4-) Jo Po *V 0 1 3 3 3 3 3 XI

4-3 3 •H 4-) co 4-1 4J CM rH

a rH 3 rH 0) #v •H

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X 3 4h

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ft 4J co CD GO 00 00 00 r—

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O CO oc 30 30 33 33 33 33 33 33 33 33

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4-4 CL) CD CD CD 00 00 00 co CO CD CD CD r—

3.u CJ 0 <j

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u

u

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0) 1 1 1 1 1 1 1 1 1 1 1 1 L__J 1 1—1 1 1 3—4 I.. 4 1 1 1 1

[-C1

qHj

4°7“ln

246.2189

Cellulose

diacetate

(s)

-326.

-1364.

[18] [— Ci

h8— 3n

152.1976

Polyacenaphthylene

(s)

+27.13

+113.51

[6]

[-Ci2Hi60e-]n

288.2565

Cellulose

triacetate

(s)

-377.

-1577.

[18]

[-C16H14O3-]

254.2882

Poly

(4, 4

'-dioxydipheny

1-2,

2-propanen

carbonate)

(s)

-103.26

-432.04

[6]
183

References

[1] Good, W. D,, Lacina, J. L., and McCullough, J. P., J. Am. Chem.

Soc. _82 , 5589-3591 (1960).

[2] Parks, G. S „ , and Mosher, H. P., J. Polymer Sci. (Part A) 1 , 1979-1984 (1963).

[3] Sinke, G. C., and Stull, D. R. , J. Phys . Chem. 62^ 397-401 (1958)

[4] Good, W. D., Lacina, J. L., DePrater, B. L., and McCullough, J. P.,

J. Phys. Chem. 68> 579-586 (1964).

[5] Domalski, E. S., and Armstrong, G. T., J. Research NBS 71A , 105-118

(1967) .

[6] Joshi, R. M., and Zwolinski, B. J., Macromolecules _1, 25-30 (1968).

[7] Kybett, B. D. , Johnson, G. K., Barker, C. K. , and Margrave, J. L.,

J. Phys. Chem. 69, 3603-3609 (1965).

[8] Breitenbach, J, W., Derkosch, J., and Wessely, F. , Monatsh. 83 , 591-598 (1952).

[9] Nelson, R. A., Jessup, R. S., and Roberts, D. E., J. Research

NBS 48, 275-280 (1952)

.

[10] Richardson, J. W., and Parks, G. S., J. Am. Chem. Soc. _61 , 3543-

3546 (1939).

[11] Parks, G. S., West, T. H., Naylor, B. F., Fujii, P. S., and

McClaine , L. A., J. Am. Chem. Soc. _68, 2524-2527 (1946).

[12] Ivin, K. J., Keith, W. A., and Mackle, H., Trans. Faraday Soc. 55 , 262-67 (1959).

[13] Jessup, R. S., and Prosen, E. J., J. Research NBS 4_4, 387-393 (1950).

[14] Estimated from data in reference [13].

[15] Emery, A. G., and Benedict, F. G., Am. J. Physiol. ^8, 301-307 (1911).

[16] Stohmann, F,, and Schmidt, R. , J. prakt. Chem. [2] _50, 385-387

(1894)

.

[17] Roberts, D. E., Walton, W. W., and Jessup, R. S., J. Polymer Sci.

2 , 420-431 (1947).
184

[18] Tavernier, P., and Lamouroux, M. , Mem. poudres _39, 335-356 (1957).

[19] Estimated from data in references [13] and [17].

[20] Evans, F. W., and Skinner, H. A., Trans. Faraday Soc. _55, 255-259

(1959)

.

[21] Good, W. D., private communication in reference [17].

[22] Desai, P. D., Ph.D. Dissertation, Texas A&M University, 1968.

[23] Jessup, R. S., and Cummings, A. D., J. Research NBS J.3, 357-369 (1934).

[24] Jessup, R. S., J. Research NBS 20, 589-597 (1938).
185

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Table

III.

Enthalpies

of

Formation

of

Inorganic

Oxides

at

298.15 K

(Cont'd)

187 • ,—, ,

4-1 1 1 1 1 1 1 1 1 l | 1—1 1 1 CM CM 1—1 1 1 1—-1

r 1 r—i 1—I I—1 3 CO CO X M3 co 5 1 rH CO CO cn CO CO CO

Pi b»»l 0

4-1 a OV

<3 T“ CM 0 00 o\ n m X CM 0 CM 00

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OV ov «—l

cn

mm 00 CTv

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4-1

4-1 VO 1—1 0 rH m 00 CO CT\ <t t

0 CO 0 r^. O CM Nt co

m CM 0 Ov 00

>N r—j | ex 3 3 1 X CM 00 1—l

vD 1—1 O 00 Ov

n vO vD

»H 0 O CN Ov CM CN

mm vO MD CM CM CM CO «H vO

nm E 1 1 I 1 rH l—1 1 CM 1 43 1 1 1 I 4-) 3w

CU

9\

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X 0 x 0 X X 0 x x 0 X CJ CJ CJ 0 CJ CJ CJ 1—1 X 0 co CO <fr 00 CM 00 00 X cd 1 O 0 X CM CTV CTv CTv Ov X CN! \—1 \ 1 n 1—1 1—1 CN! i 1 44 X 1 1 1—1 CO CO O'. rH CO n n UO 0 0 0 co 3 X O O 0 0 0 O 0 CO 5—1 CM <1- H" CTV OV OV CT\ g

Ml E

00 00 00

X CM 00 CM 00 t—1 CO

X CM CM

O 01 00 CNJ

X

X

n f^. CM CMn

X 00 00 CO OO 4H £ 1 1 i—1

CO 1—1 1 1

hexago- ) /^N 1—1 cr 3 cr ** cd —N

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a 00 V-4 '—r

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H -U 00

V—' v-—' CO ' O W CM CM CM CM 0 CM CO 0 0 0 CN! 0 0 O 0 0 0 CM 0 0 0 CM CM CM

O 0 0 OO 00 cd 3 X 3 3 rH »H 1—1 '—1 1—1 '

1 O

CJ CJX

XX

XXXX

X

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XXX

XXC

03 O4

(c)

240.7972

Cobalt

(11,111)

oxide

-213.

-891.

Cr

02

(c)

83.9948

Chromium

dioxide

-143.

-598.

CrO3

(g)

99.9942

Chromium

tioxide,

Chromic

anhydride

-92.2

-385.

"Chromic

acid"
188

1—1 (—1

r i 4-4 f 1 r—i

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d

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Table

III.

Enthalpies

of

Formation

of

Inorganic

Oxides

at

298.15 K

(Cont'd)

191

4-1 CM CM CM 1 1 1 1 i

i CM i—1 1 1 1 1 1 1 i i i 1 i—i i 1 i 1 i 1 i 1 <U i—1 <—1

T—1 1 1 X

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x 00 CN 00 rH coX o ON CN co co vO c X o i—i

rH ON

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m <1* <r CN ON CN CN co o

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monoclinic)

oxide,

Baddeleyite
200

References to Table III

[1] Robie, R. A., and Waldbaum, D. R., "Thermodynamic Properties of

Minerals and Related Substances at 298.15 K (25.0°C) and One

Atmosphere (1.013 Bars) Pressure and at Higher Temperatures,"

U. S. Department of Interior, Geological Survey Bulletin 1259,

(1968) .

[2] Rossini, F. C., Wagman, D. D,, Evans, W. H., Levine, S., and

Jaffe, I., "Selected Values of Chemical Thermodynamic Properties,"

NBS Circular 500, (Feb. 1952).

[3] Wagman, D. D., Evans, W. H. , Parker, V. B., Halow, I., Bailey,

S. M., and Schumm, R. H. , NBS Tech. Note 270-3, January 1968.

[4] Wagman, D. D., Evans, W. H. , Parker, V. B., Halow, I., Bailey,

S. M., and Schumm, R. H. , NBS Tech. Note 270-4, May 1969.

[5] Wagman, D. D., Evans, W. H., Parker, V. B., Halow, I., Bailey,

S. M., Churney, K. L., NBS Tech. Note 270-5, March 1971.

[6] Parker, V. B., Wagman, D. D. and Evans, W. H., NBS Tech. Note

270-6, November 1971.

[7] Stull, D. R. , and Prophet, H., et al., JANAF Thermo chemical

Tables, 2nd Edition, NSRDS-NBS-37 , 1141 pp . (June 1971), (U. S.

Government Printing Office, Washington, D. C. 20402).

[8] JANAF Thermo chemical Tables, Dow Chemical Company, Midland, Michigan,

Loose Leafe Supplementary Data Sheet, June 1971.

[9] Huber, E. J„, Jr., and Holley, C. E., Jr., J. Chem. Eng. Data 13,

545-546 (1968).

[10] Holley, C. E., Jr., Mulford, R. , Huber, E. J., Jr., Head, E. L.,

Ellinger, F. H., and Bjorklund, C. W., Proc. 2nd U.N. Internat.

Conf . on the Peaceful Uses of Atomic Energy 6^, 215-220 (1958), Geneva.

[11] Parker, V. B., NBS, private communication, August 1971.

[12] Schumm, R. H., NBS, private communication, August 1971.
201

26.0 Appendix

26.1 Symbols for Thermodynamic Quantities, (IUPAC) . (1) (2)

T thermodynamic temperature (absolute temperature)

t, e Celsius temperature

R molar gas constant

k Boltzmann constant

q> Q heat

w, W work

U, (E) internal energy

H enthalpy: H s U + pV

S entropy

A Helmholtz energy: A = U - TS

J Massieu function: J

= -A/T

G Gibbs energy: G = H - TS, (3) (see footnote (3), page 202 ) Y Planck function: Y

= -G/T

Z compressibility factor; Z = pV/nRT

C heat capacity

c specific heat capacity (heat capacity divided by mass)

Y ; 00 heat capacity ratio; Cp/Cv

P Joule-Thomson coefficient

\, k thermal conductivity

a thermal diffusivity: a = \/pCp

(1) Symbols adopted by the International Union of Pure and Applied

Chemistry (IUPAC), 1969.

(2) Symbols in parentheses are alternates, accepted but not recommended

by IUPAC. See Section 25.2 for other commonly used symbols and names

of quantities not accepted by IUPAC.
202

h

a

k

P

f> (P*)

n

i

a

f

Y

y

B

B

B

B

0

coefficient of heat transfer

cubic expansion coefficient: a - (6V/5T)^/V

isothermal compressibility: k = - (b V/d p) /V

pressure coefficient: p

s (6p/5T)^

chemical potential of substance B

absolute activity of substance B: \ = exp (pi /RT)

D D fugacity

osmotic pressure

2 2 ionic strength: I - b E.m.z. or I = b Z.c.z,

* l l l ill

activity^ relative activity of substance B

activity coefficient, mole fraction basis

activity coefficient, molality basis

activity coefficient, concentration basis

osmotic coefficient

(3) The Gibbs energy is frequently called free energy, Gibbs free

energy, or Gibbs function. The commonly encountered term

free energy in American work on thermodynamics almost invariably

refers to Gibbs energy. This usage of the term free energy and

the symbol F are being discouraged by the IUPAC because of confusion

with the Helmholtz energy and the common European usage of F for

the latter.

26.2 S elected Symbols for Other Quantities needed in Thermodynamics

( 1 ) (IUP AC) (see footnote (1), page 201)

A, S area

V volume

t time

m mass
density (mass divided by volume)

pressure

relative atomic mass (also called "atomic weight")

relative molecular mass (also called "molecular weight")

Avogadro constant

number of molecules

(v) amount of substance

y„ mole fraction of substance B: x„ = n /Z.n.

B B B 1 1 mass fraction of substance B

volume fraction of substance B

molality of solute substance B (amount of B divided

by the mass of solvent)

[B] concentration of substance B (amount of B divided by

the volume of the solution)

mass concentration of substance B (mass of B divided

by the volume of the solution)

stoichiometric coefficient of substance B (negative

for reactants, positive for products)

.

(The general equation for a chemical reaction is --

Z v_B - 0, [Example: for the reaction H„0 -> H„ + %0 o , D D Z Z Z H

2 + ^°2 " H

2 ° = 0]

extent of reaction: (drb

= dn. /v ) b B equilibrium constant

degree of dissociation

charge number of an ion B (positive for cations, negative

for anions)
204

2 6. 3 Units of Measurement - International System (SI)

SI - Base Units and Supplementary Units

quantity name of unit symbol

length metre m

mass kilogram kg

time second s

temperature kelvin K

electric current ampere A

luminous intensity candela cd

amount of substance mole mol

plane angle radian rad

solid angle steradian sr

Definitions of the SI Base Units

metre: The metre is the length equal to 1 650 763.73 wavelengths

in vacuum of the radiation corresponding to the transition

between the levels 2p^ Qand 5d of the krypton -86 atom.

kilogram: The kilogram is equal to the mass of the international

prototype of the kilogram.

second: The second is the duration of 9 192 631 770 periods of

the radiation corresponding to the transition between the

two hyperfine levels of the ground state of the cesium-133 at(
kelvin: The kelvin is the fraction 1/273.16 of the thermodynamic

temperature of the triple point of water. The kelvin is used

205

both for thermodynamic temperature and for thermodynamic

temperature interval.

ampere: The ampere is that constant current which, if maintained in

two straight parallel conductors of infinite length, of

negligible cross-section, and placed 1 metre apart in vacuum,

would produce between these conductors a force equal to 2xlC ^

newton per metre of length.

candela: The candela is the luminous intensity, in the perpendicular

direction, of a surface of 1/600 000 square metre of a black

body at the temperature of freezing platinum under a pressure

of 101 325 newtons per square metre.

mole: The mole is the amount of substance of a system which contains

as many elementary entities as there are carbon atoms in

0.012 kilogram of carbon-12.

Note

:

The elementary entities must be specified and may be atoms,

molecules, ions, electrons, other particles, or specified groups

of such particles.
206

26.5 Prefixes

SI Symbol Prefix name Multiplication factor

T tera io

12

G giga io

9

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6

k kilo io

3

h hecto io

+2

da deka 10

+1

d deci io

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c centi io

" 2

m mil li io

“ 3

M- micro io

' 6

n nano io

" 9

P pico io

" 12

f f emto io

' 15

a atto io

- 18
26.6

SI

Derived

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(partial

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d 3 co !4 CD U O o 3 O d 3 C •rH 3 CD CD 3 CD CD CD CD CD 00 X) 60 E O u d O 1 1 T—I T—I T—I T—I 3 C CO 3 X Cl, CD CL, CD CD CD 3 3 E •rH B 1 1

illumination
208

2 6. 7 Other Units Exactly Defined in Terms of SI Units (partial li.stin;

Quantity Name Symbol Definition

length inch in. 2.54xl0“

2m

mass pound (av.) lb 0.453 592 37 kg

force kilogram force kgf 9.806 65 N

pressure atmosphere atm 101 325 N-m"

2

pressure torr Torr (101 325/760) N-m

pressure millimetre of mmHg 13.5951x980.665

mercury -2 -2

xlO N-m

energy kilowatt-hour kWh 3.6x10^ J

energy thermochemical

calorie***

cal

th

4.184 J

energy IT calorie** Cal

IT

4.1868 J

energy IT British Btu

IT

1055.06 J*

thermal unit**

temperature degree Rankine °R 5/9 K 

(thermodynamic)

temperature degree Celsius °C K** ***

temperature degree Fahrenheit °F 5/9 K******

volume litre 1 -3 3 10 m

* The exact relationship is: 1 Btu^ = (4 . 1868/1 . 8) x435 . 592 37 J.

** IT refers to International Tables (International Steam Tables)

*** The thermochemical calorie is used in tables in this monograph.

  [ T

( °R) = 1 . 8T (K) ] ; [T(°R) - t(°F) + 459.67]; [T( C R) = 1.8t(°C)

+ 491.67]

** *** [ t (°C) = T (K) -27 3.15] ****** [ t

( °F) = 1.8t(°C) + 32]
209

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c CO 00 3 3 Vi 4-1 o c •H O 3 4-) Vi CJ 0 T 1 P-n 3 3 Vi 3

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3 CO 3 CO TO 3 3 O

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0 ro 3 CO > 3

>N 00 TO O 3 TO

TO Pd 3 3 3 O T—l E

TJ 0 3 4J 3 CU N

TO 3 Xl 3 O £ 4-1 3 TO T> x: 3 CO J-i T—l

TO T 1 P*N 0 T—l TO O O

Cm PM pd PQ W O S PQ

/—N N CJ 4J 3 •r4

4-J 3 4-1 *3 4-J

4-1 c TO 3 4-1 CU 3 cu 4-1 TO 3 c

TO 4J CO U 3 bO

4-1 CO 3 CO ob cu CO c O 3 TO B

3 0 3 O E 0

O u 3 1 O u

3 4-1 3 4-J C 3 3 •cs 4-J O

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•l—l 4-J 3 E 4-J 1—

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003

3

3W
These physical constants are excerpted from a list

recommended by the National Academy of Sciences and

adopted by the National Bureau of Standards. The

complete list is found in National Bureau of

Standards Technical News Bulletin, October, 1963.

Error limits are approximately 3 standard deviations

and apply to last digits of the value.
211

Atomic Weights (Relative Atomic Masses) of the Elements

Name Symbol Atomic number Atomic weigl

Actinium Ac 89

Aluminum Al 13 26.9815

Americium Am 95

Antimony Sb 51 121.75

Argon Ar 18 39.948

Arsenic As 33 74.9216

Astatine At 85

Barium Ba 56 137.34

Berkelium Bk 97

Beryllium Be 4 9.0122

Bismuth Bi 83 208.980

Boron B 5 10.811

3

Bromine Br 35 79.909

b

Cadmium Cd 48 112.40

Calcium Ca 20 40.08

Californium Cf 98

Carbon C 6 12.01115'

Cerium Ce 58 140.12

Cesium Cs 55 132.905

Chlorine Cl 17 35.453

b

Chromium Cr 24 51 .996

b

Cobalt Co 27 58.9332

Copper Cu 29 63.54

Curium Cm 96

Dysprosium Dy 66 162.50

Einsteinium Es 99

Erbium Er 68 167.26

Europium Eu 63 151.96

Fermium Fm 100

Fluorine F 9 18.9984

Francium Fr 87

Gadolinium Gd 64 157.25
212

Name Symbol Atomic number Atomic wei

Gallium Ga 31 69.72

Germanium Ge 32 72.59

Gold Au 79 196.967

Hafnium Hf 72 178.49

Helium He 2 4.0026

Holmium Ho 67 164.930

Hydrogen H 1 1.00797

Indium In 49 114.82

Iodine I 53 126.9044

Irid ium Ir 77 192.2

Iron Fe 26 55.847

b

Krypton Kr 36 83.80

Lanthanum La 57 138.91

Lead Pb 82 207.19

Lithium Li 3 6.939

Lutet ium Lu 71 174.97

Magnesium Mg 12 24.312

Manganese Mn 25 54.9380

Mendelevium Md 101

Mercury Hg 80 200.59

Molybdenum Mo 42 95.94

Neodymium Nd 60 144.24

Neon Ne 10 20.183

Neptunium Np 93

Nickel Ni 28 58.71

Niobium Nb 41 92.906

Nitrogen N 7 14.0067

Nobel ium No 102

Osmium Os 76 109.2

Oxygen 0 8 15.9994

a

Palladium Pd 46 106.4

Phosphorus P 15 30.9738

Platinum Pt 78 195.09

Plutonium Pu 94 0 , t , , T t , T
213

Name Symbol Atomic number Atomic weight

Polonium Po 84

Potassium K 19 39.102

Praseodymium Pr 59 140.907

Promethium Pm 61

Protactinium Pa 91

Radium Ra 88

Radon Rn 86

Rhenium Re 75 186.2

Rhodium Rh 45 102.905

Rubidium Rb 37 85.47

Ruthenium Ru 44 101.07

Samarium Sm 62 150.35

Scandium Sc 21 44.956

Selenium Se 34 78.96

Silicon Si 14 28 . 086

a

Silver Ag 47 107 .870

b

Sodium Na 11 22.9898

Strontium Sr 38 87.62

Sulfur S 16 32.064

3

Tantalum Ta 73 180.948

Technetium Tc 43

Tellurium Te 52 127.60

Terbium Tb 65 158.924

Thallium Tl 81 204.37

Thorium Th 90 232.038

Thulium Tm 69 168.934

Tin Sn 50 118.69

Titanium Ti 22 47.90

Tungsten W 74 183.85

Uranium u 92 238.03

Vanadium V 23 50.942

Xenon Xe 54 131.30

Ytterbium Yb 70 173.04
214

Name Symbol Atomic number Atomic weight

Zinc Zn 30 65.37

Zirconium Zr 40 91.22

A. E. Cameron and E. Wichers , J. Am. Chem. Soc

.

. 84, 4175-4197 (1962)

The element symbols, names, and atomic weights (relative atomic

masses) are those recommended by the International Union of Pure

and Applied Chemistry (1961) . The atomic mass unit is 1/12 the mass of the carbon isotope carbon-12.

Ii«