THERMODYNAMIC PROPERTIES OF THE SYSTEM HCL-NACL-II~O
August, 1059
1209
THE THERMODYNAMIC PROPERTIES OF THE SYSTEM: HYDROCHLORIC ACID,SODIUM CHLORIDE AND WATER FROM 0 TO 50° BY HERBERT S. HARNED Contribution No. 1626 from the Department of Chemistry of Yale University, New Haven, Conn. Received February 16, 1969
The activity coefficientsof hydrochlorjc acid in sodium chloride a t 1, 2 and 3 constant total molalities from 0 to 50” have been computed. From these results, the parameters of equations which permit a simple calculation of the activity coefficient of sodium chloride in these solutions have been calculated. These numerical procedures lead to an estimate of t h r excess heat of mixing. Tables of osmotic coefficients of the acid and the salt solutions are appended. By their use the osmotic coefficientsof the mixtures may be computed.
There are two fields for which a fundamental knowledge of the thermodynamic properties of solutions of two or more electrolytes is essential. The first of these is ion-exchange studies which require an exact knowledge of the solution medium. The second field is that of diffusion of all the components in these systems where a precise knowledge of the gradients of the chemical potentials is required. Electromotive forces of cells of the type H2/HCl(ml), NaCl(mz)/AgCl-Ag
71
= lOgYl(0)
-
a12mz.
...
(1)
when the system is maintained at constant total molality, temperature and pressure. Here log y1(0) is the activity coefficient of the pure acid of concentration m l = m and m2 is the concentration of the sodium chloride. If equation 1 is valid, then one can apply the method of McKay1s2 to compute the parameter azl in the analogous equation log
71
= log Y Z ( O )- a z m
(2)
where yz is the activity coefficient of the salt in the mixture and y z ( 0 ) is its activity coefficient a t a concentration mz = m. For systems containing two uni-univalent electrolytes, McKay’s equation for a21 is ff21m1 = [log rzco,llog rl(o,l;
1g2+
The limiting values of azl when nal approaches m, a21(m), and when ml approaches zero, az1(0),are azl(m)
= log
(Y2(0)/Yl(OJ
+ so” alzdm
TABLE I QUANTITIESFOR THE CALCULATION OF THE ACTIVITY COEFFICIENTS OF HYDROCHLORIC ACID, yl, A N D SODIUM OF 1, 2 AND 3 TOTAL CHLORIDE,yz, IN SOLUTIONS MOLALITIES 1
have shown that the activity coefficient, y ~ ,of the acid varies according to the linear equation log
mental results of Harned and Ehlersj3Harned and Nims4 and Harned and Mannweiler5 as recorded by Harned and Owen! The linear variation of log y1 has been premised and azl computed by equations 3, 4 and 5 . The result of this latter
(4)
R1ld
respectively. The azl’-lll ‘7 the quantities which maya’2beand employed for the accurate calculation of the activity coefficient of hydrochloric acid, 71, and sodium chloride, yz, in the mixtures a t total molalities 1,2, and 3 are recorded. The data employed were derived from the experi(1) H. A. C. MoKay, Trana. Faraday S o c . , 61, 903 (1955). (2) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd Edition, Reinhold Publ. Corp., New York, N. Y., 1958, p. 628-629.
log YlIOl
og
YZ(0)
m
o
+
ml na2 = 1 0.0415 -0.0735 - .0655 .0375 .0335 - ,0594 .03i5 - .O~GO ,0299 - .0544 ,0258 - .osio .0220 - .ow
i-. 9 2 5 3 1.9188 1.9118 -i.9079 -1.9041 1.8957 i.8863
1.8045 1.8122 1.8156 -i.8169 1.8176 -i.8176 1.8169
10 20 25 30 40 50
0.082~ ,0224 ,0103 .0030 i.9060 1.0824 1.9G07
m = ml mz = i.8014 0.0401 1.8142 .0365 ,0325 7.8228 ,0308 i.8261 ,0290 -i.8287 ,0252 1.8312 ,0214 i.8312
0 10 20 25
0.1620 .1464 .1287 .1192
10 20 25 30 40 50
o
-
-
+
2 -0.0670
-
.OtilO
- ,0570 - ,0550 - .os0 - ,0510 - .0500
+
ml m,2 = H 0.0396 -0.0~70 ,0360 - ,0610 - .0570 .0320 1.8716 ,0300 - .0540 1.8762 111
=
821
U21(0)
(112(0)
=
-i.8195 -1.8305
-0.0030
-
-
.OO22 ,0015
- .ooio - .0005
+
+
,0007 ,0015
-0.0080 - ,0022 - ,0015 - ,0010 - ,0005 ,0007 ,0015
+ +
-0.0015 - ,0012 - ,0008 - .0006
calculation is illustrated by Fig. 1 where ( - (YX) has been plotted against mlfor mixtures of constant t o t d niolality of 2 M . It is clear that ( - 0 1 2 1 ) varies somewhat mit8hml mid that this variation own be expressed within narrow limits by the linear cquatioii 021
=
Q2l(O)
+ Szlnh
(6)
when ml eqnxls zero. where ~ ? I ( is ~ I the value of We shall now rewrite equations 1 and 2 as log log
YI = Y, =
log log
YUO)
- orlz(o)mz- BlzmzZ
- cuzl(o)ml - h m 1 2
Y~(W
(7) (8)
where for the system under discussion PIZis zero. (3) H. S. Harned and R. W. Ehlers, J. Am. Che’hem. Soc., 65, 2179 (1933). (4) H. S. Harned and L. B. Nilns, ibid., 54, 423 (1932). ( 5 ) H. S. Harned and G. E. Mannweiler. ibid., 87, 1873 (1935). (6) Ref. 2, Tables (11-4-1A), (12-1-2A) and (14-2-1A).
HERBERT S. HARNED
1300
Vol. 63
+
+ +
O0 0.7 10"
.-
p' 0.6
20" 25 O 30"
0.5
40 50'
0
0.5
1.0 ml.
1.5
2.0
Fig. 1. - -all versus ml.
Theoretical Considerations,-As first shown by Glueckauf, McKay and Mathieson,' the cross differentiation equation
will introduce certain restrictions upon the use of equations such as (7) and (8) which are used to express the variatians of the activity coefficients. If we let m l = mx and mz = m ( l - x) and m = ml m2, substitution of equations 7 and 8 in equation 9 yields
+
+
+
+
621) d(alp(o) + a 2 1 ( o ) ) 2(plZ pzl) 2na 4Piz dnz dm - d(aizco) wwo)) dm(P1r 621) (16) dm dm - d[wzco) ~ Z I ( O ) 2 W 1 2 P21)I = (17) dm
whence
+
+
+
+
+
+
(a12(0) a21(0)) 2na(P12 P d = constant (18) The restriction imposed by this relation and the requirement of the constancy of (plz - pzl) are the only restrictions on the use of the quadratic forms imposed by thermodynamics. Critique of the Calculation by the Quadratic Forms.-Since ,312 has been assumed to be zero in these calculations and since thermodynamics requires the constancy of (piz - Pzl), pzl must be independent of the total concentration if the quadratic equations are valid. As far as could be judged from the existing data, this condition is fulfilled a t 1and 2 total molality but not a t higher concentrations. This conclusion is evidenced by the results a t 3 total molality where the values of Pzl are less than those at the lower concentrations. This discrepancy is somewhat greater a t the lower temperatures, That Pzl is less a t the higher concentration is in accord with the earlier calculations which indicated that above two molal total molality, equations 7 and 8 can be used without the quadratic terms a t 25". A very severe test illustrated by Table I1 js imposed by the condition expressed by equation 18.
TABLEI1
COMPARISON OF
(0112(0)
+
azl(0))
+ 2mPz1
AT
DIFFERENT
TOTAL MOLALITIES, m
Since log Y I ~ log , Y Z ~ ~ ~, I Z C O )~Z;(O), , PIZ and PZI are functions af m only, this equation is true for all values of .c when
-xm dGYai(o) - 2rnxPzl - m2x2dP2i - (11) dnL dm
Divide by n w , whence
--d~21co)- 2p2, - mx dPzi dna dm If this is true for all values of
(12)
5 , then
(13)
and
By synimetry
(7) E. Glueckauf, H. A. C. McI
