E.M.F.STUDIES IN AQUEOUS SOLUTIONS AT ELEVATED TEMPERATURES
2395
Electromotive Force Studies in Aqueous Solutions at Elevated Temperatures. VI.
The Thermodynamic Properties of HCl-NaCI Mixtures'
by M. H. Lietzke, H. B. Hupf,2and R. W. Stoughton Department of Chemistry, University of Tennessee, Knoxville, Tennessee, and Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee (Received February 18, 1966)
The activity coefficient of HCI in HCl-NaCI mixtures has been studied to 175'. At constant temperature and ionic strength the logarithm of the activity coefficient of HCI in the mixtures varies linearly with the molality of NaC1. The activity coefficient of NaCl in the mixtures was calculated by using the parameters describing this variation and those for the variation of the activity coefficient of NaCl with ionic strength in pure NaCl solutions. The activity coefficient behavior observed in the HCl-NaC1 mixtures is compared with that observed in the previously studied HBr-KBr mixtures.
I n a previous paper3 in this series the original e.m.f. data obtained in HCl solution^^^^ were used to recalculate the thermodynamic properties of these solutions in a manner consistent with the assumption that over the temperature range studied (25-225") the value of ACp is a constant. This assumption permitted all of the data to be used simultaneously in efkimating both the standard potential of the Ag, AgCl electrode as a function of temperature and the parameters describing the activity coefficient of HC1 as a function of temperature and ionic strength. In the present work these data have been combined with measurements of the e.m.f. of the cell, Pt-H2(p)[HCl(m2), NaCl(m3) AgCl, Ag, and of the osmotic coefficient of NaC16 to calculate the thermodynamic properties of both HC1 and KaCl in HCl-NaCl mixtures. In addition, the original e.m.f. data in the HBr-KBr system' were used to recalculate the thermodynamic properties of HBr-KBr mixtures in a manner consistent with the present calculations on HCl-NaC1 mixtures, so that a direct comparison of these two systems could be made.
1
Experimental The experimental apparatus and the preparation of electrodes and solutions were the same as described previously. 4 , 8 The e.ii1.f. measurements were carried out in the teniperature range 25-175" in solutions of total ionic strength 0.4 and 1.0 in which the ratio of
HCl to NaCl was varied. The e.m.f. values taken at the same temperature were reproducible to ca. k0.5 niv. In general, they were more reproducible in the solutions containing a higher fraction of HCI. No drift of e.m.f. with time was observed.
Results and Discussion In treating the results, the hydrogen pressure was calculated by subtracting the vapor pressure of the solution from the observed total pressure, while the vapor pressure of the solution was obtained by taking the vapor pressure of pure water a t the temperature of measurement from the steam tablesg and correcting (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) This paper is based in part on a thesis by H. B. Hupf presented to the Department of Chemistry of the University of Tennessee in partial fulfillment of the requirements for the M.S. degree, March
1965. (3) M. H. Lietzke and R. W. Stoughton, J . Phys. Chem., 68, 3043 (1964). (4) K. S.Greeley, W. T. Smith, Jr., R. W. Stoughton, and M. H. Lietzke, ibid., 64, 652 (1960). (5) R. S. Greeley, W. T. Smith, Jr., M.H. Lietake, and R. W. Stoughton, ibid., 64, 1445 (1960). (6) E. R. Gardner. E'. T. Jones, and H. J. de Nordwall, Trans.
Faraday SOC..59, 1994 (1963). (7) hl. H. Lietzke and R. W-.Stoughton, J . Phys. Chem., 67, 2573 (1963). (8) M. B. Towns, R. S. Greeley, and (1960).
M. H. Lietzke, ibid., 64,
1861
(9) E. Schniitt, Ed., "VDI-Wasserdampftafeln." 4th Ed., SpringerVerlag, Berlin, 1956, pp. 15-20.
Volume 69, Number 7
July 1966
2396
M. H. LIETZKE, H. B. HUPF,AND R. W. STOUGHTON
Table I : Values of the E.m.f. in Volts for the Cell, Pt-Hz(p)lHCl(m2), NaCl(mr)/AgCl, Ag, and Deviations" of the E.m.f. Values Calculated from Smoothed Activity Coefficients t.
mi
ms
25
0.0102
0.3903
0.3782
-
QC.
60
90
125
150
...
...
0.3488 +7
0.3334 -2
0
175
0.0309
0.3795
0.3490 -1
0.3404 -6
...
...
0.2913 - 13
0.2723 -11
0.1015
0,2975
0.3191
0.3077 0
0.2932 +5
0.2709 +11
0.2513
0,2294 +7
0
+a
0.2051
0.1986
...
0.2874 +1
0.2710 +3
0.2458 0
0.2246 -4
...
0.0302
0.9628
0.3266
0.3158 -2
0.3032
fl
+8
0.2818 -3
0.2650 -1
0.2460 -1
0.0971
0.8877
0.2961 -4
0.2822 -4
0.2660 -1
0.2421 -2
0.2223 -5
0.2010 -4
0.2484
0.7467
0.2723
0.2552 +2
0.2360 -2
0,2100 +3
0.1891
0,1660 +I1
0.2357 -3
0.2150 -8
0.1870 -5
...
+8 0.4824
,..
0.4950
+8
...
O The deviations are given below each e.m.f. as observed e.m.f. values less the values calculated from smoothed activity coefficients. Thus, a positive deviation indicates that the e.m.f. reported here is algebraically larger.
for the presence of NaCl and HC1 in solution by Raoult's law. Each e.m.f. value was corrected to 1.00 atm. of hydrogen pressure by subtracting (RT/25) In fH1, where the hydrogen fugacity fH2 was taken equal to the hydrogen pressure. The solubility of AgCl was neglected, and the ionic strength was taken to be equal to the sum of the HCl and NaCl molalities. The corrected e.m.f. values E a t each ionic strength were plotted as a function of temperature and the values corrected to the round values of the temperature, 25, 60, 90, 125, and 150". The temperature of measurement was never more than 1" from the corresponding round temperature. These corrected values are given in Table I. The activity coefficient ylt of HCl at each temperature and set of concentrations in the mixtures was evaluated by using the Nernst equation and previous values3 of the standard potential E " of the Ag, AgCl electrode.
E
=
Eo -
RT
- In
5
+
[mz(mz m3)] -
2RT
-In y&
5
(1)
In this equation m2 and m3 are the molalities of HC1 and NaC1, respectively, while T i s the absolute temperature, R the gas constant, and 5 the Faraday. A plot of In y* us. ionic strength fraction of NaCl was The Journal n j Physical Chemistry
made a t each temperature and at the total ionic strengt,hs 0.4 and 1.0. Also included in these plots were the values for pure HC13 a t all temperatures and for 0.01 m HCI in NaC1'0 at 25 and 60". (The values at 60" were obtained by extrapolations of data from 0 to 50°.) In all cases the plots were linear within experimental error in conformity with Harned's rule. Expressions for yi of HCZ and NaCl in the Mixtures. The activity coefficients of HCl were smoothed as to HCl and NaCl concentrations and temperature and those of NaCl were evaluated as follows. As shown p r e v i ~ u s l y the , ~ excess free energy of the solution G", i.e., excess over the molality and Debye-Huckel terms, may be expressed as
where n represents the numbers of moles of each solute, 20 is the number of kilograms of water, and the sums are taken over each solute i, j , k = 2 (for HC1) to 3 (for NaC1). B and C are interaction coefficients to be determined from the data. (lo) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd Ed., Reinhold Publishing Corp.. New York, N. Y., 1958, Appendix A, p. 748.
E.M.F.STUDIESIN AQUEOVS SOLUTIONS AT ELEVATED TEMPERATURES
made to express both the B and C coefficients with equations of the type
Then for either solute component In y t
=
IA(g)= 2 C B f , m l + 3 C C f j , m t m j
2 bn, RT
i
(3)
where q = 2 or 3. The coefficient 2 of the first sum results from the fact that dnq2/bn,= 2n, and from the fact that since BZ3n2n3is indistinguishable from B32. n3n2 they may be combined; the coefficient 3 in the second sum rrsults from similar reasoning. (In eq. 3 the second sum is a double sum over i and j . ) Thus, for HC1
+
+ 3 C n z m ~+~
+
+
6 C ~ ~ 3 m m3C~33m3~ = ~ ~ [ B z (B23 z (c22Z
+
c 2 3 3
- 2c223)~32]( 4 )
where the coefficient in parentheses of the x3* term is zero according to Harned’s rule (ie., that In yz varies linearly with 4 , which the data have been shown to obey. Here z represents ionic strength fraction, while m3. If Harned’s rule is the ionic strength I = m2 assumed to hold for HC1 then In yseand In ~3~ become
+
In yze
=
2I[B22
+ ( B z -~ B&31 + 312[c22z+
2(c223
- czz2)~3]
(5)
and In
-13~
+ (B23 2(Cm + =
21 [B33
-
C333)r2
B33) 1 5 2 (c333
+
+ 312[C333 + e223
-
2Cza3).h2] ( 6 )
and hence the total In y, is given by adding the DebyeHuckel term to eq. 5 or 6. The Debye-Huckel term was assumed to be identical for HCl and XaCl with the denominator parameter set equal to 1.5 at each temperature. Hence, a t each temperature In y e
=
In y q e - Sp1”&/(1
+ 1.5dT)
(7)
where S is the limiting slope and p is the density of water which corrects the ionic strength to a volume basis, as required by the Debye-Huckel theory. In the study of HBr-KBr mixtures’ the activity coefficients of HBr were smoothed as to temperature using expressions of the type
Bi,
=
Pi,
B,,
ij
In y2e = 2BZ2na2 2Bz3m3
2397
+ B”,,/T and C f j , = C’rj, + C ’ l l j , / T (8)
in eq. 5. These parameters gave temperature-independent excess free enthalpies and entropies. In the present work on HCl-NaCl mixtures these same expressions were first used to smooth the activity coefficients of HC1 as to temperature. The resulting fit was about the same as that obtained in the case of HBr. In an effort to secure a better fit, an attempt was
=
B’,,
=
C’ijq
+ B”,,/T + B”’,, log T
(9)
and C,j,
+ C”fjp/T +
C”’ijp
log T
(9’)
where the parameters B’, B”,B”’, C’, C”, and C”’ were to be determined by the method of least squares. Convergence difficulties were encountered, however, when eq. 9 and 9’ were used in eq. 5 to fit the activity coefficients of HCl, probably because the parameters in the expression for C,,, were too strongly correlated. g expressed as in eq. 10 with only two When C L J was
parameters and eq. 9 and 10 were used in eq. 5 , then no difficulties were encountered in the least-squares determination. Rioreover, the least-squares fit of the data was much better when eq. 9 and 10 were used than when the ex(variance of fit of 2.0 X pressions given in eq. 8, with two fewer parameters, were used (variance of fit of 4.3 X lop5). Equation 9 gives rise to excess enthalpies varying linearly with temperature and excess entropies varying linearly with In T , while eq. 10 is again consistent with temperature-independent values. In the ionic strength range studied (to 1.0 m) the contribution of the B terms is much more important than that of the C terms (hence, the difficulty in determining as many parameters in the C coefficients). The values of B’22,B”22, B”’22, B’23, B”23, B”’23, C’~ZZ, C”222, c’223,and C‘’223 were obtained directly by the least-squares fit, while the values of c’233 and c”233 were obtained by the application of Harned’s rule: CZZZ C233 - 2C223 = 0. The additional paraineters needed for calculating yse by eq. 6, namely, the parameters in the coefficients B33 and C333(for pure KaC1 solutions), were evaluated by the method of least squares using osmotic coefficient data6 on XaC1 solutions. I n this fit it was possible to express both B33 and C333with equations of the type given by eq. 9 and 9’, presumably because data over a wider range of concentrations (to 3 m ) were available. The parameters for calculating the various B and C coefficients are given in Table 11. Activity coefficients of HC1 and SaCl in the mixtures ( I = 0.4 and 1.0) calculated using these parameters are shown as the solid lines in Figures 1 and 2 . The values of the activity coefficient of HCl calculated froin the observed e.m.f. values are shown as data points in Figure 1. The activity coefficient of HC1 in the mixtures varies more rapidly with temperature, the smaller the ionic
+
Volume 69, Sumber 7
J u l y 1966
M. H. LIETZKE,H. B. HUPF,AND R. W. STOUGHTON
2398
L
I a . 4
25'
-
60'
i*850k-901
90"-
425. 450' '750
J
1 -u i,750
i.750
r
h '
-
1
I ' 1.0
0
-
C)
0
-
150'-
O C
-4.750 -
c
'75.-
O :
0
I
1
?
I 'HCl
Figure 2.
Table I1 : Parameters of the B and C Coefficients (eq. 9 and 10) for the HCl-NaCl System over the Range 25 t o 175"
B'22 R'23
1,86790 2 , 72576 B'33 = 2.89603 C'rpz = 0 0258302 C'223 = 0,0132623 C'233 = 0.0006944 C'333 = -0,091257 = =
B"22
=
B"23
=
-59.3857 B'"22 = -0,65366 -121 ,853 B"'23 = -0.91431 B"33 = -151,120 B"'33 = -0,96167 C"2m = -6.73533 C"253 -4.90705 C"233 = -3.07877 C"333 = 5.33016 C"'3.23 0.030096
strength fraction of SaC1. This general behavior is consistent with previous observations10Il1over a smaller temperature range. As can be seen, the activity coThe Journal of Phvsical Chemistry
Log
7
~ us.~X R~C in ~1HC1-NaC1
mixtures.
efficient of NaCl in the mixtures does not obey Harned's rule. Values of the e.m.f. E were calculated, using the previously determined E" values and the €3 arid C values for the smoothed activity coefficients (Table 11), for each experimental point. The algebraic difference between the observed E values and those calculated are given below the observed E values in Table I. It is interesting to compare the values of log yz and log 73 obtained in the present study with values coniputed from the parameters reported by Harned.l* (11) X I . (1964).
H. Lietzke and R. W. Stoughton, J . Tenn. Acad. Sci., 39, 30
(12) H. S.
Herned, J . Phys. Chem., 63, 1299 (1959).
E.M.F.STUDIES I N
AQUEOUS
SoLUTIoNS AT ELEVATED TEMPERATURES
The comparison can be made only a t I = 1.0 a t 25” since Harned’s values span the range Z = 1.0 to 3.0 a t temperatures of 0 to 50’. The results are shown in Table 111.
2399
was 2.1 X while the use of eq. 9 and 10 gave a variance of fit of only 2.1 X The effect is most pronounced when log Y K B ~is calculated and plotted us. the fraction of HBr in the mixture a t I = 1.0. The newer plots are much more nearly linear than were the plots previously given.
Table 111: A Comparison of the Values of Log y2 and Log y3 Obtained in the Present Study with Those Reported by Harned at Z = 1.0 and 25’ Log------y
7 -
x
3a
0.25 0.50 0.75
Present study
Harned
-1,9010 -1.8932
-
1.9000
-
-1,8921
1,8852
1,8843
Log
I----f-------
XP
0.25 0.50 0.75
Present study
1,8300 1.8457 1.8675 -
Harned
-
1.8310 -1.8452 1.8595
-
Table IV : Parameters of the B and C Coefficients (eq. 9 and 10) for the HBr-KBr System over the Range 25 to 100’ B‘tf = 3.95636 B I Z 3 = 2 57573 B’3aa = 0 0689068 C’zzz = 0.00216642 C’ZZ~= 0.0141473 C’233 = 0 02612818 C’jra = -0.00133241 a
B” B”
zz = - 185.972 23 = - 103.558
B”3j
=
B”’zz = B”’t3
- 1.31428
= -0 888431
-21.21950
C”zzz = -1.87841 C”223
= - 5.03595
C”233
= -8.19349
C”333
=
0.715351
The osmotic coefficients of KBr were not refitted. eters are for the B expression given in eq. 8.
Hence, these param.
Fraction of either component 2 or 3 in the mixture.
The agreement between the two sets of values of log is very good (within about 0.1%). Similar agreement between the values of log y3 is observed a t the two lower fractions ( X , ) of HCl. The values of log 7 3 a t Xz = 0.75 differ by about 1%; this may be due in part to the fact that a different set of values of osmotic coefficients of XaC1 over a wide range of temperatures (25 to ZOO’) was used in evaluating the activity coefficient of pure NaCl solutions. The relationship between the B and C coefficients as defined by eq. 9 and 10 and the cy-coefficient of Harned’s rule as well as the expressions for the partial molal free energy a,, the partial molal enthalpy I?,, and the partial molal entropy S, for component q may be calculated using the expressions previously reportedlo in the study of HBr-KBr mixtures. When the activity coefficients of HBr in the HBrKBr system were refitted using eq. 9 arid 10 in eq. 5 , then the parameters shown in Table I V were obtained. These parameters provide a significantly better fit of the activity coefficients than did the expressions in eq. 8, the paraiueters of which were given in the earlier paper.’ (When eq. 8 was used, the variance of fit yz
When the two systems are compared, it is seen that plots of log Yacld ZJS. fraction of salt in the mixtures are linear a t all temperatures a t both Z = 0.4 and 1.0 in conformity with Harned’s rule. In the HBr-KBr system these plots have a negative slope a t all teniperatures, whereas the corresponding plots in the HClSaCl system have a negative slope at I = 0.4 a t 25” and a positive slope at the higher temperatures. At I = 1.0 the plot of log YHCl decreases a t 25, 60, and go”, becomes almost flat a t 125”, then increases a t 150 and 175”. In the HC1-SaCl system the plots of log 7 ~ us. the fraction of HC1 in the mixtures are concave upward a t all temperatures a t both Z = 0.4 and 1.0, the curvature becoming more pronounced a t the higher ionic strength. In the HBr-KBr niixtures the plots of log y K B r us. the fraction of HBr a t Z = 0.4 are almost linear a t 25, 60, and 90” ; osmotic coefficient data are not available on KBr solutions above 100”. At Z = 1.0 the 25” plot is almost linear, while at the higher temperatures the curves are concave downward. Acknowledgment. The authors wish to express their sincere appreciation to R. W. Whitfield and W. D. Armstrong for their assistance in making the e.m.f. measurements.
Volume 69,Nirmber 7
J u l g 1965
~
~
1
