NSST IDb 315110 PUBLICATIONS / V \

55^ NIST SPECIAL PUBLICATION 260" 1 42

U.S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

Standard Reference Materials®

Primary Standards and

Standard Reference Materials

for Electrolytic Conductivity

R. H. Jameel, Y. C. Wu, and K. W. Pratt
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NIST Special Publication 260-142

Standard Reference Materials®

Primary Standards and Standard Reference

Materials for Electrolytic Conductivity

R. H. Jameel

Y. C. Wu

K. W. Pratt

Analytical Chemistry Division Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8390

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Dr. Cheryl L. Shavers, Under Secretary of Commerce for Technology NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director Issued February 2000
Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended

to imply recommendation or endorsement by the National Institute of Standards and

Technology, nor is it intended to imply that the materials or equipment identified are

necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 260-142

Natl. Inst. Stand. Technol. Spec. Publ. 260-142, 46 pages (Feb. 2000)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 2000

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Primary Standards and Standard Reference Materials for Electrolytic Conductivity

R. H. Jameel, Y. C. Wu, K. W. Pratt

National Institute of Standards and Technology

Gaithersburg, MD 20899-8390

Abstract

This report describes the principles and methods for measuring the electrolytic conductivity

of primary standards and NIST Standard Reference Materials (SRMs). There are two methods for

measuring conductivity: the direct current (DC) method, and the alternating current (AC) method. NIST has redetermined the conductivity of the primary standards, and determined a set of molalitybased primary standards over a temperature range of 0 °C to 50 °C. The conductivities of the

primary standards were determined using two uniquely designed conductivity cells for measuring

resistance with the AC and DC methods. The primary standards are used to determine the cell

constants of conductivity cells. In our laboratory, we used both Jones and Daggett cells for measuring conductivity. NIST issues a set of Standard Reference Materials (SRMs) available in

nominal conductivity values of 5 uS/cm, 15 uS/cm, 25 uS/cm, 100 uS/cm, 500 uS/cm,

1 000 uS/cm, 10 000 uS/cm, 20 000 uS/cm, and 100 000 uS/cm. The certified conductivity values

for the SRMs include the solvent conductivity.

Keywords: AC; benzoic acid; conductivity; conductivity cell; DC; electrolyte; hydrochloric acid;

standards; potassium chloride; primary standards; non-aqueous solvent

iii

Contents

Abstract iii

Glossary vii

1 . Introduction 1

1 . 1 Principles of the Electrolytic Conductivity Measurement 1

1 .2 Equivalent Conductivity 2

1.3 Electrolytic Conductivity of Water 4

2. General Scheme of the Electrolytic Conductivity Measurement 5

2.1 Temperature Control 5

2.2 Carbon Dioxide Contribution 6

2.3 Evaporation and Transpiration 7

3. Absolute Conductivity Measurements 8

3.1 Primary Standards 8

3.2 AC Absolute Method 11

3.2.1 Cell Design 12

3.2.1.1 Cell Cleaning Process 14

3.2.2 Instrumentation 15

3.2.3 Measurement 17

3.3 DC Absolute Method 18

v
3.3.1 Cell Design 18

3.3.2 Instrumentation 19

3.3.3 Measurement 22

3.4 AC vs. DC Method 23

3.5 Error Analysis for Primary Standards 24

4. AC Conductivity Measurement With Other Cells 26

4.1 Cell Construction 26

4.2 Calibration of Cells 28

4.2. 1 Cells With Constants Greater Than 1 .5 cm"

1 28

4.2.2 Cells With Constants Less Than 1 .5 cm"

1 28

4.3 Measurement and Instrumentation 30

5. Conductivity Standards for Industrial Applications 31

5.1 Commercial Standards 31

5.2 Standard Reference Materials (SRMs) 31

5.2. 1 Preparation and Measurements of SRMs 32

5.2.2 Error Analysis for SRMs 33

5.3 Low Conductivity Standards 34

6. Discussion and Conclusion 36

7. References

vi

38
Glossary

A constant for an electrolyte solution based on Kohlrausch's Square Root Law

A effective cross-sectional area

c concentration, units are specified as either mol/L, equivalents/L, or mol/kg

Ej potential between the potential electrodes in the DC conductance cell £s potential drop across the standard resistor in DC measurement AE average potential difference between two center Ag, AgCl electrodes in DC cell F force under which an ion moves

/ current

/ ionic strength (Section 1 .2 only)

A'ceii cell constant of a conductivity cell

A'ceii. t cell constant of the center tube of either an AC or DC absolute conductivity cell

ATceu. w cell constant of AC absolute conductivity cell with center tube

A'ceii, n cell constant of AC absolute conductivity cell without center tube

/ effective length between electrodes

q mobility function (Eq. 9) R resistance Ru resistance of a solution in the AC absolute conductivity cell without center tube Rs resistance of standard resistor used in the DC absolute measurement Rj resistance of a solution in the center tube of the DC absolute conductivity cell Rw resistance of a solution in the AC absolute conductivity cell with center tube

r radius of a sphere as defined by Stokes' Law

T absolute temperature

vii
/ temperature, °C

// mobility of an ion

v velocity of a sphere as defined by Stokes' Law

Z valence of an ion

z.\ valence of a cation

Z2 valence of an anion

e dielectric constant

77 viscosity of a homogenous medium

k electrolytic conductivity of an electrolyte solution

Kba electrolytic conductivity of benzoic acid

Kkci electrolytic conductivity of potassium chloride A equivalent conductivity of an electrolyte A

0 equivalent conductivity of an electrolyte at infinite dilution A ionic equivalent conductivity

X° ionic equivalent conductivity at infinite dilution X° ionic equivalent conductivity at infinite dilution of a cation

Xi ionic equivalent conductivity at infinite dilution of an anion p resistivity

(0 frequency

viii
X. Introduction

Electrolytic conductivity is the measure of a solution's ability to conduct current. The

magnitude of the conductivity is dependent on the nature of the ions (i.e., charge, size and mobility)

and the nature of the solvent (such as dielectric constant and viscosity). The electrolytic

conductivity is a result of ionic movement in a particular solvent, which is related to the ionic

interactions taking place within the solution. The measurement of electrolytic conductivity is a

nonspecific measurement; all ions contribute to the electrolytic conductivity of the solution.

In order to have uniform conductivity measurements, accurate electrolytic conductivity

standards must be available for industrial use. For this purpose, the National Institute of Standards

and Technology (NIST) has developed a series of electrolytic conductivity Standard Reference

Materials (SRMs) and issues them through its Standard Reference Materials Program. This report

describes the theory and practice for preparing SRMs.

1.1 Principles of the Electrolytic Conductivity Measurement

The measurement of a solution's resistance, /?, in a conductivity cell, is used to determine

the conductivity of a solution. The resistance of a solution is proportional to the distance between

the electrodes, /, and inversely proportional to the effective cross-sectional area, A:

R = p — ,ohm (1) A

The resistivity, p, is a constant for a given solution and is expressed in units of ohm-cm.

Conductivity is defined as the reciprocal of resistivity:

K = — = —— ,ohm"' cm"

1 orScm"1 (2) p R A

The cell in which the conductivity is measured has a cell constant, A^eii, which is defined as
=~ > cm "' (3) A

where / is the effective length between the electrodes and A is the effective cross sectional area. A

useful definition for the electrolytic conductivity, K, is obtained by combining Eq. (1-3),

KT = ^!L ,Scm'' (4) R

where R is the resistance of the solution and ATcen is the cell constant.

Generally, a cell can be constructed in any shape; however, the cell volume and the

positions of the electrodes must be rigidly fixed and, therefore, the effective physical dimensions of

a cell, the / and A, are constant. The cell constant is determined by measuring the geometrical

dimensions of the cell or by comparing with primary standard solutions in the cell. In the first case,

/ and A are measured directly. In the second case, the cell constant is determined from Eq. (4) with known fcand R. To determine the absolute standards, Kohlrausch measured the cell constant

mechanically [1-3]. Jones and Bradshaw [4] used mercury, which then defined the international ohm, to determine their cell constants. Both of these measurements have been reviewed and the

primary standards for determination of the cell constant were recommended [5]. NIST reconfirmed the old set of standards [6] and established a new set of primary

standards. The new primary standards are based on the molality scale. The conductivity value for

each standard has been determined at a wider range of temperatures than formerly available. In the

following sections, a detailed description of these measurements will be given and discussed.

1.2 Equivalent Conductivity

Often, referring to equivalent conductivity, A, of a solution as opposed to electrolytic

conductivity is desirable. The equivalent conductivity is related to the solution's ionic concentration. 2
A =

1000k- ,Scm 2 equiv 1 (?) c

where c is the concentration of the electrolyte expressed in equivalents per liter. The International Union of Pure and Applied Chemistry (IUPAC) has recommended that molar conductivity be used

in place of equivalent conductivity. However, the electrolytic conductivity theory was developed in

terms of equivalent conductivity and much of the data in the early work was reported in terms of

equivalent conductivity. The old usage has been retained here to avoid confusion. The equivalent conductivity, A, is the sum of the individual ionic conductivities, A,

at infinite dilution, A

0

, is the sum of the individual ionic conductivities at infinite dilution, A

0

.

Kohlrausch's Law of Independent Migration of Ions states that when ions are far enough apart that

the movement of one ion is not influenced by other ions present in solution, the ions are at infinite

dilution [7].

Conductivity is dependent on the concentration of the electrolyte in solution. The equivalent

conductivity of a strong electrolyte generally increases with increasing concentration due to an

increase in the number of ions present. For strong electrolytes in dilute solution, the equivalent

conductivity may be expressed emperically by the Kohlrausch Square Root Law [7]:

A = \ +X, + ... + An (6)

where the equivalent conductivity has units of cm

2 £T' equiv"1

. Similarly, the equivalent conductivity

A = A'-Ajc (7)

3
where A is an empirical constant for a given electrolyte. Later, Onsager [8] used Debye-Hiickel's

ionic theory to develop a limiting law for equivalent conductivity with the same form as Eq. 7, but

with a theoretical value for the constant A

A =

2801000|z 1 z 2 |<?yl" 41.25(jz,| + |z 2 |) (£7)4 + ^)

+ ipo 41 (8)

where kz2 | X' + x^

and z\ is the valency of the cation, z2 is the valency of the anion, £ is the dielectric constant, r\ is the

viscosity, T is the absolute temperature, and / is the ionic strength.

1.3 Electrolytic Conductivity of Water

The electrolytic conductivity of an electrolyte solution consists of the conductivity of the

solvent and the conductivity of the solute. Hence, the conductivity of water (typically the solvent) is

important. The equivalent conductivity, A, of pure water at 25 °C is 0.055 uS cm

2equiv"'[9].

Equation (5) can be used to calculate the theoretical electrolytic conductivity of water. For

water at 25 °C, the p/^w = 14 and therefore, the concentration of H

+ and OH" ions from dissociated

water molecules is cH+ = <:0h- = 10"7 equivalents per liter. The X° for H

+

is 349.81 S cm

2 equiv"1 and

the A

0 for OH" is 198.3 S cm

2 equiv"1 [7]. The electrolytic conductivity of water is calculated by

K*« =K* + Kh~ = [198.3 + 349.81 ]Scm 2 equivalent

1 =549.11 S cm2 equivalent"

1 Ac 549 xlO"7 k = = S/cm = 5.5 x 1 0"8 S/cm = 0.055 uS/cm

1000 1000

This theoretical value is difficult to obtain experimentally because atmospheric CO2 is readily

absorbed into water. The conductivity of C02 in water was measured and found to be 1 .05 uS/cm

4
at 25 °C [8,10]. When other ionic contaminants are also present in water, the conductivity value

will increase further. For example, when 1 ppm of Ca++ ions, or Na+ ions, is present in water (c «

5x10 5 equivalents per liter), the conductivity of this water would be approximately 3 |iS/cm. In

addition to the 1 |iS/cm from CO2 absorption, the final value for the conductivity of water would be

4 |iS/cm. Thus, the value of conductivity is an indicator for the purity of water if this value is

properly determined. To ascertain the accuracy of the measured value, low conductivity standards

are needed for calibration and for quality assurance of the purity of water (see Sec. 5.3).

2. General Scheme of the Electrolytic Conductivity Measurement

The conductivity of a solution is determined by measuring the resistance of a solution in

a given cell, using either the AC or DC method, and then calculating the conductivity from

Eq. (1). The AC method uses a Wheatstone bridge for measuring the resistance, and the DC

method uses a DC digital voltmeter (DVM). The details of the AC and DC methods will be

described in Sec. 3. The electrolytic conductivity of a solution is affected by the temperature of

the solution, the carbon dioxide content of the solution, and the amount of evaporation or

transpiration that occurs prior to the measurement.

2.1 Temperature Control

Electrolytic conductivity is very sensitive to changes in the temperature of the solution. The

conductivity of inorganic electrolytes changes about 2 % for each degree Celsius at room

temperature [7]. A 0.005 °C fluctuation will cause a ±0.01 % change in conductivity. Therefore, good temperature control is required for an accurate measurement of the conductivity of a solution. To achieve the required temperature control, the conductivity cell is placed in a constant

temperature bath. Mineral oil is typically used as the bath fluid. The equipment used at NIST for

monitoring the temperature of the constant temperature bath consists of a quartz thermometer

5
connected to a frequency counter with a digital readout. The quartz thermometer and frequency

counter were calibrated by comparison to the NIST standard platinum resistance thermometer (SPRT) and have an uncertainty not greater than 0.002 °C. When the temperature bath is correctly

adjusted, the temperature can be controlled to ±0.002 °C. When the conductivity cell is designed such that there are large electrodes in bulbs at the end

of a long narrow tube, most of the resistance is contributed by the narrow tube. The effect of

temperature, t, on the cell constant is given by [7]

where Og = 3.6 x

10"6 °C', the thermal expansion coefficient of Pyrex glass. For the whole range of

temperatures, 0 °C to 50 °C, the change in A^eii is approximately 0.02 %. This method of

determining the cell constant has been used in our laboratory for determining the temperature effect on the cell constant of an absolute conductivity cell.

2.2 Carbon Dioxide Contribution The electrolytic conductivity of pure water equilibrated with atmospheric carbon dioxide

is typically taken to be 1 uS/cm [9]. Carbon dioxide will dissolve in solution producing H

+ and HCO3", which will contribute to the conductivity of the water. The contribution of these ions to

the conductivity is referred to as Kqo-,- The concentration of these ions is dependent on the

atmospheric pressure, ventilation, and number of people in a particular laboratory. When

conditions vary, the uncertainty in Kfco-, is taken as 20 % of the typical value for the conductivity

of water in equilibrium with atmospheric C(X Therefore, for an aqueous KC1 solution, the

(10)

6
uncertainty in Kco-,is estimated to be ±0.2 uS/cm. The lower pH of the HC1 solution suppresses

carbon dioxide dissociation.

In a nonaqueous-aqueous solvent, carbon dioxide dissolution and hydrogen ion

conductivity is much less than that in water. Typically, the variation in Kco2 is less than

±0.1 uS/cm [9]. When NIST electrolytic conductivity SRMs are prepared, the solution is shaken for

several days to facilitate equilibration with carbon dioxide prior to bottling. The certified value

of the batch includes the contributions to the conductivity of all ions present in the solution,

including HCO3 . Therefore, the user does not need to degas the solution prior to use. By

equilibrating the solution with atmospheric carbon dioxide, the need to prepare and measure the

solution in a carbon dioxide free environment is avoided, making the SRMs easier to use.

2.3 Evaporation and Transpiration

Transpiration and evaporation both cause the conductivity of a solution to increase.

Transpiration, the passage of solvent through containers, has been observed in this laboratory for

bottles made of low-density polyethylene (LDPE). Solutions that will be stored for more than a

day, such as an SRM, should be packaged such that minimal transpiration occurs over the time of

storage. In this laboratory, glass bottles are used for SRMs because the amount of transpiration,

if any, is unnoticeable. For solutions that will be used immediately after they are prepared, such

as primary standards, transpiration is much less of a concern since long-term storage is not an

issue.

Evaporation may occur as a result of the measurement process, or as a result of a poor

packaging technique. When preparing the solution or filling the cell, evaporation needs to be

minimized. For primary standards, accurate concentration is necessary for accurate 7
measurement. This is much less of a concern for electrolytic conductivity SRMs, which are

certified based on conductivity and not on exact concentration. Filling the cell, with any

solution, will cause slight evaporation of the solution. Evaporation may also occur if the cap of

the bottle is not completely closed, or if the cap relaxes and loosens with time. In this laboratory, such problems have been noted for glass bottles with polypropylene caps and glass bottles with

Bakelite caps. However, serum bottles and ampoules do not appear to have a problem with

evaporation when they are sealed. To obtain an accurate measurement of the conductivity of a solution, evaporation and

transpiration must be minimized. Over time, if evaporation and transpiration due to the packaging of the solution occurs, the accuracy of the conductivity measurement will be compromised.

3. Absolute Conductivity Measurements

Absolute conductivity measurements are performed using conductivity cells, the cell

constant of which is determined by basic standards only (electrical and physical). The two

absolute methods, AC and DC, use different types of cells and instrumentation. The choice of

the AC or DC method will be described in Sec. 3.4. The absolute conductivity measurement has been used at NIST to determine the conductivity of molality-based primary standards. These

primary standards may then be used to calibrate other types of cells (section 4).

3.1 Primary Standards

Establishment of conductivity values for primary standard solutions requires the use of the

absolute method, and is the primary purpose of the absolute method. Both the AC and DC methods,

described in the following sections, have been used to measure the conductivity of the primary

8
standards. The work performed in this laboratory [8, 10-12], and described in this report, has taken

several years. The data are listed in Tables 1-3.

Table 1. Definition of Demal for 0.0 ID, 0.1D, and 1.0 D KC1 Solutions Demality grams of KC1 per kilogram of

0.01 0.7458 19

<6) 0.1 7.47458(6) 1.0 71.1352(8)

Table 2. Electrolytic Conductivity Values for 0.01 D, 0.1D, and 1.0 D

KC1 Solutions* and Water, ITS-90 Scale

t/°C 104 k:/ (jiS/cm)

0.01 D KCl(fI) 0.1 D KC1 1.0 D KC1 (8) H20^

0 773.09 713.46 65 135 0.58 5 891.17 819.97 73 860 0.68 10 1 014.2 930.82 82 871 0.79 15 1 141.7 1 045.6 92 136 0.89 18 1 220.1 1 116.1 97 804 0.95 20 1 273.2 1 163.8 101 620 0.99 25 1 408.4 1 285.1 1 1 1 300 1.10 30 1 546.8 1 408.9 121 110 1.20 35 1 688.0 1 535.0 131 050 1.30 40 1 831.5 1 662.8 141 080 1.40 45 1 976.9 1 791.9 151 150 1.51 50 2 123.8 1 921.9 161 240 1.61 * Values of conductivity for KC1 solutions do not include solvent conductivity

9
i

I

i

I

Table 3. Electrolytic Conductivity Values for the Molality-Based Primary Standard KC1 Solutions*

0.01 mol/kg, 0.1 mol/kg, and 1.0 mol/kg, ITS-90 Scale

t/°C 104 Kl (|nS/cm)

0.01 mol/kg 0.1 mol/kg 1.0 mol/kg water

value (10) 2uc(U) valued value(8) 2«c

(12) value(10) 0 0.23 2.85 63 487 25 0.58 5 0.27 3.27 72 030 29 0.68 10 1 013.95 0.30 3.72 80 844 32 0.79 15 1 141.45 0.34 10 437.1 4.2 89 900 36 0.89 18 1 219.93 0.37 11 140.6 4.5 0.95 20 1 273.03 0.38 11 615.9 4.6 99 170 40 0.99 25 1 408.23 0.42 12 824.6 5.1 108 620 43 1.10 30 1 546.63 0.46 14 059.2 5.6 118 240 47 1.20 35 1 687.79 0.51 15 316.0 6.1 127 970 51 1.30 40 1 831.27 0.55 16 591.0 6.6 137 810 55 1.40 45 1 976.62 0.59 17 880.6 7.2 147 720 59 1.51 50 2 123.43 0.64 19 180.9 7.7 157 670 63 1.61 *Values of conductivity for KC1 solutions do not include solvent conductivity

Primary standards are used for calibrating conductivity cells. The chief requirement for the

standard is accuracy. The factors affecting the accuracy of the primary standards include stability of

the chemical, purity of the solute and solvent, and concentration of the solution. Potassium chloride was chosen as the solute [1-6] because KC1 is stable and easily purified. Water is used as the

solvent because it is also stable and easily purified. These two factors are very important for

maintaining uniformity and repeatability when the solutions are prepared in different laboratories,

so that the results can be accurately compared. For high accuracy measurements, the concentration

of the primary standard solutions should be accurate to at least 5 places.

Currently, three primary standards at three temperatures are recommended by IUPAC [13] and Organization Internationale de Metrologie Legale (OLML). These primary standards are based 10
on the measurements of Jones and Bradshaw [4]. The primary standards have concentrations

defined by the so-called demal (D) scale, which is defined as an exact mass of KC1 in an exact mass

of water. This scale is not related to any other concentration scale. The demal unit is defined at

three concentrations only (Table 1): 0.01 D, 0.1 D, and 1.0 D. NIST redetermined the primary standards adopted by IUPAC and determined a new set of

molality-based primary standards. The measurements of the primary standards by Jones and Bradshaw were performed over 60 years ago and several basic standards have been changed. Moreover, the demal scale lacks a direct relationship to the common units of concentration and to

the units used in solution chemistry. The original values have been adjusted for changes in the basic

standards to obtain the values currently adopted by IUPAC. In addition, the conductivities of the recommended demal standards are only determined at three temperatures. Therefore, NIST not

only redetermined the set of primary standards adopted by IUPAC to reconfirm its value, but also

determined a set of molality-based primary standards available at temperatures from 0 °C to 50 °C

at 5 °C intervals and at 18 °C (Table 3) to expand the applicability of primary standards. The molality-based primary standards developed at NIST were prepared using potassium

chloride and water. Molality, mol/kg, is defined as the amount of solute in one kilogram of solvent

in vacuo. Molality-based primary standards at three concentrations expressed in molality

(0.01 mol/kg, 0.1 mol/kg, and 1 .0 mol/kg) in the temperature range of 0 °C to 50 °C have been

proposed to OIML and to the IUPAC for adoption [10,12].

3.2 AC Absolute Method

The AC absolute cell was designed and constructed at NIST for the measurement of the

0.01 D and 0.1 D primary standards, and the 0.01 mol/kg and 0.1 mol/kg molality-based primary

11
standards [6,10,1 1]. This AC absolute cell, its design, instrumentation, and measurement

method, are described in the following sections.

3.2.1 Cell Design The AC absolute cell, shown in Fig. 1 , is a Jones type cell with a removable center tube.

Figure 1 . AC absolute conductivity cell: a, a - electrode chambers (half-cells); b - removable

center extension tube; c, c - flanges; d, d - platinum disk electrodes; e, e - O-rings. The mating

flange ends are held together by a C-shaped Bakelite band (not shown) so that lateral movement is prevented.

The design of this cell allows determinations of the conductivity of a solution from basic standards. No calibration of the cell is necessary. The details of cell construction [9,10] are briefly described

as follows. A length of precision-bore 1 cm I. D. Pyrex tubing, with uniformity certified by the

manufacturer, was cut into 3 sections. A prefabricated flange, c, with an I. D. of 1.3 cm, O. D. of

2.5 cm, and thickness of 0.65 cm was epoxied into each of the tubes such that the face of the flange was flush with the cut end of the tube. Then, each flanged end was ground to optical flatness. The

unflanged end of each of the singly flanged tubes was joined to the corresponding electrode

chamber, a, each of which contained a 2 cm platinum disk electrode, d. The electrodes were gold

soldered to a 2 mm platinum wire, which extended through a graded-glass seal. To assemble the 12
cell, the mating flange ends are held together by a C-shaped Bakelite band which can be slightly

enlarged with a little pressure, such that the two flanges fit snugly into it, preventing the flanges from moving laterally. Lateral and rotational movements are prevented by a Bakelite two-plate assembly tightened together with four nylon screws and nuts. A rubber O-ring, e, is inserted between each plate and the rear side of the flange. The tube b of the cell is removable, and its

dimensions (length and internal diameter) were determined by the Length and Mass Division of NIST (presently, length is determined by the Precision Engineering Division; mass is determined by

the Automation Production and Technology Division).

Since the cell constant in a Jones-type conductance cell is determined by the lines of force between the two electrodes, the center section of the tube may be removed in order to shorten the

distance between the electrodes, thereby reducing the resistance. Subsequently, the same section may be put back, lengthening the distance and increasing the resistance, provided that the lines of

force are not disturbed. Thus, there are essentially two cells: one is with the center tube b, and the

other is without the center tube b. When the conductivity, K, of a solution with fixed concentration

is measured with the two cells, we will obtain the resistance of the solution in the cell with the

center tube, /?w,

cell.w K = (ID

K

and the resistance of the solution in the cell without the center tube, R^,

cell.N (12) K

13
where /fceii.w and KCd\, n are the cell constants with and without the center tube, respectively.

Similarly, /?w and RN are measured resistances when using the cell with the center tube and without

the center tube, respectively.

Equation (11) and Eq. (12) may be combined by subtracting from /?w and solving for jc

/?w -RN/? w - fl N The cell constant of the center tube, ATCeii,T = IIA, is determined by physical measurements of / and A

and is equal to ATce ii, w - ATce n. N . All the quantities on the right-hand side of Eq. (13) are known by means of physical measurement. Therefore /cis absolutely determined and values for Kce\], w and

A^eiLN can then be calculated from Eq. (11) and Eq. (12).

3.2.1.1 Cell Cleaning Process When the cell is newly constructed, it is cleaned with chromic acid cleaning solution, rinsed

with water, soaked in a 6 mol/L HC1 solution for 1 h, washed with water, soaked in distilled water

overnight, and dried at room temperature. In cases where the HC1 soaking, water washing, soaking,

and vacuum drying do not remove the last traces of adsorbed chromate ions, the process must be

repeated. (Strong acids and organic solvents have been tried as a replacement for chromic acid

cleaning solution, without success.) After the cell is thoroughly clean and dry, it is assembled and

filled with a standard KC1 solution. If no leak is detected at the joints after the filled cell stands for

1 h, the cell is put into the bath for 30 min to 40 min until the solution reaches thermal equilibrium

with the bath temperature. The reading is then recorded. If no drift is noted over a 1 h period, the

cell is emptied and refilled to obtain measurements in triplicate. If the deviation of the results is less

than 0.01 % and random, the mean is taken as the final result. If the deviation shows a trend toward

increasing or decreasing resistance, there are two probable causes: cell contamination and loss of 14
water from the solution by evaporation. Cell contamination is generally caused by adsorption of

foreign substances on the cell walls and/or electrodes. There is no easy way out of this except either

to repeat the experiment until the foreign substances are leached out and the readings are constant,

or to repeat the cleaning process. If the drift is due to concentration increase by evaporation, a new

solution will generally cure it. The procedures for changing from one concentration to another and/or for replacing the

center tube of the cell are similar. The cell is taken out from the bath, the outside wall of the cell and

the whole assembly are washed with soap solution and rinsed with water. The inside of the cell is

flushed with distilled water continuously for about 30 min. The whole unit is dried with paper

towels and is disassembled. The joints of the cell are cleaned with soap and water. When everything

is dry, they are re-assembled. Caution is always exercised to prevent the oil on the outside of the cell from creeping inside. If this occurs, the cleaning process must be repeated.

3.2.2 Instrumentation The AC method for conductivity measurement consists of a constant temperature bath and

the resistance measurement instrumentation. The constant temperature bath used when measuring

the primary standards [1 1] is briefly described below. The bath consisted of a rectangular, steel,

open-top box surrounded by a wood cabinet with a hinged cover that can be opened or closed. The

space between the sides of the steel box and the wood cabinet was insulated with glass wool.

Within the steel box were vertical, open-ended rectangular walls around which a piece of copper

tubing was looped. The tubing led to the outside of the wood cabinet for connection to a

temperature-controlled fluid. A stirrer was mounted on the inside wall to provide good circulation.

Studs were mounted in the front side of the steel box to allow for support and manipulation of the

conductivity cell. Twenty gallons of petroleum oil were used as bath fluid, and the oil was changed

15
every 6 months to 8 months. Water was circulated through the copper coil and back for cooling by

an auxiliary constant-temperature bath. The heating is facilitated with a quartz heater submerged

into the bath. The whole unit was connected to a proportional temperature control unit. A

thermistor is used as the sensor for the temperature controller. A quartz thermometer and frequency

counter are used as the bath temperature indicator. The AC instrumentation [10,1 1] is described as follows. The AC measurement uses a Jones

bridge [14,15], which is a Wheatstone bridge with capacitance compensation that is specifically

designed for conductivity measurements. The Jones bridge is equipped with a capacitor and resistor

in parallel to balance the impedance of the conductivity cell. The bridge also employs a Wagner

ground to minimize the effects of stray capacitance on the accuracy of the null point. The ratio- arms are held exactly equal.

Alternating current is supplied to the bridge by a signal generator. The signal generator can

be operated from 20 Hz to 15 kHz. The normal operating range of frequency, ft), is 1 kHz to 5 kHz. The resistance is corrected for the effect of polarization by plotting R versus ft)

1 and extrapolating to

a) = oo [7]. The signal generator was modified by floating the secondary of the output transformer to

obtain an ungrounded output, which is required to make use of the Wagner ground of the Jones

bridge. A single-ended (unbalanced) output was obtained from a secondary winding of the output

transformer and was used as the phase reference for the detector. The applied AC voltage to the

bridge is 1.2 V RMS. A differential input preamplifier, tuned amplifier, and oscilloscope are used

in the detector circuit. The differential input of the preamplifier preserves the balance of the Wagner ground and eliminates the need for an input transformer. The tuned amplifier is used in the

bandpass mode at a Q (Q is the ratio of the frequency to the bandwidth, thus, the smaller the

bandwidth, the larger the Q) of 10 to 50, to attenuate the second and higher harmonics at the null 16
point. The output of the tuned amplifier and the reference signal from the signal generator are

connected to the vertical and horizontal inputs of the oscilloscope, respectively. The displayed

pattern on the oscilloscope is a Lissajous figure and is used to indicate both capacitive and resistive

balance of the bridge simultaneously [16]. (The technique was superior to using the in-phase and

quadrature output meters of the lock-in amplifier to indicate resistive and capacitive balance of the

bridge.)With this setup, a 0.001 % change in cell resistance may be detected on the oscilloscope. Hence, a change of 0.001 °C in the bath temperature (0.002 % in R) can be observed. The

uncertainty in the null point measurement did not contribute significantly to the overall uncertainty

of the measurement of the resistance of the primary standard.

3.2.3 Measurement

In the AC measurement of conductivity, the cell will generally have an impedance Z\ that is

not purely resistive. However, there are other sources of impedance such as the Parker effect [17] and the effect of a conducting thermostat medium [14]. These effects can be avoided by proper cell

design. When measuring the resistance of a solution, the combination of the solution conductivity

and cell constant is chosen such that the measured resistance is within the optimum range of

resistances for the bridge. The optimum range for resistances when using the Jones bridge is

1 000 Q. < R < 10 000 Q. The Jones bridge has five decade resistors plus the slide wire resistor. The maximum uncertainty of the nominal readings of the dials is less than 0.005 % as stated by the

manufacturer. The cell is placed into the conductivity bath for about 30 min, so that the solution in the cell

can reach thermal equilibrium with the temperature of the bath. Resistance readings are taken at 1 17
kHz and 2 kHz at 10 min intervals to determine that the solution's temperature is constant. The

polarization correction is made by plotting the measured resistance, R, vs. ft)

1 and extrapolating to

l/ft)= 0 [7]. The resistance of the solution is then calculated by correcting the extrapolated

resistance for the lead resistance (from the electrodes to the binding posts of the bridge). If the

resistance continuously drifts upward or downward for 30 min, this indicates that the concentration

of ions in the solution is changing, or that the temperature is changing. In this instance, the measurement should be stopped, the cause of the drift determined, and the measurement repeated.

3.3 DC Absolute Method

At NIST, the DC absolute cell was designed for the measurement of the 1 D primary

standard and the 1 mol/kg molality-based primary standard [8]. The DC absolute cell, its design,

instrumentation, and measurement method, are described in the following sections.

3.3.1 Cell Design The DC absolute cell is a four-electrode conductivity cell (Fig. 2). The two inner electrodes

are used to measure potential drop and the outer two electrodes are used to measure the applied

current, /. In order to eliminate polarization effects, all four electrodes must be reversible to the

solution. For primary standard KC1 solutions, Ag, AgCl electrodes are suitable.

For an absolute determination of conductivity, the cell constant needs to be determined with

the same basic standards (e.g., length measurement) as the AC cell. To accomplish this

requirement, a precision bore Pyrex tubing is cut into three pieces, so that the center section of the

cell could be removed and that the internal diameter and length of this center section could be measured accurately by physical methods. The two ends of the center section were polished to

flatness, while the surfaces of the ends of the other two pieces, which will join with the center

section, were ground to a roughness of about 25 um. A slight gap was formed between the joined 18
ends of the tubing to effect a miniscule flow of solution, when the sections are rejoined using a

nylon union. The other two ends of the cut tubing are fused to Pyrex tubing comprising the current compartments of the cell. A U-shaped capillary separates the current-electrode chamber from the

connecting chamber to minimize the effect of electrolysis products on the measurement. A third

tube is joined at each of the junctions of the center section with the end sections using a nylon-union

tee. These compartments contain the potential leads for the measurements. The final assembly is shown schematically in Figure 2.

1 2 2 1

Figure 2. DC Absolute conductivity cell: 1,1- current electrodes; 2, 2 - potential difference sensing electrodes; 3 - nylon tee joints; 4,4 - O-rings.

Cleaning of the cell when it is newly constructed, and when changing concentrations, is the same as described in Sec. 3.2. 1 .

3.3.2 Instrumentation The DC method is much simpler in principle than the AC method and is determined by

Ohm's law [8]. A high precision digital voltmeter (DVM), an accurate standard resistor, and a

constant current supply are needed for the measurement of R. Both the DVM and the standard

resistor were calibrated by the Electricity Division at NIST. The constant current supply can 19
provide current from 25 u A to 250 mA and has a stability of ±0.005 % over 14 h. A schematic diagram of the operating circuit is shown in Fig. 3.

d

Figure 3. Schematic of DC Operating and Switching Circuitry: a - conductivity cell with gaps A, A; b - digital voltmeter; c - constant current supply; d - switch with position 1 and 2; e - switch with position 3 and 4; /?s - standard resistor

With switch d in the 2 position and switch e in the 3 position, current flows through the standard

resistor and the conductance cell, and the 1R drop across the standard resistor, £s , is measured by the DVM as

ES =1RS (14)

where R& is the resistance of the standard resistor and / is the current. / is thus determined. Moving

switch d to the 1 position while switch e remains in the 3 position effects the measurement of the

voltage between the potential electrodes in the conductance cell, Ej,

ET = IRT (15)

where Rj is the resistance of the solution in the conductance cell. Switching e to the 4 position

reverses the flow of current and the polarity of the current electrodes. A data point at a singe

20
current consisted of four measurements as shown in Table 4. Any difference between the standard

redox potentials, £°, of the potential difference-sensing electrodes was eliminated by reversing the

direction of the current, /, and averaging the magnitudes of the two measured potential differences.

This averaged potential difference, AE, was related to conductivity by

where Kce\\ j is the cell constant of the center tube, and Rj is the resistance of the solution in tube.

Table 4. Measurement Sequence' Measurement Switch d Switch e

1 2 3 2 1 3

3 1 4

4 2 4

Two pairs of matched Ag, AgCl electrodes were used in the conductance cell: one pair for the

current electrodes and the other for the potential electrodes. The preparation and calibration of these

electrodes have been described in conjunction with the pH studies at NIST [18]. All four electrodes were within ± 0.05 mV of each other. Reversible electrodes are required to eliminate polarization

effects. Ag, AgCl electrodes, appropriate for KC1 solutions, were used for all four electrodes to

minimize the effects of electrolysis and polarization. Two constant temperature baths were used at NIST: an oil bath [10] in which the

temperature could be controlled to ±0.002 °C (described in Sec. 3.2.2) and a water bath [1 1] in 21

-
which the temperature could be controlled to ±0.001 °C to ±0.002 °C for temperatures above 0°C.

3.3.3 Measurement

After the cell is assembled, and filled with solution, the electrodes are placed in the

appropriate chambers. The whole cell assembly is put into the bath, and its temperature is adjusted

and controlled as designated. Usually, the starting temperature is 25.000 °C, and a steady state is

reached after about 30 min. The wiring to the electrodes was connected according to the scheme shown in Fig. 3. The

outer electrodes are connected to a constant current supply, c. A standard resistor, Rs , is inserted between an outer electrode and the constant current supply, so that the current passing through the

cell and the Rs is the same (see Fig. 3). The inner electrodes are connected to the digital voltmeter,

b. The gaps, A, are the opening for connecting the inner electrodes (Fig. 3). Platinum wires may

serve as the outer electrodes. The inner electrodes are preferably reversible to the electrolyte

solution, such as Ag/AgCl to KC1, in order to eliminate polarization. For a solution without

reversible electrodes, e.g., NH4NO3, calomel electrodes with liquid junction may be used to measure

the potential drop across the fixed points a. The cell is modified with four side tubes to accommodate the liquid junction at the inner electrodes, and to minimize the hydrolysis effect at the

outer electrodes.

It took approximately 3 s for a reading, and there were four readings for a selected current, two each for each direction (as described in Sec. 3.3.2). Each data point was taken as the mean of

three different currents. At each temperature, the current flowed through the cell for approximately 30 s. Thus, the power dissipated in the cell was less than 1 mW, and its effect was much smaller

22
than a millidegree per second change for the solution. Therefore, there is no significant heating

effect.

3.4 AC vs. DC Method

For absolute measurement of conductivity, there are limitations of dimension for the

constant temperature bath and for the conductivity cell. Hence, the range of cell constants is

limited. Thus, the AC method is preferred for solutions of low conductivity and high resistance due to lower experimental uncertainties. The DC method is preferred for solutions of high

conductivity, and hence low resistance. For the AC method, an optimum range of resistance is

required for the best accuracy. Typically, an error in the resistance of a few hundredths of an ohm would result from either the bridge or the lead resistance. For example, if R is 100 Q, an

error of 0.05 Q absolute is equivalent to an error of 0.05 % relative. If R is 1000 Q, an error of

0.05 Q. absolute is equivalent to an error 0.005 % relative. Therefore, a larger cell constant, which is difficult to achieve, is necessary when using the AC method to minimize these effects. When the DC method is used, errors due to the bridge and the lead resistance are eliminated. Because the potential measured does not include the leads, the lead resistance is eliminated. The

accuracy of a voltmeter can reach 10"7 to 10"8 V. An applied current may be selected from 10"5 to

10 " A. For a given cell constant, Kcan be varied a thousandfold and can be determined without

sacrificing accuracy. The conductivities of the 1 mol/kg molality-based primary standard and the 1 D primary

standard were determined using the DC method (Table 2-3). The conductivities of the 0.01 mol/kg

and 0.1 mol/kg molality-based primary standards and the 0.01 D and 0.1 D primary standards were

determined using the AC method (Table 2-3).

23
3.5 Error Analysis for Primary Standards The error analysis performed at NIST for the conductivity measurements of the molality- based primary standards using the AC and DC measurement methods [6,8-1 1] is briefly discussed

below. The errors calculated for each value of conductivity [12] are listed in Table 3. The values for

the conductivity of the primary standards (Table 3) were calculated using Eq. (17), which is a polynomial fit of the values for conductivity at each temperature:

K = a + bt + ct

2 +dt* (17)

The values for a, b, c, and d are given in Table 5. The standard uncertainty of the differences between the smoothed values of jcand the discrete values of /care 0.0046 %, 0.0126 %, and

0.0145 % for the 0.01 mol/kg, 0.1 mol/kg, and 1.0 mol/kg molality-based KC1 primary standards,

respectively.

Table 5. Parameters in the Polynomial Fit for Electrolytic Conductivity Versus Temperature*

Molality, mol/kg Parameters

a b c d

0.01 0.0772921 2.30846 x

10"-' 1.07715 x 10"5 -5.84084 x

10"* 0.1 0.711685 2.09002 x 10

2 8.99144 x

10"' -5.07124 x

10"' 1.0 6.34882 1.6913 x 10

1 6.00781 x 10"4 -3.83702 x

10"°

The uncertainty in the measurements of #cen, t was based on the measurement of the length and

diameter of the tube. The values for the standard uncertainty are 0.0065 % for 0.01 mol/kg and

0.1 mol/kg, and 0.0085 % for the 1.0 mol/kg molality-based primary standard. 24
The effect of changes in temperature on A'ceii.T may be calculated from Eq. (10), which

applies to both AC and DC measurements. For the AC measurements, the values of jcfor each

molality were calculated using the corrected value of A'ceii.T- The uncertainty in this correction for AC measurements was negligible. For the DC measurements, no correction was applied to A'ceii.T- The standard uncertainty is taken as 0.0052 % for the DC measurements, based on the estimated change in A'ce ii, t with temperature. The uncertainty in the measurement of temperature, arising from the calibration of the

thermometer, was ±0.002 K. The temperature coefficient at each temperature was determined

directly from the smoothed polynomial fit of k

- versus t. The largest temperature coefficient, which was at 0 °C, was multiplied by ±0.002 K. The standard uncertainty, ±0.0034 %, was treated as a uniform probability distribution, and has been divided by 3

>/2 [19]. The effect of impurities in the KC1 for the primary standards was estimated to contribute an

uncertainty of 0.0025 % to the conductivity. The standard uncertainty due to evaporation of the

primary standard solutions during transfer to the conductivity cell is estimated to be 0.0025 %. The resistors in the AC conductivity bridge were calibrated and the uncertainty in this

calibration, 0.001 %, was treated as a uniform probability distribution. The standard uncertainty was thus taken as 0.0057 %. The standard uncertainty of the DC measurements of current and

potential was taken as 0.00061 %. The uncertainty in the solvent correction was taken as 0.2 uS/cm. The standard uncertainty,

treated as a uniform probability distribution, was less than 0.0015 % in all cases. The uncertainties for each primary standard were calculated as the root sum of squares. The

actual uncertainties were conservatively estimated to be 0.03 % for the 0.01 mol/kg primary

25
standard, and 0.04 % for both the 0.1 mol/kg and 1 .0 mol/kg primary standards. Uncertainties

calculated for each primary standard at each temperature are given in Table 3.

4. AC Conductivity Measurement With Other Cells As mentioned in Sec. 3, the primary standards are used to calibrate conductivity cells. Absolute cells are used when the best possible accuracy is needed. Some solutions, such as SRMs, do not require the high accuracy measurement that primary standards require. For SRMs,

Jones and Daggett cells [7], which are calibrated using primary standards, are used for making

the resistance measurements.

4.1 Cell Construction The Jones and Daggett cells used at NIST are made of borosilicate glass and use platinum

electrodes. Jones cells are usually composed of two glass bulbs, each containing a platinum disk

electrode, separated by a piece of glass tubing to give a large cell constant (Fig. 4).

Figure 4. Jones Cell: Jones cell is similar to the AC absolute cell except that it does not have a removable center tube.

To minimize evaporation when filling the cell, the solution is poured through a funnel and into

the cell. Less evaporation occurred with this type of filling than with the other methods examined in this laboratory. 26
Daggett cells consist of an Erlenmeyer flask that is connected to a glass bulb containing

the electrodes (Fig. 5). The use of the Erlenmeyer flask facilitates filling of the cell.

Figure 5. Daggett cell: diagram is similar to the Jones cell, except that an Erlenmeyer flask is attached to facilitate filling of the cell.

However, an Erlenmeyer flask can only be attached to cells with small cell constants due to

design problems. Daggett cells are typically used for low conductivity solutions.

All of the Jones and Daggett cells used at NIST were made on-site. Several items must

be considered when making a conductivity cell. The cells should contain no rough edges and

ridges. Any microcracks where the solute could be trapped must also be eliminated. When

adding a solution to the cell, any trapped solute would dissolve and the concentration of ions, and

therefore the conductivity, would change. Two types of microcracks were observed with commercial cells: ( 1

) at the joining of the platinum wire to the disk, and (2) at the joining of the

platinum to the glass. The lack of a smooth surface when spot welding the platinum disk onto the

platinum lead left small cracks where KC1 could be trapped. These cracks were eliminated by

using gold to smooth out the surface. Because Pyrex does not wet platinum, the glass would pull away from the lead leaving small cracks where KC1 could be trapped. This problem was solved

27
by using a type of soda lime glass that does wet platinum. A graded seal was used to fuse the soda lime glass to Pyrex.

4.2 Calibration of Cells

Presently, the Jones and Daggett cells at NIST have cell constants ranging from about

0.05 cm'

1 to 1 10 cm"1 . The standards used for calibrating these cells must be accurately

prepared, as was mentioned in Sec. 3.1 for the primary standards. Solutions should be used

within several hours of preparation to minimize evaporation and transpiration. Several different

standard solutions should be used and, when possible, at least two of the solutions should have

concentrations that are one order of magnitude different. The cell should be calibrated at the

temperature, or temperatures, that will be used for measuring the conductivity of solutions.

4.2.1 Cells With Constants Greater Than 1.5 cm

1

For calibrating a cell at 25 °C, molality-based primary standards are available in the

conductivity range of approximately 1 400 uS/cm to 1 10 000 uS/cm. The combination of solution and cell should result in a resistance in the optimum range. This is easily achieved for cells with

A'ceii > 1.5 cm"

1

. For example, a cell with #ce n = 2 cm'

1 would be calibrated with the primary

standard having a molality of 0.01 mol/kg which has a conductivity of 1409.33 uS/cm, including

the solvent conductivity. In this example, the measured resistance would be about 1 400 £1. A

cell with A'ceii = 1 10 cm"

1 would be calibrated with the primary standard having a molality of

1 .0 mol/kg. The measured resistance would be about 1 000 Q.

4.2.2 Cells With Constants Less Than 1.5 cm"

1

As mentioned above, for calibrating a cell at 25 °C, primary standards are available in the

conductivity range of approximately 1 400 uS/cm to 1 10 000 uS/cm. If #ceii ^ 1-5 cm"', the

resistances of the primary standards will be in the range of 900 Q. to 10 Q. The accuracy of a 28
resistance measurement would be compromised because an uncertainty of ±0.1 Q. in the measured

resistance would cause a 0.014 % to 1 % uncertainty in conductivity. If the primary standard is

used for calibrating a cell with A^ii ~ 0.1 cm"

1 , the uncertainty will increase according to Eq. (4).

Therefore, working solutions must be used.

At NIST, working solutions are prepared for calibrating conductivity cells by estimating the amount of KC1 necessary to give the desired conductivity. The resistance of the working solution is

then measured in a cell that was calibrated with a primary standard. The conductivity of the working solution is calculated from Eq. (4). The resistance of the same working solution is then measured in the cell to be calibrated. Since the conductivity of the working solution is known, the

cell constant may be calculated from Eq. (4). Some workers in this field employ the Onsager limiting law equation [5,20] for KC1 as a

function of concentration to prepare secondary standards of the desired conductivity. The

equivalent conductivity is calculated for the low concentration of aqueous potassium chloride so

that a solution of low conductivity, and optimum resistance, may be used to calibrate the cell. The

equivalent conductivity of KC1 solutions having concentrations less than 0.05 moles/L may be

calculated by

AKC! = 149.83 -95.09Vc+ 38.66c logc + 183.9c (18)

where c has units of mol/L and y\ Kci has units of Sm2/mol. Equation ( 1 8) is based on the literature

values for A° [5] and has been corrected for the change from international ohm to the absolute ohm,

the change 1948 EPTS units to 1990 IPTS units, the change in the liter unit, and changes in the

atomic masses of K and CI. The electrolytic conductivity is calculated from Eq. (5). Thus, for a KC1 solution of molality 0.0001 mol/kg, k= 14.888 u.S/cm, not including the solvent conductivity. 29
If Keen is approximately 0.05 cm"

1 , then R is approximately 3 400 Q, which is in the range of optimum resistance. This calibrating equation may yield reasonable accuracy provided the

preparation and measurement of the solution are done with pure water and under a C02 free

atmosphere. Under these conditions, the solvent conductivity correction is near the theoretical

value, i.e., 0.055 |iS/cm. Otherwise, the solution conductivity must be corrected for a solvent

conductivity of 1 . 1 uS/cm with an uncertainty of ±0. 1 uS/cm to ±0.3 |iS/cm. This solvent

correction would cause an uncertainty of 7 % for a solution having k= 14.888 uS/cm. HC1 solutions may also be used for calibrating a cell that has a low cell constant. The

theoretical equation [21] for calculating the conductivity of dilute HQ can be written as:

AHC1 =426.16-158.68V? + 185.60clogc + 500c (19)

At 0.0001 mol/L, Kis 42.46 (iS/cm for a cell with Kce\\ ~ 0.05 cm"

1 and the resistance measured would be approximately 1 200 Q. Since the HC1 solution has a lower pH than an aqueous KC1

solution, CO2 dissociation is suppressed. Therefore, the uncertainty due to the solvent correction is much smaller. In a carbon dioxide free environment, Eq. (19) yields reasonable accuracy.

4.3 Measurement and Instrumentation

In general, the Jones and Daggett cells are used at NIST to measure the conductivity of SRMs. Measurements made to calibrate the cell or to determine the conductivity of a solution

use the instrumentation as described for the AC absolute method (Sec. 3.2.2 and Sec. 3.2.3). When first constructed, the cell is cleaned as described in Sec. 3.2.1.1. Prior to a measurement, the cell may be cleaned by soaking with water and drying under clean air, argon,

or nitrogen. A clean, dry cell is typically rinsed 3 times with the solution to be measured prior to

filling the cell. In this laboratory, when several solutions are to be measured in a row, such as 30
when certifying an SRM, cleaning and drying the cell is not practical due to the amount of time

required. Rinsing the cell 5 times with the solution to be measured is sufficient to remove any

noticeable effects of the solution previously in the cell.

5. Conductivity Standards for Industrial Applications

When the high accuracy of primary standards discussed in Sec. 3.1 is not needed, commercial standards are sufficient. The most common application of conductivity standards is cell

calibration. Two types of industrial standards for electrolytic conductivity are available: commercial standards, many of which claim NIST traceability, and NIST SRMs. The standards must be readily available and easy to use.

5.1 Commercial Standards Commercial standards are available at conductivities from 100 uS/cm to 100 000 uS/cm. The uncertainties of some of these standards can be as high as 0.5 %.

5.2 Standard Reference Materials (SRMs) To satisfy industrial needs, NIST certifies and issues certifies a series of electrolytic

conductivity SRMs. The SRMs may be divided into two groups: aqueous (nominal values of 25 uS/cm, 100 uS/cm, 500 uS/cm, 1 000 uS/cm, 10 000 uS/cm, 100 000 uS/cm, 20 000 uS/cm),

and mixed aqueous-nonaqueous (5 uS/cm and 15 |iS/cm). The conductivity of these standards

includes the solvent conductivity.

All but two of the aqueous SRMs are prepared as KC1 in water. The solute for the 25 uS/cm

solution is hydrochloric acid. Hydrochloric acid is used for lower conductivity solutions because it

suppresses carbon dioxide dissociation at its low pH. The solute for the 20 000 uS/cm solution is

NaCl. The use of NaCl was specifically requested by clinical laboratories. When the 20 000 uS/cm

31
solution is made with NaCl, the ionic strength of the solution approximates the ionic strength of body fluid. The two lowest conductivity SRMs are prepared using KC1 in 30 % n-propanol 70 % water. These SRMs are discussed further in Sec. 5.2.3.

5.2.1 Preparation and Measurement of SRMs

The SRMs are prepared initially by underestimating the amount of solute needed for a given amount of solvent that will give the desired conductivity. Since the SRMs are certified based on

conductivity, the exact concentration of ions, or more specifically KC1, is not critical. Any minor

contamination of the bulk solution (prior to certification) will not spoil the SRM. The bulk solution

is then shaken for several days to ensure that the solution is homogenous, and to ensure that the

solution has equilibrated with atmospheric C02 . Using the AC method (Sec. 3.2.2 and Sec. 3.2.3) and a calibrated Jones or Daggett cell (Sec. 4), the resistance of a sample of the bulk solution is measured over several hours. If there is no drift in the conductivity, the solution is equilibrated with

atmospheric CCX The concentration is then adjusted by adding solute or solvent as required to get

closer to the nominal value of conductivity. The solution is bottled, typically yielding 80 units of the SRMs. A stratified random

sampling, based on the bottling order, is used to determine which units will be measured. The

measurements of these units are randomized so that trends in bottling order and measurement order may be differentiated. The mean value of these units is called the determined value. This

determined value is adjusted upward to correct for changes in the conductivity due to evaporation

and/or transpiration, and leaching as needed, to yield the final certified value.

32
5.2.2 Error Analysis for SRMs

The calculation of the certified value for SRMs has recently been reevaluated. For SRMs,

the uncertainty consists of 5 components: 1 ) random variations in the measurement of conductivity,

2) standard uncertainty of the cell constant, 3) resistance measurements, 4) temperature fluctuation

observed during the measurements, and 5) carbon dioxide contribution to the conductivity of the

solution. Depending on the bottling type, the effects of transpiration, evaporation, and leaching must also be considered. The uncertainties for each SRM are expressed in absolute terms in each SRM certificate. To generalize the uncertainties for all SRMs, most of the standard uncertainties

described below are expressed in relative terms, and are only approximations. A complete

uncertainty analysis is required for each SRM batch to determine the uncertainty portion of the

certified value of the given SRM.

The random variation in the measurement of conductivity is determined from the standard

deviation of the mean and is generally less than 0.008 %. The combined standard uncertainty of the

cell constant from a complete uncertainty analysis is used as the standard uncertainty of the cell

constant.The standard uncertainty in the resistance measurements is stated by the manufacturer of the

conductivity bridge to be ±0.005 % RforR> 100 Q. (95 % confidence interval). The standard uncertainty of small resistances measured with the digital voltmeter, such as

the lead resistance, is stated by the manufacturer of the digital voltmeter to be 0.0012 Q, absolute. The standard uncertainty for temperature is taken as the temperature variation observed while making the resistance measurements, which is typically ±0.002 °C. The standard uncertainty of the

lead resistance and temperature is modeled as a uniform probability distribution and is, therefore,

divided by f\

33
The standard uncertainty due to the thermometer calibration has not previously been

included in the determination of the uncertainty of a given SRM. The standard uncertainty of the thermometer calibration is typically 0.002 °C for 95 % confidence interval. The standard uncertainty of the contribution of CO2 to the total conductivity is estimated from the possible existing conditions in users' laboratories. The concentration of CO2 is highly

environmentally sensitive and, therefore, can vary due to changes in temperature, atmospheric

pressure, and laboratory ventilation. In addition, the CO2 concentration in a laboratory is higher if more people are in the laboratory. The variation in concentration of CO2 is estimated to give a

variation of ±0.2 uS/cm, absolute, in solvent conductivity. This uncertainty is also modeled as a uniform probability distribution.

Transpiration and evaporation are major concerns when determining the value of an SRM. Unlike primary standards which should be prepared and used immediately, SRMs may

not be used for several months after they are packaged. The appropriate packaging must be chosen to minimize the effects of evaporation and transpiration.

5.3 Low Conductivity Standards

For low conductivity standards, it is important to limit the amount of carbon dioxide

absoiption into the solution and to reduce the uncertainty associated with this absorption. In order

to achieve this, a mixed aqueous-nonaqueous solvent is used. When an aqueous solution is used, the major concern is the CO2 content in the atmosphere, which varies from 300 ppm to 600 ppm or higher, from one time and place to another [22]. This

variation causes a variation in conductivity of about ±0.2 uS/cm, corresponding to an additional

4 % uncertainty for a 5 |iS/cm standard. A mixed aqueous-nonaqueous solvent is desirable,

because the CO2 effect in such a solvent is less than 0.1 |iS/cm [9]. Therefore, the 5 uS/cm and 34
15 uS/cm SRMs consist of KC1 in 30 % n-propanol 70 % water. NIST has studied solutions of KC1 in 30 % n-propanol 70 % water and solutions of benzoic

acid (BA) in 30 % n-propanol 70 % water [9]. The 100 % pure n-propanol is obtainable on the open market, and both KG and BA are available as NIST SRMs. The conductivities of the KC1 and BA solutions are linear functions of their concentrations at low concentration. They may be

expressed empirically as follows [9]:

KKa = 0.35 + 6.38xl04 c (20)

and

k- ba = 0.04 + 376c^ (21)

where c is in the units of molality, mol/kg, and K"is in units of uS/cm. The uncertainty of kKC\ is

±0.01 uS/cm and the uncertainty of kba is ±0.2 uS/cm. The temperature effect on the conductivity was also examined and found to be 2.9 %/°C for KC1 and 2.6 %/°C for BA at 25 °C [9]. Equation

(20) and Eq. (2 1 ) may be used to obtain the concentration for the desired standard. A list of the

required concentrations in molality and in mass fraction for the round values of standard

conductivity is given in the following Table 6.

35
Table 6. Molality and Mass Fraction (Given in Grams Solute per Kilogram Solution, In Vacuum)

of Low Conductivity Standards in 30 % n-PrOH-H2 0

(

K/0iS/cm) Potassium Chloride (KC1) Benzoic Acid (C6H5 COOH)

molality/(10"

3 mol/kg) n7(g/kg) molality/(10"

3 mol/kg) W(g/kg)

5.00 0.072 9 0.005 43 0.174 0.021 3 10.0 0.151 0.011 3 0.702 0.085 7 15.0 0.230 0.017 1 1.58 0.193

20.0 0.308 0.023 0 2.82 0.344

25.0 0.386 0.028 8 4.41 0.538

6. Discussion and Conclusion

The standards described in this report have a variety of characteristics and applications. The

primary standards, described here, are used for high accuracy work and are determined absolutely by physical and electrical means, without any calibration. The uncertainties associated with the

primary standards are low if the solution is kept free of acid fumes and carbon dioxide. The industrial standards are given in a form that is easy to use at the expense of high accuracy. The

conductivity of the solvent in equilibrium with atmospheric CCb is included, which causes a somewhat higher uncertainty. The low conductivity standards are intended for water quality

control. To avoid the problem of the variation of COt content, 30 % n-propanol 70 % water mixed

solvent is used in which the CO2 effect is minimal.

Conductivity measurement is one of the most precise, accurate, and relatively inexpensive methods for determining the ionic properties of electrolyte solutions. To ascertain the accuracy of a measurement, a calibrated cell must be used. When calibrating cells, several standards, such as SRMs, should be measured to validate the calibration. If the cell constants from several measurements agree to within the measurement uncertainty, then one can be sure that the results are 36
accurate. If the results do not agree, the source of errors must be found and eliminated before

further measurements are made.

37
7. References

1 . F. Kohlrausch and W. A. Nippoldt, Gott. Nach. 415 ( 1 868).

2. F. Kohlrausch and W. A. Nippoldt, W.A., Ann. Physik 138, 280, 370 ( 1 869).

3. F. Kohlrausch, L. Holborn, and H. Dieselhorst, Weid. Ann. 64, 625 ( 1 898).

4. G. Jones and B. C. Bradshaw, J. Am. Chem. Soc. 55, 1 780 ( 1 933).

5. Y. C. Wu, W. F. Koch, W. J. Hamer, and R. L. Kay, J. Solution Chem. 16, 985 (1987); 19, 1053

(1990).

6. Y. C. Wu. K. W. Pratt, and W. F. Koch, J. Solution Chem. 18, 515 (1989).

7. R. A. Robinson and R. H. Stokes, Electrolyte Solutions, 3

ld ed., Butterworths, London (1959).

8. Y. C. Wu, W. F. Koch, D. Feng, L. A. Holland, E. Juhasz, E. Arvay, and A. Tomek, J. Res.

Natl. Inst. Stand. Technol. 99, 241 (1994).

9. Y. C. Wu and P. Berezansky, J. Res. Natl. Inst. Stand. Technol. 100. 521 (1995).

10. Y. C. Wu, W. F. Koch, and K. W. Pratt, J. Res. Natl. Inst. Stand. Technol. 96, 191 (1991).

1 1 . Y. C. Wu and W. F. Koch, J. Solution Chem. 20, 39 1 ( 1 99 1 ).

12. K. W. Pratt, W. F. Koch, Y. C. Wu, and P. A. Berezansky, submitted for publication

13. IUPAC Commission on Physicochemical Measurements and Standards, Pure and Appl. Chem.

53, 1841 (1981).

14. G. Jones and R. C. Josephs, J. Am. Chem. Soc. 50, 1049 (1928).

15. P. H. Dike, Rev. Sci. Instruments. 2, 379 (1931).

16 H. W. Lamson, Rev. Sci. Instruments. 9, 272 (1938).

17. H. C. Parker and E. W. Parker, J. Am. Chem. Soc. 46, 312 (1924).

18. Y. C. Wu, W. F. Koch, and G. Marinenko, J. Res. Natl. Bur. Stand. 89, 395 (1984); Y. C. Wu, W. F. Koch, and R. A. Durst, NBS Special Publ. 260-53 (1988). 38
19. Guide to the Expression of Uncertainty in Measurement, ISBN 92-67-10188-9, 1

st Ed.,

International Organization for Standardization, Geneva, Switzerland, 1993.

20. L. Onsager and R. M. Fuoss, J. Phys. Chem. 36, 2689 (1932).

21. Y. C. Wu, W. F. Koch, P. A. Berezansky, and L. A. Holland, J. Solution Chem. 21, 383 (1992).

22. R. Sams, private communication.

About the authors: Rubina H. Jameel and Kenneth W. Pratt are research chemists in the

Analytical Chemistry Division of the NIST Chemical Science and Technology Laboratory.

Yung Chi Wu is a retired senior chemist from the Analytical Chemistry Division of the NIST

Chemical Science and Technology Laboratory.

39

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