HERBERT S. HARNED AND MELVINA. COOK
1890
perchlorate is, however, troublesome because of its corrosive nature in contact with the skin,
10
20 30 Temperature, "C. Fig. 2.-Refractive index of saturated silver perchlorate solutions a t 15-35'.
VOl. 59
was checked in the usual manner and the authors find the value 43.0'. Perchloric Acid Solubility of Anhydrous Silver Perchlorate.-The solubility determinations in strong perchloric acid and the density determinations of these solutions were carried out as previously described for the aqueous solutions. Anhydrous silver perchlorate was used as solute. The constant boiling perchloric acid (73.60% HCIOI) was prepared by the Smith and Koch method.a More dilute solutions of perchloric acid were made from this product by weight dilution. The data for the perchloric acid solubilities and solution densities are given in Table 11.
Summay
1. A redetermination of the solubility of silver perchlorate in the temperature range 0-35 O has been made. The previously reported data by TABLE I1 THESOLUBILITY AND SOLUTION DENSITYOF ANHYDROUS Hill1 and the present data were found to be in SILVER PERCHLORATE IN 60-73.6% PERCHLORIC ACID AT substantial agreement. 25 AND 0" 2 . The refractive index of saturated aqueous Acid Solubility, g. AgClOa per Temp., concn., 100 Density solutions of silver perchlorate over the tempera'C. % ml. sol. ff"% 25/4' 0/4' ture range 15-35' has been given. 25 73.60 5.252 3.011 1.7436 .... 3. The solubility of anhydrous silver perchlo25 68.02 10.332 6.080 1.6993 ... . rate in strong perchloric acid (60-73.6010) a t 0 and 25 64.08 20.080 11.765 1.7066 ... . 25 60.00 38.449 21.611 1.7790 .... 25' has been determined. Solution densities are 2.136 . . . . 1.7575 3.754 0 73.60 also given. The value of Hill for the transition temperature of silver perchlorate monohydrate to the anhydrous salt (43.1')
0 0 0
68.08
64.31 60.16
7.104 13.478 30.500
4.151 7.931 17.41
.... . ... ....
[CONTRIBUTION FROM THE
1.7107 1.6987 1.7520
(2) Smith and Koch, I n d . E r g . Chcm., Anal. Ed., 8, 52 (1931). URBANA,
ILLINOIS
RECEIVED JUNE 14, 1937
DEPARTMENT OF CHEMISTRY O F YALE UNIVERSITY]
The Activity and Osmotic Coefficients of Some Hydroxide-Chloride Mixtures in Aqueous Solution BY HERBERTS. HARNEDAND MELVINA. COOK The cells H2
1 MOH(nti), MX(%) 1 M,Hg I MOH(%) I
Hz
(1)
and Ag-AgX
I MOH(mi), MX(m2)
M,Hg 1 MX(m6) 1 AgX-Ag
(2)
in which X equals C1, Br, are peculiarly adapted for the study of hydroxide-halide mixtures since by the first the activity coefficient of the hydroxide and by the second the activity coefficient of the halide may be evaluated in a given mixture. The first of these cells has been e m p l ~ y e d l -for ~ determining the activity coefficient of a hydrox(1) Harned, THISJOURNAL, 47, 684, 689 (1925). ( 2 ) Harned and Swindells, ibid., 48, 126 (1926). (3) Harned and James, J . Phys. Chem., SO, 1060 (1926). (4) Harned and Harris, J r . , THISJOURNAL. 60. 2633 (1928).
ide in a halide solution, but measurements of both cells have never been used before for the determination of the activity coefficients of both electrolytic components in the mixtures. We have restricted this study to the inve5tigation of sodium and potassium hydroxidechloride mixtures in water a t 25" at constant total molalities of 0.5 and 1 M. As shown by Harned and Harris, Jr.,4 the hydroxide-chloride mixtures differ from other mixtures of strong uni-univalent electrolytes in that the logarithm of the activity coeficients of the hydroxide does not vary linearly with the hydroxide concentration a t constant total molality. Our results will be shown t o confirm this observation. Further, since the measurements of both cells lead to the
ACTIVITY COEFFIC~ENTS OF HYDROXIDE-CHLORIDE MTXTURES
Oct., 1937
determination of the thermodynamic properties of two of the three components of the system, and since the Gibbs-Duhem equation permits us to evaluate those of the third component, our knowledge of this subject is extended considerably by the more comprehensive method and treatment of the present study. TABLE I ELECTROMOTIVE FORCES AT 25' OF THE CELLS H2 I MOH(ml), MCl(m2) M,Hg I MOH(mo) I HI: EI Ag-AgC1 I MOH(ml), MCl(mz) 1 MzHg I MCl(m:) 1 AgC1-Ag: Ez AND CONSTANTS OF EQUATIONS (6) AND (6)
I
M = K ; ml
ml ,9110 .8140 ,7431 ,6439 ,5725 ,4141 ,3370 ,2213 ,1478 ,1068 .OS54
.oooo
.oooo
0.5000 ,4670 ,4317 ,3956 ,3840 ,3099 ,2218 ,2211 ,1223 ,1124 ,0885 ,0000
21 log @ P
E2
71
Y?
(#(d - +(a))
0.1524 . . . . 0,0073 0.736 (0.639) ,4186 0.0719 ,0072 ,736 .639 .1444 ,0763 ,0071 .718 .631 ,1409 ,0981 .0070 ,701 ,625 ,1365 ,1060 ,0069 ,691 ,620 ,1321 ,1104 .0068 ,673 ,615 ,1230 ,1179 ,0067 ,663 ,609 ,1171 .1206 ,0066 ,655 ,607 .lo56 .1248 ,0066 .646 .604 ,0947 ... ,0065 .640 .. . ,0864 ,1284 ,0064 .641 ,605 ,0802 ... ,0064 .635 .. . .1313 .., ( ,638) ,605
0.123 ,099 ,075 ,060
,042 ,032 ,014 .008
,002 ,000 - ,0005
-
.
M = N a ; mnl 1,0000 ,9174 ,8706 ,7230 ,6635 ,5702 ,4738 ,3471 ,2817 ,1854 ,1032
+
ffl2
= 1; mo = 0.1349; m' = 0,0952; y o = 0.780839
0.0991 . . . . 0.0064 ,0961 0.0469 ,0063 ,0945 ,0585 ,0063 ,0890 ,0782 ,0063
.OS60 .OS19 ,0771 ,0689 ,0633 .0530 8
.0833 ,0898 ,0946
,1001 .I027 ,1064 .lo94 .1120
.0063 ,0063 ,0063 ,0063 .0063 .0063 ,0063 ...
.
= 0.742;'
'(0
0.679 (0.644) ,668 ,644 .665 ,645 ,656 ,646 ,655 ,648 ,646 ,651 .644 .64B ,640 ,645 ,638 ,647 ,643 ,663 .642 ,660 ( .638) ,658
M = N a ; ml 4- mz = 0.5 0,0640 . . . . 0.0026 0.691 (0.677) ,0615 0.0079 ,0025 .686 .674 .0592 ,0269 .0023 ,678 .678 ,0566 .0378 ,0025 ,673 ,078 ,0559 .0402 ,0025 ,675 ,674 ,0504 ,0532 .0025 ,674 ,678 ,0419 ,0628 ,0024 ,669 .676 ,0412 .... ,0024 ,668 . ,0261 ,0709 ,0024 .069 ,679 ,0238 .0718 ,0024 ,667 ,682 ,0176 ,0733 ,0024 .667 ,682 ., .. ,0784 . . . . ( .666) .683
..
,0005 ,000
0.023 ,013 IO09 ,003 ,007 - ,010 - ,018 - ,013 - ,012
-
-
,010 .00.5 .000
0.020 ,014 ,010 ,007 .006 ,0026
- ,0005 - ,0005 - ,0015 - ,001
-
,001 ,000
Numerical Constants of Equations ( 5 ) and (6) -log -log nil+mz rl(o) ai 81 YZ(0) L2? Br M = K 1 0.1220 0.129 -0.056 0.2185 0.007 -0.034 M = Na 1 .1690 . O S 5 .029 .1818 .029 ,020 M = Na 0 . 5 ,1606 ,072 .OS0 .1656 .OOG .OOO
-
( 5 ) Harned and
Cook, THISJOURXAI., 59, 498 (1937).
( l i ) Harned and Cook, ibid., OS, 1200 (1937). 1 7 ) JTarnerl and Hecker. ibid., 56, 4838 fl9331, ( S ) 13rowi and h l ; i r l n ~ ~ e si ,b i d . , 67, I:jri6 ~ I ! l 3 5 ) . (!I)
Experimental Results The electromotive forces are recorded in Table I.
Thermodynamic Considerations The activity coefficients of the hydroxides and chlorides in the mixtures may be computed from the cell equations E1 (ml + mz) '13 ml% log Yo = -1 log Po -
0.1183 - log
- E-2
0.1183
log
+
mo
+ m6
(ml m2)' 1 2 ~ $ 1 2
+
2 t J log (3)
r, + log 76 = log Yt
(4)
y o and 7;are the activity coefficients of the elec+ m2 = 1; mo = 0.04781; m ; = 0.05754; yo = 0.827;6 trolyte in the reference solutions at the concen7 : = 0.803'
El
1,0000
1891
1l;irticd ;uid
h'iinq,
i h i r l , 64, 423 l l ! U 4 ) .
-
trations m, and m;, respectively. The values employed with references are given in Table I. 71 and 7 2 are the activity coefficients of the hydroxides and chlorides, respectively, in the mixtures. nzl and wz2 are the molal concentrations of the hydroxides and chlorides, respectively. Both the potassium hydroxide-chloride and sodium hydroxide-chloride mixtures were investigated at a constant total molality of 1 114, and the sodium hydroxide-chloride mixture was also studied at 0.5 ilf. Values of y1 and y2 in each of the mixtures are recorded in Table I. In order to compute yl, it is necessary to evaluate the vapor pressure correction to the electromotive force on the right side of eyuation (3). fro is the vapor pressure of the reference solution and p that of the solution under consideration. In the pure hydroxide or salt solution, these were determined by the usual graphical integration using the Gibbs-Duhem equation. The values in the mixtures were obtained by a method which will be developed in the subsequent discussion. The variation of the logarithm of the activity coefficients of the electrolytes at constant rnolality has been expressed as a function of their concentrations by the equations -log 7 1 = -log -log YZ = -log
Y~(O)
+ almz + plm;
(5)
4- hnz: (6) 71 and 72 as before are the activity coefficients of the hydroxides and chlorides in the mixtures at concentrations nzl and m2, respectively. Y ~ ( and Y ~ ( are ~ ) the activity coefficients of the hydroxides and chlorides in the pure aqueous solutions at the constant total molalities under consideration. (YI, ( Y Z , 131 and Bz are the coefficients of the quadratic equations. The vapor pressures aiicl osmotic coefficients Yz(o) f a2m1
~ )
HERBERT s. HARNEDAND MELVINA. COOK
1892
may be computed by employing the Gibbs-Duhem equation in the form
+ 2m2 a log y2 = -55.51
2m1 b log
b log a,
where a, is the activity of the water. ml = xm; ma = (1
- x)m
(7)
We let (8)
where x has all values from 0 to 1. Differentiating (5), (6) and (8) and substituting in (7), and integrating from 0 to x a2x
- 51 (a,+ a2)x2 -
PI - b)xa
+ 22 m(P1 - &)xa =
is obtained, upon substitution of the vapor pressure of water, p , for its activity. Since d log a, = -(2m/55.51 X 2.3303) d4, the change in osmotic coefficient, 4, with change in composition of mixture is given by +(o)
- &)
1
[( a d -2 3 (a13. ad xz m (61 - PM + 3 m - ~ x a ] (10)
= 2.303 m
(PI
The vapor pressure term on the right of equation (3) given in the fourth column of Table I was determined by arithmetical approximation.
-
1.80 +
1
I
0
-0.5
Log
Yl(0)
i.80
I
ml
ml 0 of log y1 and y2 versus m2 and ml at a total molality of 1 M . Two curves a t top represent KOH-KC1 mixtures; two curves at bottom NaOH-NaCl mixtures. Diameter of circles equals 0.5 mv. 1 Fig. 1.-Plots
The vapor pressure, p , of the solution containing one electrolyte must be corrected for the change produced upon adding the second electrolyte.
VOl. 59
This change was computed in the following manner. A preliminary value of log rl was obtained by equation (3) by taking p equal the vapor pressure of the pure hydroxide solution. These values were employed in equation (5) to give preliminary values of a1 and PI, and then p,,) was computed by equation (9). From these the vapor pressure term on the right of equation (3) was computed, and corrected values of log ~1 were then computed. By repetition of this process until all equations were satisfied, final values of the vapor pressure term, rl, cyl and PI were obtained. From these q5(x) - q5(o) was determined by equation (10). Values of this quantity are given in the last column of the table. We note that q 5 ( ~is the osmotic coefficient of pure chloride, c#J(%)that of the mixture, and 4(,= that of pure hydroxide. Values of log yl(o),log y2(0),a1, PI, (112 and PZ required for these calculations are given a t the bottom of the table. General Characteristics of the Mixtures The characteristics of the results at a total molality of unity are illustrated in Fig. l. The two curves a t the upper part of the figure represent the behavior of the potassium hydroxide-chloride mixtures while the two curves at the bottom of the figure represent the sodium hydroxide-chloride mixtures, both a t 1 M. At the top (circles) the logarithm of the activity coefficient of potassium hydroxide in the chloride solutions is plotted against its concentrations. The curve below this (dots) represents the logarithm of the activity coefficient of the chloride in the hydroxide solution. log the activity coefficient of the hydroxide, and log Y ~ ( ~that ) , of the chloride, both in pure water are indicated. Similarly, the two lower curves represent the behavior of the sodium hydroxide-chloride system. The circles are the values of the logarithm of the activity coefficient of sodium hydroxide in the chloride solution, and the dots represent the activity coefficient of the sodium chloride in the same mixtures. In all cases the solid curves are those calculated by equations ( 5 ) and (6) employing the values of the parameters a t the bottom of Table I. The characteristics of these results may be summarized briefly : I. Potassium Hydroxide-Potassium Chloride Mixtures.-(1) Neither log y1 or log 7.2 varies linearly with the concentration of a component of the mixtures, a fact previously noted by Harned
1893
ACTKVITY COEFFICIENTS OF HYDROXIDE~HLORIDE MIXTURES
Oct., 1937
TABLEI1 v.4L.UES OF OSMOTIC COEFFICIENTS AND (+L=1)-
(ml 4- ma)
NaOH NaCl KOH KCl NaOH NaCl
0.5
.5 1
1
1 1
Ref.
d26
(7)
0.938 .923 1.006 0.898
(8)(9) (5) (6) (7) (8)(9)
i(0))ZS
(d(.-l)-do)za Eq. 10
...
...
0.015
0.020
...
...
.lo8
,123
,956
...
...
.936
.020
.023
and Harris, Jr., for the variation of log 71 a t higher total molalities. (2) The results may be expressed by quadratic equations (5) and (6). (3) Since a quadratic is necessary to express the variation of log v1 and log YZ, the osmotic coefficient varies according to equation (lo), a cubic. (4) log y1 in a pure potassium chloride solution does not equal log yz in the pure hydroxide solution. These extrapolated values are given in parentheses in Table I.
II. Sodium Hydroxide-Sodium Chloride Mixtures.-( 1) At 1 M total concentration log y1 and log YZ vary according to a quadratic equation but a t 0.5 M log 7 2 may be expressed by a linear equation. ( 2 ) This leads according to equation (10) to a cubic variation of the osmotic coefficient, 6. (3)log y1 in the pure salt solution does not equal log 7 2 in the pure aqueous hydroxide solution. (4) The sodium chloride-hydroxide mixtures possess a further peculiarity. The curves slope in opposite directions, a behavior not previously observed with uni-univalent electrolyte mixtures.
THEIRDIFFERENCES $0
E. rn. f .
0.933 .918 1.009 0.885 .941 .923
do
(+(z-l)-+(dh
F. p.
E. m. 1.
(%-I)-
+(o)),
F. p.
...
*..
...
0.913
0.015
0 * 020
...
...
...
.882
...
.124
...
.127
.916
,018
.025
...
hydroxides and chlorides determined in this manner, and the sixth column contains this computed from the present data by equation (10). The agreement between the values of ( C # J ( # - ~ ) C#Jco)) obtained by the two methods is satisfactory since i t involves the errors of four independent series of measurements. A further check has been made with the data obtained by Scatchard and Prentiss'O from freezing point measurements. Their values of 4, given a t the freezing point of the solution, were altered slightly so as to be comparable with the values obtained from electromotive forces a t 0". The differences between the values of 6 a t 0 O determined by freezing point and electromotive forces are caused principally by difficulties encountered in the extrapolations involved. In the last two columns of the table are given the differences between the osmotic coefficients of the hydroxides and their corresponding halides as determined by the two methods. These differences compare favorably with those obtained a t 25' by equation (10). summary
1. By measuring suitable cells, the activity coefficient of the hydroxide and the activity coThe value of (q5(x=1) - $0) is the difference efficient of the chloride in a mixture of chloride between the osmotic coefficient of the pure hyand hydroxide a t 0.5 and 1 M total concentradroxide and pure chloride. This quantity may tions have been determined. This is the first be calculated a t 25" from the activity coeffitime this has been accomplished. The procedure cients of the pure salt and hydroxide solutions by makes possible a thorough study of the thermomeans of the equation, q5 = 1 2.3026/m m dynamics of such mixtures. 2. It is found that the logarithm of the acb log y. We have evaluated this quantity by tivity coeEcients varies with their concentrations graphical integration of values of y recently deaccording to a quadratic function. This behavior termined from electromotive force measurements is different than that yet observed for other and have collected the results in Table 11. The uni-univalent electrolyte mixtures. third column indicates the source of data emNEW HAVEN, CONN. RECEIVED JUNE 26, 1937 ployed. The fifth column contains the differences between the osmotic coefficients of the (IO) Scatchnrd and Prentiss, THISJOURNAL, 66, 4365 (1933).
0smotic Coefficients
+
I"
