NOTES
August, 1963 Acknowledgment.--The authors acknowledge with gratitude the generous support of the National Institutes of Health for this research.
TABLE I DATAFOR THE CALCULATION OF HYDROCHLORIC ACIDIN LITHIUM CHLORIDE SOLUTIONS t , OC.
THE THERMODYYBMIC PROPERTIES OF THE SYSTEM: HYDROCHLORIC ACID, LITHIUM CHLORIDE, AND WATER FROM 15 TO 35’ BYHERBERT S. HARNED Contributzon No. lY3d from the Department of Chemistry of Yale University, New Haven, Connecticut Received March 87, 1968
In two earlier communications, the thermodynamics of the systems hydrochloric acid, sodium chloride‘ and hydrochloric acid, potassium ch30ride2 in aqueous solution over considerable temperature ranges were discussed. In this contribution, a similar study of hydrochloric acid-lithium chloride mixtures is presented. The activity coefficientsof the two electrolytes may be represented by the linear equations log Yl(0) -
alZ(0)mz
log yz = log 7”;)-
azl(0)ml
log y1
=
(1)
(2) when the system is at constant total molality, temperature, and pressure. The activity coefficients of the acid and salt in the mixtures are represented by y1 and yz, and their molalities by ml and mz, respectively. The activity coefficientsof the acid and salt in water at a molality, m = ml mz, are represented by yl(u)and ~ z ( o ) . The parameters, aI2(o) and azl(o), are constant a t a given temperature and pressure a t constant total molality. Since the magnitudes of ~ I Z ( O )and a21(o) for this system are $mall, being one-fifth to one-tenth of those for the systems containing sodium and potassium chlorides, quadratic terms in eq. 1 and 2 would be extremely difficult to detect and are not required to express the known properties of this system. Values of were computed from the electromotive force data of Harned and C ~ p s o n . ~ These results were smoothed graphically and are recorded in Table I a t total constant molalities of 0.5, 1, 1.5,2, 3, and 4 and at 5’ intervals from 15 to 25’. We note that these values are in close agreement with those previously determined. Calculation of the Parameter, azl(,,),in Eq. 2 and the is Excess Heat of Dilution.-If the parameter, a12(0), known for a system which is represented by eq. 1 and 2, then azl(0)may be computed by means of the equation
+
4c6
where Cplto) and Cpzcoi are the osmotic coefficients of the acid and salt in water at a concentration, nz.6 By this equation and the osmotic coefficients given by Robinson and Stokes’ and the values of alz(o~in Table I, we find (1) H. S. Harned, J . P h y s . Chem., 63, 1299 (1959). (2) H. S. Harned, zbtd., 64, 112 (1960). (3) H. S. Harned and H. R. Copson, J . Am. Chern. Soc., 6 5 , 2206 (1933). (4) H. 5 . Harned, zbid., 57, 1865 (1935). (5) H. S . Harned and E. B. Owen, “The Physical Chemistry of Eleotrolytie Solutions.” 3rd Ed., Reinhold Publ. Carp., New Pork, 1c’. Y., 1958,
608, (6) Ref. 5, p. 603,eq. (14-5-7). (7) R. A. Robinson and R. €1. Stokes, “Electrolyte Solutions,” Butterworths Science Publications, London, 1955,p. 468. p.
1739
log
YXO)
15 20 25 30 35 15 20 25 30 35
-i .8841 -1.8817
- ml f -1.9616 -1.9574
... ...
0.0062 .0058 ,0054 .0049 .0043
1.9118 -1,9079 1,9041 1,8999
+
ml 0.0166 .0103 - .0039 1.9969 1.9894
0.0059 ,0054 ,0049 .0044 .0040
+ mz = 3
0.1377 .1287 .1192
L112(0)
-1.9153
m~ = 1.5
1,9524 -1.9469 1.9415
YXO)
m1 f m2 = 1
0.0065 .0061 ,0056 .0050 .0046
1,8792 1 - .8766 I .8737
m~
15 20 25 30 35
log
UlZ(0)
+ m2 = 0.5
ml
ml
0.0050 ,0045 .0040 ,0035 .0031
+
m2
= 2
0.0056 .0051 ,0046 .0041 .0037 nz2
0.2700 .2582 .2460
= 4
0 0044 ,0039 ,0033 .0029 ,0024
... ...
that azl(o)at 25’ equals -0.014 a t total concentrations from 0.5 to 3 molal. The excess heat of mixing, A H M ~may , be calculated by the equation8
Since the osmotic coefficient of lithium chloride is known at 26’ only, C Y Z ~ (cannot ~) at present be evaluated at other temperatures by eq. 3. However, it is z (cono), reasonable to assume that the ratio, a ~ l ( o ~ / a lis stant over a short range of temperature. This ratio i:$ constant for the hydrochloric acid-potassium chloride system from 0 to 40’ and varies only 10% for the hydrochloric acid-sodium chloride system from 0 to 50’. For the system under discussion, this ratio equals -2.6 and this value leads to the results a t one molal total concentration given in Table 11. TABLE I1 VALUESOF THE PARAMETERS OF EQ. 1 AND 2 FROM 15 TO 35” FOR THE HYDROCHLORIC ACID, LITHIUMCHLORIDE SYSTEMAT 1 m TOTAL COXCENTRATION
+ -0.0099 - .0093 - .OD86
t, OC.
0112(0)
(IWQ)
(112(0)
15 20 25 30 35
0 0062
-0.0161 - .0151 ,0140 ,0127 - ,0112
-
,0058 .0054 .0049 .0043
-
UZl(0)
.0078 ,0069
These results yield a temperature coefficient of (a12(o) 4- a ~ 1 ( 0of ) ) 0.00015 at 25’. Consequently, the heat of mixing at equimolal r;olutions is AHM’ = 2.303 X 2 X (298.16)2(0.5)2X 0.00015 -15 eal. per mole of solute at 25’
Young, Wu, and Krawetz’s9 calorimetric determination of this quantity is approximately 13 cal. Acknowledgment.--This contribution was supported in part by the Atomic Energy Commission under Contract AT(30-1) 1375. (8) €1. A. C. MoKay, Dascussions Faraday Soc., 24, 76 (1957). (9) T. F.Young, Y. C. Wo, and A. A. Krawetz, zbid., 24, 37 (1957).
