910
J. N. BUTLER, P. Hsu, AND J. C. SYNNOTT
Activity Coefficient Measurements in Aqueous Sodium ChlorideSodium Sulfate Electrolytes Using Sodium Amalgam Electrodes
by James N. Butler, Philomena T. ,“I
and John C. Synnott
Tyco Laboratories, Ine.,Waltham, Massachusetts 02164
(Received August 29, 1966)
Measurements of the activity coefficient of NaCl in NaC1-NazS04 electrolytes have been made using the cell Na, HglNaf, C1-, S042-IAgC11Ag,and have been compared with literature values obtained using cation-sensitive glass electrodes. Harned’s rule is shown to be obeyed for both components within experimental errors over the ionic strength range from 0 to 6 m.
Introduction The activity of NaCl in a multicomponent salt solution can be obtained by measuring the emf of a sodium amalgam-silver chloride cell Sa(Hg)I NaC1, MX, HzOl AgCll Ag where MX is a salt whose ions do not interfere with the reversibility of the two electrodes, such as NkS04. By using two identical cells, one containing only KaCl solution and the other containing the multicomponent salt solution, the activity of NaCl in the multicomponent solution can be compared directly with a solution of known activity. The amalgam composition need not be known accurately provided it is the same for both cells. This method has been used to determine the activity coefficients of KaC1 in NaC1-KaOH electrolytes, but has not been applied to other multicomponent systems. Recently, Lanier2and Gieskes3 have reported activity coefficient data for XaC1 in multicomponent electrolytes obtained using a cation-sensitive glass electrode. The results reported in this paper are compared with those obtained with the glass electrode, and are in general agreement.
to clean the cell and to prepare all solutions. To minimize effects due to corrosion of the sodium amalgam, the pH of the solution was adjusted t o 11 or 12 with NaOH of accurately known concentration. Solutions were deoxygenated by passing hydrogen over a large platinum black electrode in the solution for several hours. The hydrogen was obtained by electrolysis of water in a cell with a silver-palladium cathode and contained less than 0.1 ppm of oxygen. Silver-silver chloride electrodes were prepared by the thermal electrolytic process4 and aged for several weeks in 1 m NaCl before use. Because of the large mass of the electrode (0.2 g), up to 1 hr was required to reach equilibrium with the solution, but after that the potential was stable. Normally, the electrodes were equilibrated overnight with the solution to be measured. Bias potentials between different electrodes were less than 0.05 mv and changed by less than 0.005 mv over periods of several days. Sodium amalgam was prepared by electrolysis of saturated NaOH solution at a mercury cathode and stored under a prepurified argon atmosphere. The amalgam was analyzed by treating it with standard H2S04 and back-titrating with NaOH. A single reservoir fed two dropping amalgam electrodes in the
Experimental Section Solutions were prepared from reagent grade salts (Fisher Scientific Co.). The sodium chloride stock solutions mere analyzed for chloride by the Volhard method and the sodium sulfate stock solutions were analyzed gravimet,rically by precipitation as barium sulfate. Triply distilled conductivity Water Was used The Journal of Physical Chemistry
(1) H. 9. Harned and M. A. Cook, J . Am. C,\W.
SOC.,
59, 1890
(1937)* (2) R. D. Lanier, J . Phys. Chem., 69, 3992 (1965).
(3) J. M. T. M. Gieskes, J . Physik. Chem. (Frankfurt), 5 0 , 78 (1966). (4) D. J. G. Ives and G. J. Janz, “Reference Electrodes,” Academic Press, New York, N. Y., 1961, Chapter 4.
ACTIVITYCOEFFICIENT MEASUREMEKTS IN AQUEOUS KaC1-NazSOc
test cell and reference cell. The electrodes were prepared by attaching l-cm lengths of polarographic capillary to a l-mm i.d. capillary stem using thinwalled Teflon tubing. In this way the capillary could easily be changed when it became plugged with solid material from the amalgam. The most precise measurements were obtained with capillaries which were kept scrupulously dry until after the amalgam was flowing. Drops with a maximum diameter of 1 mm were formed at a rate of approximately one per second. The cell was constructed so the drops from the capillary fell through a 4-mm diameter hole in the bottom of the cell, through a gas space, and into a waste compartment. Solution was prevented from flowing through this hole by a slight back pressure of hydrogen. When it was desired to drain the cell, a vacuum was applied to the waste compartment, which drew the solution through the hole in the bottom of the cell. Fresh deoxygenated solution was then added from a solution reservoir without opening the cell to the air. All measurements were conducted in a thermostat at 25.00 f 0.02”. Potentials were measured with a Leeds and Northrup Model K-3 potentiometer using a Honeywell Model 104W1-G galvanometer with a sensitivity of 0.001 pa/mm and a response time of approximately 0.2 sec for full-scale deflection (40 mm). The standard cell (Eppley Laboratory Type 100) was calibrated against a U. S.National Bureau of Standards cell and guaranteed to have the value 1.01922 f 0.00005 v. The potential of the combined cell Ag/AgCl/IYaCl,HzO(Sa,HgNa, HglNaC1, Na?SO4, H201AgClIAg was measured during the period when the drops of both amalgam electrodes were nearly fully formed; such potentials were reproducible to f0.02 mv for periods of up to 1 hr under favorable conditions. Changes of solution sometimes had a negligible effect on the potential, but at other times produced changes as large as 0.5 mv. These large changes were attributed to traces of oxygen being admitted to one of the cells and whenever possible, the value taken to be correct was one which remained constant through several changes of solution as well as at least 0.5 hour of amalgam flow.
Results and Discussion The results obtained for emf and the activity coefficients calculated from these values are given in Table I. The mean activity coefficient, y12, of NaCl in the mixed electrolyte was calculated using the equation which follows.
911
where m N a + and m l - are the molalities of Na+ and C1in the mixed electrolyte, m N s + O and nzc1-O are the molalities in the reference solution, and ylois the mean activity coefficient of NaCl in the reference solution. E is the measured emf of the combined cells, R is the gas constant, T is the absolute temperature, and F is the Faraday constant. The electrolyte in the reference cell was in each case the solution listed as “100% ionic strength XaC1,” the first entry in each part of Table I. The other electrolytes were made by mixing accurately weighed amounts of this solution with Na2S04 stock solution of approximately the same ionic strength. To minimize the possible interference from hydrogen evolution at the amalgam electrodes, the solutions were made 0.098 m in NaOH. The ionic strength listed in Table I includes a contribution from the S a O H present; but since this was a constant amount, it was not included in calculating the ionic strength fraction present as NaC1. Thus the stock solution (designated “100% NaCI”) really was 0.098 m in S a O H and 0.986 m in NaCI, making a total ionic strength of 1.084, as listed. The activity coefficients of the stock solutions were calculated using the activity coefficient values for pure KaCl solutions given by Robinson and stoke^,^ together with values of the Harned’s rule constants for NaOHNaCl mixtures obtained by Harned and C0ok.l The replacement of 0.098 m KaCl by SaOH at a total ionic strength of 1.084 m changes log YNaCl from -0.1838 to -0.1864. This corresponds to an emf difference of 0.35 mv, which is of the same order of magnitude as the uncertainty in the literature values for yNsC1. The effect of NaOH on the activity coefficient of XaC1 in solutions containing large fractions of Na2S04may be somewhat different, but no data yet exist by which further corrections may be made. Figure 1 compares our measurements with those made by Lanier2using a cation-sensitive glass electrode. The different value of -log y at 100% KaCl reflects the presence of added NaOH as well as the range of choice for literature values. In most mixed aqueous electrolytes, the activity coefficient of at least one of the components has been found to obey Harned’s r ~ l e . ~ , 6
( 5 ) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and CO. Ltd., London, 1959, Chapter 15 and Appendix
8.10. (6) H. S. Harned and B. B. Owen, “The Physical Chemistry of
Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y.,1958,Chapter 14.
Volume 7 1 , Number 4
March 1067
912
J. N. BUTLER, P. Hsu, AND J. C. SYNNOTT
Table I: Mean Activity Coefficient of NaCl in NaC1-Na2SO4 E1ect)rolytes a t 25” Total ionic strengtha
-
-0.15
Ionic E, mv
-Log
--Log Y *
% NaClb
Y=
cord
1.084 1.085 1.086 1.170 1,090 1.124 1,102 1.089 1.093 1.083
100.00 89.47 74.70 49.93 35.00 24.63 12.13 5.02 2.28 0 90
0 4.53 11.02 26.85 36.10 49.65 70.00 93.94 110.5 132.3
0.1864‘ 0.1938 0.1995 0.2144 0,2169 0.2242 0.2261 0.2272 0.2242 0.173
0.1856 0.1925 0.1976 0.2088 0.2132 0.2186 0.2208 0.2223 0.2189 0.168
3.080 3.072 3.065 3.040 3.020 3.008
100.00 90.01 75.00 49.89 25.06 10.01
0 5.35 15.33 30.94 56.50 83.5
0.1462’ 0.1605 0.1927 0.2133 0.2546 0.266
0,1491 0.1625 0.1943 0.2138 0.2546 0.266
strength
-0.20
-I u 0
x‘ -
0
2
5
~
~
1
2
~
0
0
I=loo,{O 4 9 0 THIS WORK LANIER
(+
+
0
1=3’00m
10
20
30
40
50
60
70
THIS WORK LANIER
80
90
i 100
IONIC STRENGTH % N a C l
Figure 1. Dependence of activity coefficient for NaCl on composition of electrolyte at constant ionic strength and comparison with the data of Lanier.2
’
Based on total Containing 0.098 m NaOH to adjust pH. of NaCl and NazSOa, but excluding NaOH. Activity coefficients of pure NaCl from ref 5, Appendix 8. 10, and Harned rule coefficients for NaC1-NaOH mixtures from ref 1. Corrected to Z = 1.000 for the first set and I = 3.000 for the second set, assuming cy12 = 0.048, and using data for pure NaCl from ref 5.
Duhem relation, it is possible to derive an expression relating a21to aI2which involves only the properties of the pure component electrolyte^.^^^ For KaCl(component l)-Na2SO4(component 2) electrolyte mixtures, this takes the form a21
log
712
= log
710
- a1zXzI
721
= log
720
- a21X1I
(3)
is obeyed as well as eq 2, and making use of the GibbsThe Journal of Physical Chemistry
2 2.3031
- -[2410
(2)
where 7 1 2 is the activity coefficient of component 1 (NaC1) in the mixed electrolyte of ionic strength I , -&‘is the activity coefficient of component 1 alone at ionic strength I (our reference solution), X2 is the ionic strength fraction of component 2 (SaSO4) in the mixed electrolyte, a12 is the Harned rule coefficient, which depends to some extent on the total ionic strength I , but not on the fraction of the second component XZ. From Figure 1 it is apparent that the activity coefficient of NaCl in NaCI-NaZSO4 electrolytes obeys Harned’s rule within experimental error from lOOyo NaCl to 5 or 10% SaC1. The positive deviations at low fractions of NaCl were also observed by Lanier2 and probably reflect a systematic error resulting from the effect of Sod2- ions on the AgCl electrode, not a true thermodynamic deviation from Harned’s rule. Gieskes3 did not make measurements at low fractions of NaC1. If both components of a mixed electrolyte obey Harned’s rule, then log
= 2a12
-
420
- 11
(4)
where c $ ~and ~ c&O are the osmotic coefficientsof the pure electrolytes at ionic strengthI. I n Table I1 are given the values of a12 obtained from our data and the values of a21 calculated from them, together with the values of the osmotic coefficients used in the calculation. Note that the values obtained for the Harned rule coefficients are quite different from those obtained by Lanier.2 If both electrolytes obey Harned’s rule, then thermodynamic cross-diff erentiation relations require that a further test of thermodynamic consistency be satisfied.5j6 The quantity SI
= 6 ~ ~ 1f 2 3 ~ ~ 2 1
(5)
should be independent of ionic strength. Lanier2 found that S’ varied with ionic strength and from this concluded that the activity coefficients of NaS04 did not necessarily obey Harned’s rule. Our data also show that S‘ is different for ionic strengths of 1 and 3 m, but the difference is in the opposite direction to that reported by Lanier. The comparison of values cyIz, a21, and S’is most clearly seen in Figure 2. An estimate of the error in A” is most clearly seen in Figure 2.
913
ACTIVITYCOEFFICIENT MEASUREMENTS I N AQUEOUS NaC1-Ns2S04
Table 11: Activity Coefficient Parameters Parameter a12 a12
I = 1
I = 3
0.0453 0.0605
0.0490 0.0537
Ref
This work 2
Log 701(exptl) Log 701(exptl) Log yol (Brgnsted) theory)
-0,231 -0,243 -0.235
-0.296 -0.307 -0.288
This work 2 2
- 01
Log
-0.059 0.9363 0.717
-0.690 1.042 0.642
5 5 5
-.03
-0,0431 -0,0141
-0.0319 -0.0205
This work 2
0.142 0.321
0.198 0.261
This work 2
720
$1
$3
a21 a21
S' S'
An estimate of the error in S' resulting from all the random and systematic errors in our experimental measurements is approximately f0.05, which implies that within the experimental errors, S' is independent of ionic strength. This conclusion is confirmed by the recent measurements of Gieskes3 at ionic strength 0.7, using a cation-sensitive glass electrode. His three series of measurements gave a12 = 0.0511, 0.0517, and 0.0589, resDectivelv. These values are indicated in ~i~~~ 2. Note that Gieskes' values fall between Lanier's and ours, but agree with both sets within experimentalerror. Note also that Lanier's data can give values of S' which are independent of ionic strength if osmotic coefficients are used which vary by less than 1% from those in Table 11. If S' is assumed to be independent of ionic strength, then the precise dependence of a12 and a21 on ionic strength can be calculated. Combining eq 4 and 5, we obtain a12 a21
= =
+ 3B)/12
(6)
(SI - 3B)/6
(7)
(S'
where B is defined by B=-
2 [2h0 2.3031
$20
- 11
Using tabulated values5 for the osmotic coefficients of NaCl and Na804, B can be calculated as a function of ionic strength and a value for S' can be chosen which best fits the experimental data at all values of ionic strength. I n Figure 2, the broken lines are calculated values of a 1 2 and a21 based on the assumption S' = 0.190. Increasing the assumed value of S' makes both
az'
1
-'O2I
4
-.04L
30
I+
1
A
' 2 1 L 20
- - ---- ----- 0----_-- - _ _ _
0
1
2
3
4
TOTAL IONIC STRENGTH
5
6
(rn)
Figure 2, Variation of the Harried rule coefficients with The quantity s f is by thermodynamic consistencv to be indeDendent of ionic strength if Harned's rule is obeyed. The broken lines were calculated using tabulated values of osmotic coefficients &9 described in the text. Experimental values of this work (a), Laniera (+), and Gieskess (A) are shown.
-
a12and more positive, but does not change the shape of the curves. Thus, if one places more weight on our measurements at 1 m ionic strength, one might choose a smaller value of S', perhaps as low as 0.16. The results of this investigation may be best summarized as follows: eq 2 and 3 can be used to predict the activity coefficients of NaCl and NazSOc in electrolytes containing both components using the tabulated activity coefficients of the pure componentss and taking the Harned rule coefficients to be a 1 2 = 0.048 and aZ1= -0.034. These values may be assumed to hold for any composition from pure NaCl to pure NazSOl and for any ionic strength from 0 to 6, and the calculated values will agree with experimental results within hO.01 in log y . This limit of error is only a factor of 2 or 3 larger than the experimental errors in the measurements and represents a substantial improvement over the assumption that ionic strength alone determines the activity coefficient of a given component.
Volume 71 Number .G March 1967
G. A. CROWDER AND BOBBYR.
914
Acknowledgments. This research was supported by the U. S. Department of the Interior, Office of Saline Water. The authors thank Drs. W. H. RlcCoy and A. B. Gancy for helpful discussions during the course
COOK
of the work and Drs. R. A. Robinson and R. D. Lanier for criticism of the manuscript. A h . Mary L. Meehan assisted in the design of the apparatus and in the preliminary experiments.
Acetonitrile: Far-Infrared Spectra and Chemical Thermodynamic Properties. Discussion of an Entropy Discrepancy
by G. A. Crowder' and Bobby R. Cook Department of Chemistry, West Texas State University, Canyon, Texas
(Received August 51, 1966)
Liquid- and vapor-state infrared spectra in the region 75-650 cm-' were obtained for acetonitrile. The entropy discrepancy a t 298.15"K was shown to result partially from the use of the liquid-state frequency for the skeletal bending vibration. The remaining entropy discrepancy is discussed. A table of the chemical thermodynamic properties of acetonitrile at selected temperatures was prepared.
Introduction The entropy of acetonitrile a t 298.15"K, corrected to the ide:tl gas state at 1 atm, was determined by Putnam, AlcEachern, and Kilpatrick (PMK)2* to be 58.67 f 0.20 cal deg-' mole-'. This value is 0.66 cal larger than the value of 58.01 cal deg-' mole-' calculated by Giinthard and KovatsZbusing the rigid rotatorharmonic oscillator model. This discrepancy suggests an error either in the vibrational assignment or molecular parameters used in the calculation or in the experimental data. The present work was undertaken to examine the discrepancy. The examination consisted of a recalculation of the statistical mechanical entropy using vapor-state wavenumbers and a revised set of molecular parameters and a critical look at the gas imperfection correction and experimental entropy of vaporization.
Experimental Section Far-infrared spectra of acetonitrile were determined at room temperature with a Perkin-Elmer Model 301 spectrophotometer. A stainless steel cell, with path The Journal of Physical Chemistry
length variable in increments of 1-6 m, was used in obtaining the vapor-state spectrum. The sample of acetonitrile was obtained from the Eastman Kodak Co. Infrared spectra in the region 650-4000 cm-' did not show any impurity bands.
Results and Discussion Far-Infrared Spectra. It has been shown that vibrations with a wavenumber lower than about 250 cm-' usually have a lower wavenumber in the vapor than in the liquid statea3 Since the lorn-frequency vibrations contribute the most to the thermodynamic functions, vapor-state values for these vibrational frequencies are necessary in calculations of vapor-state thermodynamic properties. Gunthard and Kovats (1) To whom all correspondence should be addressed at Department of Chemistry, West Texas State University, Canyon, Texas 79015. (2) (a) W. E. Putnam, D. M. McEachern, Jr., and J. E. Kilpatrick, J . Chem. Phys., 42, 749 (1965); (b) H. H. Gunthard and E. Kovats, Helv. Chim. Acta, 35, 1190 (1952). (3) W. G. Fateley, I. Matsubara, and R. E. Witkowski, Spectrochim. Acta, 20, 1461 (1964); G. A. Crowder and D. W. Scott, J . Mol. Spectry., 16, 122 (1965).
