Calorimetric Determination of the Heat of Ionization of Water at 10° and 40°C*

Thermochimica Acta Elsevier Publishing Company, Amsterdam Printed in Belgium

CALORIMETRIC DETERMINATION OF THE HEAT OF IONIZATION OF WATER AT 10° AND 40°C* J. J. CHRISTENSEN, G. L. KIMBALL, H. D. JOHNSTON, and R. M. IZATT Department of Chemical Engineering and Chemistry, and Center for Thermochemical Studies, Brigham Young University, Provo, Utah 84601 (U.S. A.)

(Received January 21st, 1972)

ABSTRACT

The heat of neutralization, LJ H n, of perchloric acid with sodium hydroxide has been determined at 10° and 40° in a low ionic strength (p,) region using a nonisothermal, constant-temperature-environment solution calorimeter. Correction of the data to infinite dilution by extrapolation of a plot of LJHn vs. p, 0 • 5 gives values at zero ionic strength, for the heat of ionization of water, of 14.216 and 12.695 kcalfmole, at 10° and 40°, respectively. The data are correlated with those of earlier workers to give an equation allowing the calculation of the heat of ionization of water at zero ionic strength over the temperature range 0-55°. INTRODUCTION

Early calorimetric work 1- 6 produced values for the heat of ionization, LJH~, of water which, when corrected to 25° and zero ionic strength, p, = 0, ranged from 13.323 to 13.367 kcalfmole. These values were lower by at least 110 calfmole than the LJH~ value obtained from the temperature dependence of the ionization constant of water using electro-chemical cell data 7 • This disagreement appeared to be resolved in 1956 when Papee et al. 8 , using a microcalorimetric technique, and working in low ionic strength regions, reported a LJHf value of 13.50 ±0.05 kcalfmole. Papee et al. attributed the earlier lower calorimetric values to the fact that the investigators had to use substantial corrections for heats of dilution because they used solutions having final concentrations of 0.5 M and higher. However, subsequent investigations in independent laboratories have indicated that the correct LJHf value lies below 13.5 kcalfmole. Sacconi et a/. 9 , Hale et a/. 10 , and Vanderzee and Swanson 11 obtained 13.336, 13.337, and 13.336 kcalfmole, respectively, for the standard heat of ionization of water at 25° and p, = 0. The latter two groups agreed that the work of Papee et al. 8 was difficult to evaluate. Vanderzee and Swanson concluded 11 that the disagreement between their value and that resulting from electrochemical cell data could not be attributed to uncertainties in the heats of dilution but rather resulted from "small systematic effects ... associated with the treatment of the e.m.f. data." Vasil'ev and *Contribution No. 25 from the Center for Thermochemical Studies. Thermochim. Acta, 4 (1972)

141

Lobanov 12 determined the heat of ionization of water as a function of both temperature and Jl, primarily in solutions having J1 values of 0.5 and higher. To ensure that their measurements involved no appreciable systematic errors, they determined Ll H~ using their data at 25° and J1 = 0.0416 with heat of dilution data taken from the literature. They reported a value of 13.349 ±0.020 kcal/mole. They also reported a LIH~ value of 13.695 ±0.028 kcalfmole at 18° which agrees well with the value of 13.721 ±0.016 kcalfmole reported earlier by Rossini 13 . Values for LIH~ at 25° of 13.334 ±0.013 kcaljmole and 13.346 ±0.002 kcalfmole have been reported recently by Leung and Grunwald 14 and by Grenthe et a!. 1 5 , respectively. It appears that the value of 13.34 kcal/mole for LIH~ at 25° and J1 = 0 is now clearly established. Since many reactions in aqueous solution, including virtually all biological reactions, occur at temperatures other than 25°, it is important that LIH~ be evaluated as a function of temperature at least over the range 0-50°. Several calorimetric determinations of LIH~ as a function of temperature have been reported. Vasil'ev and Lobanov 12 tabulate data which ostensibly are LIH~ values obtained from the results of their experiments at several temperatures from 0 to 70° inclusive, and at J1 values of 0.0416, 0.515, 1.00, and 2.98. Careful examination, however, reveals that these tabulated values are not LIH~ values; rather, each is an intercept value resulting from extrapolating to J1 = 0 the plot of an equation proposed by one of the authors 16 , which has the form LIHn- f(Jl) = LIH~ + ijl. In a plot of LIHn -f(Jl) vs. Jl, the slope is iand the intercept is LIHio according to the equation. More will be said about determining LIH~ by this method in the discussion. Leung and Grunwald 14 report, for the selfionization of water, Lie; values as a function of temperature. In their study LIH~ values determined calorimetrically at 0° and at 10° intervals from 5 to 55° were used to formulate a temperature-dependent equation. The first derivative of this equation gives a temperature-dependent equation for L1 Grenthe and co-workers 1 5 have obtained calorimetrically LIH~ values at 5, 20, 25, 35, and 50°. The LIH~ values reported by Leung and Grunwald and by Grenthe et a!. differ at 5° by 65 cal and at 35° by 122 cal. At each temperature the difference is greater than the sum of the experimental errors of the reported values. The only other attempt to determine LIH~ as a function of temperature by calorimetry was a qualitative study reported by Anderson et a!. 1 7 • These workers report LIH~ values of 13.90 ±0.070, 13.33 ±0.070, and 12.47 ±0.100 kcalfmole at 10, 25, and 40°, respectively. The value at 25° agrees very well with the accepted value. Interpolating the data of Leung and Grunwald yields, for I 0° and 40°, the values 14.19 and 12.71 kcalfmole, respectively, which differ significantly from those reported by Anderson et a!. Several investigators have proposed methods other than calorimetry for obtaining the heat of ionization of water at temperatures removed from 25°. Ackermann 18 , using heat capacity data, obtained a third order temperature-dependent equation for calculating LIH~ values. Harned and Owen 19 calculated LIH~ values at 5° temperature intervals, from 0 to 50°, using an equation derived from the temperature dependence of the ionization constant of water. Larson and Hepler 20 have proposed a series of temperature-dependent equations based on the "best available data for the heat of

c;.

142

ionization of water", from which may be calculated at temperatures near 25° several thermodynamic values including AHf. In the present study, heat of neutralization, AH0 , values are reported for the reaction of perchloric acid with sodium hydroxide at 10° and 40° in a low ionic strength region. Values of AHf are obtained by extrapolating to J1 = 0 a plot of AHn vs. J1°' 5 • The "best" literature AH~ values over the temperature range 0-55° are correlated with the values obtained in this study and a consistent set of the thermodynamic quantities AH~, A G?, and AS~, valid at J1 = 0, is given at 5° intervals in this temperature range. EXPERIMENTAL

Materials.- Reagent grade perchloric acid (Baker and Adamson) was used to prepare stock solutions of the required concentration. The sodium hydroxide solutions were prepared by diluting with freshly-boiled, double-distilled water, a 50% NaOH solution (Mallinckrodt, Analytical Reagent). Prior to, and after use, all sodium hydroxide solutions were tested with a Ba(Cl04 ) 2 solution. The procedure used was found to be capable of detecting carbonate ion in concentrations as low as 5 x 10- 6 M which is the maximum allowable concentration that permits 0.1% accuracy with the least concentrated NaOH solution ( -0.005M). No carbonate ion was detected in any of the solutions. The sodium hydroxide solutions were standardized against National Bureau of Standards primary standard potassium hydrogen phthalate (standard sample 84 h). The solutions of perchloric acid were first standardized with tris(hydroxymethyl)aminomethane (Fisher Certified THAM., Lot No. 772419, Assay 99.9%, and Lot No. 76815, Assay 100.0%) and then checked with the standard sodium hydroxide solutions. A pH meter was used to detect end points in the standardization of both the NaOH and HC10 4 solutions. Apparatus. - The acid-base reactions were carried out in two non-isothermal, constant-temperature-environment calorimeters 10 . Each calorimeter consisted of a 225-ml, silvered dewar vessel on the top of which a metal plate was cemented. The dewar with the metal plate was then placed in position by bolting it to a second metal plate, with an "0" ring serving as a seal between the plates. A thermistor was incorporated as one arm of a wheatstone bridge whose circuits were well shielded to eliminate parasitic currents. A calibrated, decade resistance box served as the corresponding arm of the wheatstone bridge. Both the measurement of the bridge voltage and the calibration of the resistance box were done with a Leeds and Northrup K-3 Universal Potentiometer. In operation, the thermistor resistance change due to the reaction or electrical calibration resulted in an unbalanced bridge potential which was fed through a microvolt amplifier, set at an amplification of 5, to a MinneapolisHoneywell strip chart recorder having a span of 2.5 millivolts. The pen was kept on the chart by adjusting the resistance of the calibrated decade resistance box. A 100-ohm heater constructed from Karma alloy wire was used in the electrical caliThermochim. Acta, 4 (1972)

143

bration. The 6-volt lead storage battery used to supply power during calibration was discharged continuously into a dummy heater (a 100-ohm resistor) except during the actual electrical calibration. Current was fed simultaneously through the calorimeter heater and electric timers. The voltage across a 10.000-ohm standard resistor, placed in series with the heater and across a voltage divider in parallel with the heater, was measured by the K-3 potentiometer. The current through the heater was calculated from the measured voltages and the time of electrical calibration. The temperature of the inner bath was controlled to within ±0.0002°. A unique feature of the inner bath was the fact that during operation it could be completely immersed in the outer bath, which helped to minimize temperature fluctuations. Details of the calorimeter construction and electrical circuitry are available 21 . Thermistor calibration. - Thermistors were calibrated at 10° and 40° as previously described 10 for 25°, except that a relationship between temperature change and resistance change, as measured by the calibrated decade resistance box, was determined instead of that between temperature change and recorder deflection. Procedure.- Several determinations of AHf were carried out at 25°. The value obtained, 13.336 ±0.016 kcal/mole, verified the reagent concentrations and indicated that no significant systematic errors were associated with the equipment or procedures. In the determinations at each temperature, solutions of acids and bases were prepared so that in the subsequent reaction, 10 ml of acid would react with 175 ml of base leaving a slight excess of acid, except in the case of the reactions at 40° and Jl = 0.02480 in which there was a slight excess of base. The acid solution was pipetted into very thin-walled glass ampoules which were carefully sealed with Parafilm. The ampoule was then attached by electrical tape to a rod within the calorimeter to which was added 17 5 ml of base. All work with solutions was done under a nitrogen atmosphere. After positioning the calorimeter vessel, the temperature inside the calorimeter was brought to the desired initial temperature using the internal heater. After allowing for thermal equilibrium to be established, the glass ampoule was broken by turning it into the stirrer blades. Blank determinations showed no significant heat effects from breaking the ampoule. The acid-base reaction was complete within 2 min. After the reaction was complete, time was allowed for a stirring slope and then the calorimeter vessel with its contents was calibrated electrically. Further details of procedure and details of chart analysis are available 21 . Calculations. - In Table I are given the data necessary for calculating the heat of neutralization, AHn, of perchloric acid with sodium hydroxide at 10° and 40° at the indicated Jl values. The equations used to make the calculations are as follows:

+ B[Iog1o (RTJRT 2W

(1)

ATe = A log1o (RHJRH 2 ) + B[logto (RH,IRH 2W

(2)

AT, = A log1o (RTJRT,)

Qc

CP

= Ehtr X Estd X k X t = QJATc

Q,=CpxAT, 144

(3)

(4) (5)

TABLE I VALUES OF .dHn FOR THE REACfiON OF HC104 WITH NaOH AT to• (RUNS 1-18) AND 40° (RUNS 19-38)

Run No.

C9 (calfdeg)

p.= 0.03532 1 194.33 194.03 2 194.05 3 4 194.15 5 193.69 6 193.66

Q. (cal)

.dT, ("C)

Q, (cal)

H 2 0 formed (mmo/es)

-.dHn (kca/fmole)

-11.981 -15.317 -27.162 -17.100 -15.980 -20.632

0.4706 0.4718 0.4706 0.4707 0.4706 0.4700

-91.453 -91.541 -91.321 -91.386 -91.151 -91.020

6.4969 6.4969 6.4969 6.4969

Average

14.076 14.090 14.056 14.066 14.106 14.086 14.080

(0.004) (0.010) (0.024) (0.014) (0.026) (0.006) ±0.018

6.4619 6.4619

(Dev)

Jl. = 0.01432

193.98 193.99 193.73 193.66 194.37

-17.890 -21.621 -14.579 -13.405 -16.415

0.1903 0.1901 0.1901 0.1901 0.1901

-36.919 -36.883 -36.824 -36.814 -36.951

2.6086 2.6086 2.6086 2.6086 2.6086 Average

14.153 14.139 14.116 14.113 14.125 14.129

(0.024) (0.010) (0.013) (0.016) (0.004) ±0.017

p.=0.00985 193.71 12 13 194.02 14 193.90 15 193.94 16 193.96 193.93 17 18 194.08

-30.253 -21.413 -15.825 -25.901 -24.407 -17.767 -18.378

0.1314 0.1319 0.1315 0.1319 0.1315 0.1318 0.1315

-25.451 -25.587 -25.488 -25.588 -25.511 -25.566 -25.526

1.8050 1.8050 1.8050 1.8050 1.8050 1.8050 1.8050 Average

14.100 14.176 14.121 14.176 14.133 14.164 14.142 14.144

(0.044) (0.032) (0.023) (0.032) (0.011) (0.020) (0.002) ±0.029

p.=0.02480 19 191.61 20 191.48 21 191.39 22 191.06 23 191.06 191.38 24 25 191.35

-35.822 -37.162 -28.373 -27.742 -31.061 -25.902 -25.536

0.2987 0.2982 0.2985 0.2989 0.2988 0.2986 0.2982

-57.225 -57.103 -57.135 -57.109 -57.082 -57.147 -57.063

4.3965 4.3965 4.3965 4.3965 4.3965 4.3965 4.3965 Average

13.016 12.988 12.996 12.990 12.984 12.998 12.979 12.993

(0.023) (0.005) (0.003) (0.003) (0.009) (0.005) (0.014) ±0.012

p.=O.Ol429 26 192.20 27 192.14 28 192.20 29 192.20 30 192.23 31 192.76

-13.481 -13.506 -21.217 -10.301 -13.456 -27.529

0.1743 0.1745 0.1743 0.1740 0.1737 0.1734

-33.499 -33.537 -33.508 -33.437 -33.390 -33.433

2.5916 2.5916 2.5916 2.5916 2.5916 Average

12.926 12.941 12.929 12.902 12.884 12.901 12.914

(0.020) (0.035) (0.023) (0.004) (0.022) (0.005) ±0.021

0.9493 0.9493 0.9493 0.9493 0.9493 0.9493 0.9493 Average

12.858 12.804 12.887 12.826 12.820 12.830 12.826 12.836

(0.022) (0.032) (0.051) (0.010) (0.016) (0.006) (0.010) ±0.028

7 8 9 10 11

2.5916

Jl. =0.00536

32 33 34 35 36 37 38

190.99 190.91 190.91 190.91 191.15 190.91 190.91

-20.540 -9.943 -11.579 -12.669 -11.760 -11.831 -11.611

Thermochim. Acta, 4 (1972)

0.06391 0.06367 0.06408 0.06378 0.06367 0.06380 0.06378

-12.206 -12.155 -12.233 -12.176 -12.170 -12.180 -12.176

145

in which A and B are thermistor constants determined by thermistor calibration, RT. =resistance before the reaction, RT2 =resistance after the reaction, R 81 = resistance before electrical calibration, R 82 = resistance after calibration, Qc = the total

heat input from the heater during calibration, Ehtr = voltage across the voltage divider as measured by the K-3 potentiometer, Estd =voltage across the standard resistor, k =apparatus constant, t =time of heat flow during electrical calibration, CP =heat capacity of calorimeter vessel and contents at constant pressure, A Tc = change in temperature during the calibration, Qr =the heat resulting from the chemical reaction, and A Tr = change in temperature during the reaction. The constant k in Eqn. (3) was calculated to be 0.14326 amp-calfjoule-volt. Only AT., Qc, CP, and Qr values are reported here; however the remaining data are available 21 . RESULTS

Values of AHn at 10° and 40°, calculated from data obtained in this study for the reaction of HC104 with NaOH, are plotted vs. J1°· 5 in Figs. I and 2, respectively. The probable error (two-thirds of the standard deviation) is indicated by the size of each bracket. Extrapolation of the plots to Jl = 0 results in AH~ values of 14.216 and 12.695 kcalfmole at 10° and 40°, respectively. The estimated uncertainties of the AH~ values are ±0.020 kcalfmole.

14.20

"'~ '

14.15

0

~

:{ 14.10
14.05 -

0.0

0.050

0.100

0.150

0.200

VjJ Fig. I. Plot of - LJHn vs.

y fl at 10 °C.

DISCUSSION

The AH~ values determined in this study agree well with the interpolated values obtained from AH~ values reported by Leung and Grunwald 14 and together with those of Leung and Grunwald form a consistent set of data form which AH~ values may be obtained over the temperature range 0-55°. 146

., 0

E

..... c 0

-"'

:f
0.0

0.050

0.100

0.150

0.200

ff Fig. 2. Plot of -L1Hn vs.yp, at 40°C.

The lack of agreement between the present results and those of Vasil'ev and Lobanov 12 is not unexpected since their experiments were conducted in rather high ionic strength regions and their stated purpose was not to determine AHf values at several temperatures (even though the data were reported as such) but rather to "test experimentally the applicability of the equation proposed by one of the present authors (Vasil'ev 16) for the calculation of the standard heat change from direct calorimetric data." Their results provide an interesting and useful relationship involving .a, temperature, and AHi. Unfortunately, they report AHf values only at 18° and 25° although heat of neutralization data were obtained from 0 to 70°. Their AH~ values at 18° and 25° agree well with previously reported values suggesting that their data at high .u values at the other temperatures are valid. The values that they report as AH~ values at temperatures other than 18° and 25°, however, should not be compared with those of this or other studies done in low ionic strength media. The AHt value at 25° reported by Anderson et a/. 17 , compares favorably with that reported here; however, the values at 10° and 40° reported by them are 300 and 150 calories, respectively, lower than the corresponding values reported in this study. The differences in the values reported in the two studies at both 10° and 40° are larger than can be accounted for by experimental uncertainty. The temperature-dependent equation used by Harned and Owen 1 9 to predict AHf values is AH~ (calc.)= 23984.15-23.497T-0.039025T 2

(6) 14

The data of the present study and those of Leung and Grunwald suggest that at temperatures near 10° Eqn. (6) predicts AHf values in agreement with accepted AHf calorimetric values; however, good agreement between Eqn. (6) and calorimetric values is not obtained at temperatures near or greater than 25°. Thermochim. Acta, 4 (1972)

147

A LJH~ value of 13.522 kcalfmole has been attributed to Ackermann 10 • 12 ; however, such is not the case. This value was calculated an reported by Harned and Robinson 2 2 and was used, not reported, by Ackermann 18 to evaluate an integration constant in an equation for LJH~ which he obtained by integrating the equation LJC~ = -806.529+4.4663T-0.00653T 2 (7) Ackermann obtained this equation from his heat capacity data and had he used the value for LJH~ at 25° of 13.337 kcalfmole, he would have obtained the following temperature-dependent equation for predicting LJH~ values AH~ = 112989.62-806.529T+2.23315T2 -0.002177T 3 (8) Values of LJH~ predicted from this equation agree reasonably well with those obtained calorimetrically near 25° and below, but are in poorer agreement with those reported at higher temperatures. The equation seems to predict LJH~ values better than Eqn. (6). Larson and Hepler 2 0 , utilizing data summarized by Parker 2 3 , obtain the following relationships (9) AH~ = 69,280-321.8T+0.45T2 (10) LJC~ = -321.8+0.9T

• 14.620 15

14.50

14.555 14

14.216 (Thio otudy)

.,

13.866 14

0

13.721 13

E

'0

13.69512

13.63015

0

.><

113.52

~.

:x:
24

8

13.33710 13.3369

l

13.33611 13.336

{/

I

13.50 6 ---13.36712

~{13.34915 13.346

(This study}

13.334 14

12.928 12.806

15

14

• 12.695 (Thio otudy) 12.467 14

20 30 Temperature,

•c

Fig. 3. Plot of AH~ of H20 vs. temperature.

148

1.0

-""'

~

s

,..... ""'

~

~

~·

s.

~

~

~

11.950

12.928 12.71" 12.467

13.334

14.998 14.555 14.19" 13.866

Leung and Grunwald 14

13.349

13.695

Vasil'ev and Lobanov 12

12.103

12.806

13.630 13.346

14.620

Grenthe et. af.1 5

12.695

13.336

14.216

This study

LIH: values (kca/fmole) obtained calorimetrically

"Interpolated value. bExtrapolated value.

0 5 10 15 18 20 25 30 35 40 45 50 55

T("C)

15.001 14.564 14.191 13.872 13.702 13.596 13.352 13.129 12.916 12.703 12.478 12.230 11.950

Calculated from Eqn. 10

13.744 13.520 13.272 13.025 12.768 12.525 12.275

14.645 14.435 14.198 13.980

From e.m.f. data 19

LIH: values (kcalfmole)

VALUES OF LIH:, LIG;, AND LIS; FOR THE HEAT OF IONIZATION OF H 2 0

TABLE II

7.464b

0.1135 0.1847 0.2923 0.4521 0.5770 0.6808 1.008 1.462 2.084 2.918 4.012 5.450

Values 19 for ionization constant of HzOX J014

18.680 18.753 18.831 18.914 18.970 19.004 19.095 19.192 19.291 19.395 19.503 19.613 19.711

LIG; (kcal/mole)

-13.469 -15.060 -16.388 -17.497 -18.093 -18.446 -19.263 -19.998 -20.687 -21.369 -22.081 -22.844 -23.651

LIS; (gibbs)

Larson and Hepler believe these equations to be valid in the temperature range near 25° where d(LIC;)/dT = 0.9 calfdeg 2jmole. The calorimetric data obtained in this study and those of Leung and Grunwald suggest that for calculating LIH~ values, Eqns. (9) and (10) are limited to the range 0-35°. Using the data of this study, that of Leung and Grunwald 14, and the LIH~ value at 18° reported by Vasil'ev and Lobanov12, the following temperature-dependent equation for LIH~ is obtained LIH~ = 448.5945-4.160828T+0.01337779T2-0.0000144844T 3 (11) Values for LIH~ over the temperature range 0-55°, calculated from this equation, are given in Table II together with LIG~ values and LIS~ values calculated from the relationship Ll G~ = LlHf- T LlSf

(12)

where at each temperature, LIH~ was calculated from Eqn. (II). Eqn. (II) is graphically represented in Fig. 3.as a part of LIH~ values of water vs. temperature. Other reported values for the heat of ionization of water, LIH~, have also been included in Fig. 3 in order to provide rapid access to these frequently used values. For each LIH~ value, the original literature reference is given. REFERENCES 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24

T. W. Richards and A. W. Rowe, J. Am. Chern. Soc., 44 (1922) 684. T. W. Richards and L. P. Hall, J. Am. Chern. Soc., 51 (1929) 731. F. D. Rossini, J. Res. Nat. Bur. Std., 6 (1931) 847. K. S. Pitzer, J. Am. Chern. Soc., 59 (1937) 2365. G. Kegeles, J. Am. Chern. Soc., 62 (1940) 3230. T. Davies, S. S. Singer, and L. A. K. Staveley, J. Chern. Soc., (1954) 2304. H. S. Harned and B. B. Owen, Chern. Rev., 25 (1939) 31. H. M. Papee, W. T. Canady, and K. J. Laidler, Can. J. Chern., 34 (1956) 1677. L. Sacconi, P. Paoletti, and M. Ciampolini, Ric. Sci., 29 (1959) 2412. J.D. Hale, R. M. Izatt, and J. J. Christensen, J. Phys. Chern., 67 (1963) 2605. C. E. Vanderzee and J. A. Swanson, J. Phys. Chern., 67 (1963) 2608. V. P. Vasil'ev and G. A. Lobanov, Russ. J. Phys. Chern., 41 (1967) 434; [original ref. in Russian, Zh. Fiz. Khim., 41 (1967) 8381. F. D. Rossini, J. Res. Nat. Bur. Std., 6 (1935) 855. C. S. Leung and E. Grunwald, J. Phys. Chern., 74 (1970) 687. I. Grenthe, H. Ots, and 0. Ginstrup, Acta Chern. Scand., 24 (1970) 21. V. P. Vasil'ev, Russ. J. Phys. Chern., 41 (1967) 61; [original ref. in Russian, Zh. Fiz. Khim., 41 (1967) 1211. K. P. Anderson, D. A. Newell, and R. M. Izatt, Inorg. Chern., 5 (1966) 62. T. Ackermann, Z. Electrochem., 62 (1958) 41 I. H. S. Harned and B. B. Owen, Physical Chemistry of Electrolytic Solutions, 3rd edn., Reinhold, New York, 1958, p. 754. J. W. Larson and L. G. Hepler, in J. F. Coetzee and C. D. Ritchie, (Eds.), Solute-Solvent Interactions, Marcel Dekker, New York, 1969, p. 6. G. L. Kimball, M. Sc. Thesis, Brigham Young University, May 1972. H. S. Harned and R. A. Robinson, Trans. Faraday Soc., 36 (1940) 973. V. B. Parker, National Bureau of Standards Data System, NSRDS-NBS 2, U. S. Government Printing Office, Washington, D.C. 20402. L. Avedikian, Bull. Soc. Chim. Fr., (1966) 2570.

150