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CUMMERCE 8 1971 NBS TECHNICAL NOTE 270-5

MIST

PUBLICATiONS REFERENCE i

U.S.

DEPARTMENT

OF

COMMERCE

National

R'ireau

wit

Selected Values of

Chemical Thermodynamic

Properties

Tables for Elements 54 Through 61 in the

Standard Order of Arrangement
NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director ^^^TECHNICAL NOTE 270-5

ISSUED MARCH 1971

Nat. Bur. Stand. (U.S.), Tech. Note 270-5, 49 pages (IVlar. 1971)

CODEN: NBTNA

Selected Values of Chemical Thermodynamic Properties

Tables for Elements 54 Through 61 in the

Standard Order of Arrangement

D. D. Wagman, W. H. Evans, V. B. Parker, I. Halow,

S. M. Bailey, R. H. Schumm, K. L Churney

Physical Chemistry Division

Institute for Material Research

National Bureau of Standards

Washington, D.C. 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402.

(Order by SD Catalog No. C 13.46:270-5). Price 55 cents.
ABSTRACT

Contains tables of values for the standard heats and Gibbs (free)

energies of formation, entropies and enthalpies at 298.15 K and heats

of fornnation at K for compounds of vanadium, niobium, tantalum,

titanium, zirconiunn, hafniunn, scandium, and yttrium (eleinents 54-

61 in the Standard Order of Arrangement). These tables are a continuation of the comprehensive revision of NBS Circular 500.

Key words: Enthalpy; entropy; Gibbs energy of formation; hafnium

compounds; heat of formation; niobium compounds; scandium compounds; tantalum compounds; titanium compounds; vanadium compounds; yttrium compounds; zirconium compounds.

11
PREFACE

This is the fifth of a series of Technical Notes containing the

tables of material prepared as a revision of National Bureau of

Standards Circular 500, Selected Values of Chemical Thermodynamic Properties, by F. D. Rossini, D. D. Wagman,

W. H. Evans, S. Levine and I, Jaffe, This Note contains data

for compounds of eight elements, numbered 54 through 61 in the

Standard Order of Arrangement. The Appendix contains a list

of corrections for errors and misprints that have been detected

in summary Note TN 2 70-3 and in TN 2 70-4.

The continued encouragement and support of the Office of

Standard Reference Data of the National Bureau of Standards is

gratefully acknowledged.

Ill
CONTENTS

Preface iii

Introduction v

Standard Order of Arrangement of the Elements , Figure 1 . . x

Table A. Conversion Factors for Units of Molecular Energy . xi

Table 54 Vanadium 1

Table 55 Niobium 6

Table 56 Tantalum 10

Table 57 Titanium 12

Table 58 Zirconium 18

Table 59 Hafnium 22

Table 60 Scandium 24

Table 6l Yttrium 28

Appendix 35

Index of Contents 36

IV
SELECTED VALUES OF CHEMICAL THERMODYNAMIC PROPERTIES

INTRODUCTION

Substances and Properties Included in the Tables

The tables contain values where known of the enthalpy and Gibbs

energy of forination, enthalpy, entropy and heat capacity at 298.15 K

(25°C), and the enthalpy of formation at K, for all inorganic substances

and organic molecules containing not more than two carbon atoms. In

some instances such as metal-organic compounds, data are given for

substances in which each organic radical contains one or two carbon

atoms

.

No values are given in these tables for metal alloys or other

solid solutions, fused salts, or for substances of undefined chemical

composition.

Physical States

The physical state of each substance is indicated in the column

headed "State" as crystalline solid (c), liquid (liq), glassy or amorphous

(amorp), or gaseous (g). Solutions in water are listed as aqueous (aq).

For non -aqueous systems the physical state is that normal for the

indicated solvent at 298.15 K.

Definition of Symbols

The symbols used in these tables are defined as follows: P = pressure; V = volume; T = absolute temperature; E = intrinsic or

internal energy; S = entropy; H = E + PV = enthalpy (heat content);

G = H - TS = Gibbs energy (formerly the free energy); C = (dH/dT)^ = heat capacity at constant pressure.
Conventions Regarding Pure Substances

The values of the thermodynamic properties of the pure substances

given in these tables are for the substances in their standard states

(indicated by the superscript " on the thermodynamic symbol). These

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 hypothetical ideal gas at unit

fugacity, in which state the enthalpy is that of the real gas at the same

temperature and at zero pressure.

The values of A Hf° and AGf* given in the tables represent the change

in the appropriate thermodynamic quantity when one gram -formula

weight of the substance in its standard state is formed, isothermally at

the indicated temperature, from the elements, each in its appropriate

standard reference state. The standard reference state at 25 "C for

each element except phosphorus has been chosen to be the standard

state that is thermodynamically stable at 25 "C and at one atmosphere

pressure. For phosphorus the standard reference state is the crystalline

white form; the more stable forms have not been well characterized

thermochemically. The same reference states have been maintained for

the elements at K except for the liquid elements bromine and mercury,

for which the reference states have been chosen as the stable crystalline

forms. The standard reference states are indicated in the tables by the

fact that the values of A Hf " and A Gf ° are exactly zero.

The values of H^qq -Hq represent the enthalpy difference for the

given substance between 298.15 K and K. If the indicated standard

state at 2 5 °C is the gas, the corresponding state at K is the hypothetical ideal gas; if the state at 25*'C is solid or liqviid, the corresponding state at K is the thermodynamically stable crystalline

solid, unless otherwise specifically indicated.

The values of S" represent the virtual or "thermal" entropy of the

substance in the standard state at 298.15 K, omitting contributions from

nuclear spins. Isotope mixing effects, etc. , are also excluded except

in the case of the hydrogen-deuterium ( H- H) system. Where data have

been available only for a particular isotope, they have been corrected

when possible to the normal isotopic connposition.

The values of the enthalpies of formation of gaseous ionic species

are computed on the convention that the value of AHf ° for the electron

is zero. Conversions between and 298.15 K are calculated using

the value of HIgg-HQ = 1.481 kcal per mole of electrons, and assioming

that the values of H2Q3-H5 for the ionized and un-ionized molecules are

the same.

VI
Conventions Regarding Solutions

Solutions in water are designated as aqueous (aq); other solvents

are designated by name or chemical formula. The concentration of the

solution is expressed in terms of the number of moles of solvent associated with one mole of the solute. If no concentration is indicated, the

solution is assumed to be "dilute".

The standard state for a solute in aqueous solution is taken as the

hypothetical ideal solution of unit molality (indicated as "std. state,

m = 1"). In this state the partial molal enthalpy and heat capacity of the

solute are the same as in the infinitely dilute real solution. For nonaqueous solutions the standard state of the solute is the hypothetical

ideal solution of unit mole fraction of solute ("std. state, X2 = 1").

The value of A Hf ° given in the tables for a solute in its standard

state is the apparent molal enthalpy of formation of the substance in

the infinitely dilute real solution. At this dilution the partial molal

enthalpy is equal to the apparent molal quantity. At concentrations

other than the standard state, the value of A Hf " represents the apparent

enthalpy of the reaction of formation of the solution from the elements

comprising the solute, each in its standard reference state, and the

appropriate total number of moles of solvent. In this representation

the value of A Hf " for the solvent is not required. The experimental value

for a heat of dilution is obtained directly as the difference between the

two values of A Hf ° at the corresponding concentrations.

The values of the thermodynamic properties tabulated for the

individual ions in aqueous solution are based on the usual convention

that the values of AHf % AGf, S" and Cp" for H"*" (aq, std. state, m = 1) are zero. The properties of a neutral electrolyte in aqueous solution

in the standard state are equal to the algebraic sum of these values for

the appropriate kinds and number of individual ions assiomed to constitute

the molecule of the given electrolyte. When the undissociated species,

rather than the s\rm of the ions, is meant, the notation "undissociated"

or "\an-ionized" is used. For an ionic species the properties tabulated

refer to thatvindissociated ion. By adopting the above convention with

respect to aqueous H , it follows that the thermodynamic relation A Gf ° = A Hf° - T A Sf " will not hold for an individual ionic species. However

no problem arises when neutral chemical systems are considered.

Vll
Unit of Energy and Fundamental Constants

All of the energy values given in these tables are expressed in terms

of the thermochemical calorie. This unit, defined as equal to 4.1840

joules, is generally accepted for the presentation of chemical thermodynamic data. Values reported in other units have been converted to

calories by means of the conversion factors for molecular energy given

in Table A.

The following values of the fundamental physical constants have

been used in these calculations:

R = gas constant = 8. 3143 + 0. 0012 J/deg mol = 1.98717 + 0. 00029

cal/deg mol

F = Faraday constant = 96487.0 + 1.6 coulombs /nnol

= 23060.9 ±0.4 cal/volt equivalent

Z = Nhc = 11. 96258 + 0- 00107 J/cm"^ mol = 2. 85912 -L 0. 00026 cal/cm"^ mol

c^ = second radiation constant = hc/k = 1.43879 ± 0.00015 cm deg

0°C = 273.15 K

These constants are consistent with those given in the Table of General

Physical Constants, recommended by the National Academy of Sciences - National Research Council . The formula weights in the tables have

been calculated for the nnolecular formula given in the Formula and

Description column using the 1961 Table of Relative Atonmic Weights based

on the atomic mass of ^^C = 12 exactly^.

Internal Consistency of the Tables

All of the values given in these tables have been calculated from

the original articles, using consistent values for all subsidiary and

auxiliary quantities. The original data were corrected where possible

for differences in energy units, molecular weights, temperature scales,

etc. Thus we have sought to maintain a uniform scale of energies for

all the substances in the tables. In addition the tabulated values of the

properties of a substance satisfy all the known physical and thermodynamic

relationships annong these properties. The quantities A Hf ", A Gf °, and

S" at 298.15 K satisfy the relation:

tGf = ^ Hf - T ASf .

NBS Technical News Bulletin, October 1963.

2

A. E. Cameron and E. Wichers, J. Am. Chem. Soc. 84, 4192 (1962).

Vlll
Furthermore the calculated value of any thermodynamic quantity for a

reaction is independent of the path chosen for the evaluation.

In some cases newer data may have become available on certain

substances after the values were selected for these tables. Because

of the need to maintain the internal consistency of the tables, it is not

always possible to incorporate these new^er data into the tables w^ithout a detailed analysis of the effect of such a change. Unless great care is

used, relatively significant errors in calculated values of A H" or A G"

for specific reactions may result from the introduction of such data.

Uncertainties

The uncertainty in any value in the tables depends on the uncertainties of all the determinations in the total chain of reactions used to

establish the value.

A discussion of the uncertainties will be included in the final

publication of these tables in the National Standard Reference Data

System. However we have followed certain rules with respect to

significant figures to indicate these uncertainties. Values are tabulated

in general such that the overall iincertainty lies between 2 and 20 units

of the last figure. On the other hand, values are given so that the

experimental data from which they are derived may be recovered with

an accuracy equal to that of the original quantities. Thus the nximber

of significant figures for any one value in the tables need not represent

the absolute accuracy of that value. For solutions of varying composition

values are frequently tabulated to more figures to make possible the

recovery of enthalpies of solution and dilution. Similarly values of

A HfQ and AHflqo -ir may be given to different niombers of significant

figures. In this instance the quantity with the lesser number of figures

is used to represent the uncertainty estimate. The larger number of

figures is used for the other quantity to retain the significance of the

temperature correction term.

Arrangement of the Tables

The compounds in the tables are entered according to the Standard

Order of Arrangement, (see Figure 1), by the principle of latest position.

In this scheme, a compound is listed \inder the element occurring latest

in the list; water of hydration is neglected. Within a given elementtable will be found all of the compo\inds of that element with elements

occurring earlier in the order; the arrangement within a table follows

the same ordering. An exception occurs in the carbon tables (Table 23),

which is divided into subgroups consisting of all compounds with one

carbon atom, then all with two carbon atoms, etc.

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TABLES OF SELECTED VALUES OF PROPERTIES

SERIES I

Enthalpy of Formation at K

Enthalpy of Formation at 298. 15 K

Gibbs Energy of Formation at 298. 15 K

Enthalpy at 298. 15 K

Entropy at 298. 15 K

Heat Capacity at 298. 15 K

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TN

APPENDIX

Errata for Technical Note 270-3 and 270-4

(See also TN 270-4, page 139)

'age

48 H2S2(liq)

H2S2(g)

H2S3(liq)

H2S3(g)

H2S4(liq)

^^S^ig)

H2S5(liq)

H2S5(g)

H2S^(liq)

87 H3PO^ in 0.7 5 H2O

97 AsCl3(liq)

AHf°2Qg = -4. 33 kcal/mol

3. 71 kcal/mol

-3. 57 kcal/mol

7.29 kcal/mol

= -2. 99 kcal/mol

= 10. 57 kcal/mol

= -2. 49 kcal/mol

= 1 3, 84 kcal/mol

= -1 . 99 kcal/mol

3 87 ^3^^4 ^^ O.75H2O = -304.35 kcal/mol

3 97 AsCl3(liq) AGf°2Q8 = -62.0 kcal/mol

S° = 51. 7 cal/deg mol

AsCl3(g) ^^^°0 ^ -62.12 kcal/mol

AHf°2Q8 = -62.5 kcal/mol

AGf° qo = -59.5 kcal/mol

208 Al-0_(c); the third, fourth and fifth lines should read:

(p) '^^f°298 " "^*^^- kcal/mol

(K) = -397. kcal/mol

(Delete value for AGf°2Qo)

(v) ^^^°298 ^ "^^^- kcal/mol

3 Hgl(g) ^f°0 ^ ^^'^ kcal/mol

AHf° = 31.64 kcal/mol

AGf°2Qg = 21. 14 kcal/mol

108 Mnl2-4H20(c) AHf°2Q8= -343.9 kcal/mol

113 MnC20.(c) = -246.2 kcal/mol

MnC20^-2H20(c) AHf°2Q8= -389.2 kcal/mol

S° = 48. cal/deg mol

MnC204- 3H20(c) AHf°2Q8= -459.1 kcal/mol

35
Chemical

Symbol

Ag

Al

Ar

As

At

Au

B

Bi

Br

C

Cd

CI

Co

Cr

Cu

F

Fe

Ga

Ge

H

He

Hf

Hg

IIn

IrKr

Mn

Mo

N

INDEX OF CONTENTS

Element Table Volume - Number Page Number

Silver 37 4- 29

Aluminum 29 3-207

Argon 5 3- 17

Arsenic 20 3- 95

Astatine 13 3- 42

Gold 38 4- 39

Boron 28 3-196

Bismuth 22 3-103

Bromine 11 3- 31

Carbon 23 3-106

Cadmium 34 3-248

Chlorine 10 3- 24

Cobalt 40 4- 54

Chromium 51 4-120

Copper 36 4- 13

Fluorine 9 3- 21

Iron 41 4- 74

Gallium 30 3-218

Germanium 25 3-177

Hydrogen 2 3- 12 Helium 3 3- 15

Ha fnium 59 5- 22

Mercury 35 4- 1 Iodine 12 3- 36

Indium 31 3-223

Iridium 46 4-103

Krypton 6 3- 18

Manganese 48 4-106

Molybdenum 52 4-129

Nitrogen 18 3- 61

36
chemical Elemient Table Volume - Symbol Number Page Number

Nb Niobium 55 5- 6 Ne Neon 4 3- 16

Ni Nickel 39 4- 43

O Oxygen 1 3- 11

Os Osmium 47 4-104

P Phosphorus 19 3- 84

Pb Lead 27 3-187

Pd Palladiumi 42 4- 90

Po Poloniumi 17 3- 60

Pt Platinum 45 4- 96

Re Rhenium 50 4-117

Rh Rhodiuim 43 4- 93

Rn Radon 8 3- 20

Ru Ruthsnium 44 4- 94

S Sulfur 14 3- 43

Sb Antimony 21 3- 99

Sc Scandium 60 5- 24

Se Seleniumi 15 3- 56

Si Silicon 24 3-171

Sn Tin 26 3-181

Ta Tantalumi 56 5- 10

Tc Technetiumi 49 4-116

Te Tellurium 16 3- 58

Ti Titanium 57 5- 12 Tl Thallium 32 3-227

V Vanadiumi 54 5- 1 W Tungsten 53 4-134

Xe Xenon 7 3- 19

Y Yttrium 61 5- 28

Zn Zinc 33 3-233

Zr Zirconium 58 5- 18

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