HERBERTS. HARNED AND ROBERT GARY
5924
[COXTRIBUTION NO. 1246 FROM
THE
Vol. i t i
DEPARTMENT OF CHEMISTRY OF YALE UNIVERSITY]
The Activity Coefficient of Hydrochloric Acid in Concentrated Aqueous Higher Valence Type Chloride Solutions at 25 I. The System Hydrochloric Acid-Barium Chloride O.
BY HERBERTS. HARNED AND ROBERT GARY RECEIVED AUGUST24. 1954 From electromotive force measurements of suitable cells, the activity coefficient of hydrochloric acid in barium chloride solutions has been computed in mixtures of 1,2 and 3 ionic strengths. It is shown that at these concentrations, the logarithm of the activity coefficient of the acid varies linearly with the acid concentration. Following a procedure adopted by Harned which employed the Gibbs-Duhem equation and considerations arising from the application of cross differentiation relations as suggested by Glueckauf, these data are subjected to a critical examination.
From measurements of the electromotive forces of cells of the type Hz I HX(mi), MXdwz) I AgX-Ag
the activity coefficient of the acid may be determined in the presence of the salt a t all compositions a t a given constant total molality. With cells containing 1-1 chlorides, Harnedl and Hawkins2 showed that a t constant total molalities varying from 1 to 6 M , the logarithm of the activity coefficient of the acid varied linearly with its concentration. Since the use of these cells has not been fully exploited for studying mixtures containing unsymmetrical type electrolytes, measurements of high accuracy of cells containing the systems HCI-BaC12, HCl-SrCb, HCl-AlC13, HCIThCld, etc., are being carried out in this Laboratory. The principal object of these experiments is to test the limits of validity of the linear relationship. Thermodynamic Development-Applications of the Gibbs-Duhem Equation The thermodynamic theory of systems containing two electrolytes and the solvent component has recently been developed by Glueckauf,a McKay4 and their colleagues. These contributions have been largely concerned with the computation of the activity coefficients of the components from measurements of the vapor pressure. Since the electromotive force method leads to the determination of one of the electrolytic components, the method employed by Harnedj is a suitable one for the present occasion and in the sequel will be extended to systems containing two electrolytes of any valence types in a given solvent. Since a t constant total ionic strength the logarithms of the activity coefficients of many electrolytes appear to vary linearly with their ionic strengths, we shall assume a linear variation of both electrolytic components (1) and ( 2 ) as log 71 = log log yz = log pi
+
-
YI(O) 01izpz zt AI yz(n) - azipi i Az p2 = p = constant
(1) (2)
(31
I n these equations, y1 and y2 are the activity
CO-
(1) H. S. Harned, THISJOURNAL, 48, 326 (1926). (2) J. E. Hawkins, ibid., 5 4 , 4480 (1932). (3) E. Glueckauf, H. A . C. McKay and A. R . Mathieson, J. Chcm. Soc., S 299 (1949); Tuans. Favaday SOL.,47, 428 (1951). (4) H. A. C . McKay, ibid., 48, 1103 (1952); 49, 237 (1953); H. A. C. McKay and A. R . IMathieson, ibid., 47, 428 (1951); I. L. J e n k i n s and H A. C. McKay, ibid., 60, 107 (1954). (.5) IT. S. Harned, THISJ O U R N A L , 57, 186,s (1935); €1 S. Harned a n d B. B. Oven, “The Physical Chemistry of Electrolytic Solutions,” Reinhold Publ. Corp , S e w Yo&, N. I’ , 1950, p. 462.
efficients of components 1 and 2 in the mixtures, yl(0) and ~ z ( o ) their activity coefficients in pure solvent, p1 and p~ their concentrations expressed as ionic strengths, and 0112 and cyZ1 are the linear constants a t a given total ionic strength. The quantities A1 and A2 represent deviations, to be determined by experiment for each individual system. To avoid complicating the subsequent algebraic expressions, we shall omit any speculation as to the nature or magnitude of these deviations since in many cases they are known to be small, even negligible. Since we consider only that weight of solution containing 1000 g. of water, the Gibbs-Duhem equation may be written in the form vim1 d
I11
y1 f vznz? d In y~
+
+
vldml v2dm2 = - 55.5 d In a,
(4)
where a, is the activity of the water. This equation is subject to the restriction that the pressure and temperature remain constant and that the system be in equilibrium. Although there are no restrictions on composition inherent in equation 4, we impose the condition that all variations in composition occur in such a way that the total ionic strength, p, remains constant. The ionic strength is defined by (5)
where mi is the molality of the ion and zi its valence and where the summation is for all the ions in the solution. For any two electrolytes in a mixture, we may relate the ionic strength of each to its respective stoichiometric concentration by ~1
= jml
PZ =
kmz
(6)
where ml, m2 are the molalities and j and k are constants each of which is characteristic of the valence type of electrolyte. By utilizing these relations, equation 4 becomes vidpi vzdp2 % d l n ~ l + ~ * d l n y z + f -k-
k
I
3
=
- 55.5 d In aa
(7)
Consider the hypothetical system in which both linearity rules 1 and 2 are simultaneously valid and introduce a variable 0 _< x 5 1 defined by the equations pi = x p p7 =
S(J
(1 - r ; p
(8) 19)
th:lt tl log 7 1 = -01izdp*? = c z i ~ p [ I t tl log y j = -widpi = - - ( Y L I ~ ~ x
(10)
(11)
ACTIVITY COEFFICIENT OF HYDROCHLORIC ACIDIN BARIUMCHLORIDE
Dec. 5, 1954
with the restriction that dpi = -dw
(12)
5925
This equation in combination with (14) yields the expression
Upon utilization of these relations, equation 7 becomes which may be used to calculate the osmotic coefficient and, hence, the water activity and vapor pressure for a solution of any composition of two upon suitable rearrangement. Integrating be- strong electrolytes provided that a12 and a21 are tween the limits x = 0 and x known a t a particular total ionic strength, p , of the mixture, that the osmotic coefficient $2 for electrolyte 2 alone is available, and that both linearity rules 1 and 2 are obeyed. The experiments under consideration determine This equation expresses the solvent activity in all the activity coefficient of the acid in the salt solusolutions a t constant pressure, temperature a t a tion from which a12 may be computed. No fixed total ionic strength providing a12 and azl method is known to evaluate the activity coefficient which are functions of p are known. For con- of the salt in these acid solutions and, subsequently, venience in the subsequent calculations, i t is C Y Z ~ . To obtain this quantity, equation 13 is customary to express the water activity in terms of integrated over the entire range of x, that is, from x = 0, corresponding to a solution of electrolyte 1 the practical osmotic coefficient, C#L The practical osmotic coefficient for aqueous alone, to x = 1, which corresponds to a solution of electrolyte 2. The result is solutions is defined by @ T 2 1 a12 v t all) 2* (p - an) = pw = p$ - - Zmi (15)
(y +
55.5
where
is the chemical potential of the solvent, its chemical potential in a chosen standard state and the summation is over the molalities of all the ionic species present. Since the solvent activity is defined by the expression
Sp2
+
2 (2% 2 . 3 ~ZI+ZI-
pw
p o w is
= pow
pw
+ RT In aw
i t follows that
In a, =
-
2y5
vlml
(17)
1n a, =
- 00.5 $ v2m2
(18)
for the single electrolytes 1 and 2, respectively. I n a solution containing both electrolytes 1 and 2 p1
p2
=
ml 2
= xp = -
(1
- *)p
(YI+Z?+
m2
+
= - (v2+2&
2
(19)
Vl-&)
+
2 2.3~
z1+z1-
ZWZ2-
a12
(16)
-
ZI+ZI-
- ff2l e _ _ _ - _
'
v2-2&)
(20)
(26)
which, after replacingj and k by their equivalents p l / m l and p2/mz and rearranging, reduces to ZZ+ZZ-
In a,v = - 55.5 - Zmi
A) ZZ+ZZ-
Zl+ 21-
z2+ 22-
(27)
For mixtures of hydrochloric acid and higher valence type chlorides, ZI+ = 21- = ZZ- = 1 it follows that
Further Thermodynamic Developments Application of the Cross Differentiation Products ,4 very valuable contribution recently has been made by Glueckauf3 who has applied the fundamental cross differentiation equations
Electrical neutrality requires the equalities VI+Zl+
and since v 1
=
= vl+
Vl-Zl-,
+ vl-,
v2+22+
v2 =
=
v2-22-
+
VZ+
v2-
to the problem of mixed electrolytes. Using our notation, PI = jml, pz = kmz under the condition that p = p~ p2 is constant, (29) becomes
+
If both equations 1 and 2 are valid, that is, if
Therefore
+,
I n these equations the subscripts 1 1 - ,2+, 2 - , indicate, respectively, the cations and anions of electrolytes 1 and 2. As a consequence of equations 10, 11 and 23
log 1%
Y1 = 7 2
log
Yl(0)
- a12(LI - P l )
= 1% YZ(0) - ffZl(P -
N2)
then according to (30)
Since yl(o), yz(o), a12 and
a21
are functioris of
only,
HERBERT S. HARNED AND ROBERT GARY
5926
Vol. 76
the coefficient of ,ul must vanish if the equality is to hold for all values of ,u and p l . Thus
atmosphere hydrogen pressure. Since the water vapor pressure varies considerably in passing from the pure acid to the pure salt solution, it was necessary t o use the actual vapor pressure of each solution in making the correction. The vapor pressure data, computed from the osmotic coefficients given in Table I\', were employed for this purpose.' a result first established by Glueckauf. Table I contains the mean experimental results a t the This result is most useful as a criterion for ionic strengths and acid molalities designated therein. deciding whether or not equation 2 is obeyed when total The present values 0.18642 and 0.15133 for the cells conequation 1 is known to be valid on the basis of taining the acid only at 2 and 3 p agree nith the electroexperimental data. To use equation 32, the value motive forces 0.18640 and 0.15189 obtained by Harned and of a12 must be known for a t least two values of 1.1 Ehlers.8 -4t 1 p , however, the latter obtained 0.23336 is somewhat higher than our values, 0.23322. and a21 calculated for each value of by equation 27. which The activity coefficients recorded in Table I1 were coniIf puted by the equation ulkollz u 2 j a 2 1 = constant = S (33) E = Eo 0.1183 log yi2mi(mi 2~22) (34) for the different total ionic strengths, then equation using the value of 0.22246 for Eo a t 2 5 O . a At the top of 2 is a valid representation of the behavior of the the table are given the numerical equations, corresponding to equation 1, which were derived from thrse results. The second electrolyte. deviations of the observed results, A y l , from those computed by these equations are also tabulated. The smallness TABLEI of these deviations is excellent proof of the validity of the ELECTROMOTIVE FORCES IN ABSOLUTE VOLTSOF THE CELL linear relationship as expressed by equation 1. As may hc Hz(1 atm.) 1 HCl(p1 = m J , BaCl!(pZ) [ AgC1-Ag a t 25" a t 1 , 2 readily Estimated from equation 34 a deviation of 0 . l c , in yl correqponds to about 0.05 millivolt. A majority of and 3 total ionic strengths the results lie within this limit. a==3 P-=1 P - 2
+
ml
E
ml
E
ml
E
1.0 0.9
0.23322 .23768 ,24220 .24740 .25299 .25954 .26712 .27638 ,28866 .30855
2.0 1.7 1.4 1.1 0.5 0.2
0.18642 .19418 .20282 ,21288 ,24095 .26866
3.0 2.4 1.8 1.5 1.2 0.9 .3 .2
0.15183 ,16404 ,17807 ,18619 .19531 ,20618 .24151 ,25319 .27223
.8 .7
.6 .5 .4
.3 .2
.1
+
-
.1
Further Thermodynamic Calculations Upon the asszmption that equation 2 is valid, cy21 was evaluated by means of equation 28 using the values of the osmotic coefficients obtained from the isopiestic vapor pressure measurements of StokesLoand Robinson and Stokes.11 The values of the osmotic coefficients employed in this computation are given in the second and third columns of Table I11 and computed values of 0121 in the next to last column.
TABLE I1 OBSERVED AND CALCULATED ACTIVITYCOEFFICIENTS:A y l = yl(obsd.) - yl(ca1cd.) P z 1; log y i = -0.09r)86 - 0.0651 p? Equations used for calculations p = 2; log yt = $0.00396 - 0.0653 P == 3; log yi = +0. 12059 - 0.0673 ~ L P u = l mr
1.0 0.9 .8 .7 .G
.5 .4
.3 .2
.1 .019
0.8111 .7972 ,7881 ,7755 ,7640 ,7529 .7413 .7302 .7201 .7077 .6990
P = 3
A = = ?
71
-0.0001 .0020 ,0009 . 0000 .0000 ,0003 - .OD01 .0002 .0006 ,0011 .0000
-
+ + + +
mi
Yl
2.0 1.7 1.4 1.1
1.008 0.9647 ,9231 ,8812
0.5
.SO58
.2
.7690
AYI
-0.0010
+ + + -
,0001 .0011 .0002 .0006 ,0007
-
Experimental Data The experiments were carried out in cells of the type described in detail by Harned and Morrison.6 The solutions were made by weighing suitable portions of gravimetrically analyzed hydrochloric acid and barium chloride solutions and diluting with the required amount of water. They were rendered oxygen free by means of nitrogen presaturated with water vapor from solutions of the same composition. All the usual precautions were adopted in manipulating the cells. The silver chloride electrodes were made by heating silver oxide paste and subsequent electrolysis in hydrochloric acid. The cells were run in triplicate and the values recorded in Table I represent their mean. The average deviation from the mean of three measurements wab abont 0.03 millivolt. As usual, all cell measurements were corrected to one (6) H. S. Harned and J. 0. Morrison, A m . J . Soc., 33, lG7 (1937)
mi
Yl
3.0 2.4
1.318 1.202 1.097 1.046 ,9994 .9541 ,8696 .8554 .8419
1.8 1.5 1.2 0.9 .3 .2 .1
A Y ~
-0.002 - ,001 .001 ,000 .0005 ,0005 .0006 - .0002 .0006
+ + + + -
TABLE III DATAEMPLOYED IN EQUATIONS 28 A N D 33 01
= 1 p = 2 p = 3 p
02
an
a2 L
.S
1.039 0.864 0.0651 -0.0716 0.176 ,145 ,996 ,0653 - ,0824 1.188 ,143 ,934 ,0672 - ,0866 1.348
In the last colunin of this table, values of (7) A very careful analysis of all the errors involved in these measurements is contained in a doctoral dissertation by RobFrt Gary, Yale University, June, 1954. ( 8 ) H. S. Harned and R. W. Ehlers, THIS J O U H N A I - . 5 4 , 1350 (lW3:II (9) This result was obtained by 11. S . Harned and C. G . Geary, t b i t f . , 59, 2032 (1937). (10) R . H. Stokes, Trans. Faraday Soc., 4 4 , 295 (1948). (11) R . A. Robinson and R. H. Stokes, ibid., 4 6 , 612 (1049).
$3
Dec. 5, 1954
AND
$5 ARSENICIN HYDROCHLORIC ACIDSOLUTIONS
+
S(= 60112 3~~21) according to equation 33 are recorded. It is to be observed that S a t 1 p is considerably larger than a t the higher ionic strengths and that it is practically the same a t 2 and 3 p . Although the computation of a21 is quite sensitive, depending as i t does on the accuracy of knowledge of t$l and 42, we have reason to believe that the variation in S is real and greater than can be accounted for by experimental error. If this is a true statement, then one would expect that equation 2 is not strictly valid a t 1 p but approaches an exact representation of the facts a t the higher concentrations. A similar conclusion has been drawn by HarnedI2 from results on HX-MX mixtures. Recent isopiestic vapor pressure measurements by Robinson13 on the system sodium chloride-cesium chloride also substantiate the conclusion that the rule of linear variation of the logarithm of the activity coefficient becomes valid for both electrolytes in the more concentrated solutions. TABLE IV OSMOTIC COEFFICIENTS AND VAPORPRESSURES AT 25' OF THE SYSTEM HCl-BaC12-H20 ACCORDING TO EQUATION 25 mi 1.0 0.9 .8
.7 .6 .5 .4
.3 .2 .1
.O
* = I 6, 1.039 1.026 1.012 0.977 ,981 ,964 .945
.924 .901 ,896 .846
P
mi
22.88 22.91 22.99 23.04 23.09 23.14 23.20 23.25 23.29 23.35 23.40
2.0 1.7 1.4 1.1 0.8 .5 .2 .O
r = 2 @x 1.188 1.156 1.121 1.083 1.040 0.990 ,932 ,886
P
nil
21.75 21.99 22.18 22.36 22.54 22.72 22.89 23.01
3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 .6 .3
.O
a = 3 +x 1.348 1.319 1.287 1.255 1.220 1.183 1.142 1098 1.0.30 0 996 0 934
P 20.53 20.75 20.96 21.17 21.38 21.58 21.79 21.99 22.19 22.39 22.61
(12) H. S. Harned, Table I. J. Phys. Chem.. 68, 683 (1954). (13) R . A. Robinson, TEISJOURNAL, 74, 6035 (1952); R. A. Robinson and C. K.Lim, Tuans. Faraday Soc., 49, 1144 (1953); R . A. Robinson, ibid., 49, 1147, 1411 (1953).
[CONTRIBUTION NO.
1185 FROM
THE
5927
We conclude these thermodynamical considerations by presenting in Table IV the osmotic coefficients, t$= calculated by equation 25 and the water vapor pressures derived from these osmotic coefficients. It is to be noticed that if the logarithms of both activity coefficients in the mixtures obey equations 1 and 2 , then t$x must vary quadratically as evidenced by equation 25. Conclusions (1) The activity coefficients from electromotive force measurements confirm within narrow limits the validity of equation 1 for the logarithm of the activity coefficient of hydrochloric acid in barium chloride solutions a t 1, 2 and 3 p. The negative deviations a t the higher and lower acid concentrations and the positive deviations between these concentrations for log y1 a t 3 p may indicate a slight bow convex upward from the linear relationship. ( 2 ) The values of a12 are nearly the same a t all three ionic strengths. That S is considerably higher a t 1 p than a t the higher concentrations is evidence that equation 2 is not strictly valid for the variation of the activity coefficient of barium chloride in hydrochloric acid solutions a t an ionic strength of unity. (3) At the higher ionic strengths, these calculations indicate that both equations 1 and 2 are valid within narrow limits. (4) In the investigations of these solutions, we believe that considerations of the deviations A, and A2 in equations 1 and 2 should be explored experimentally for each system. This contribution was supported in part by the Atomic Energy Commission under Contract AT(30-1)-1375. NEWHAVEN, CONN.
DEPARTMENT OF CHEMISTRY
OF Y A L E UNIVERSITY]
Polarographic Characteristics of + 3 and + 5 Arsenic in Hydrochloric Acid Solutions BY LOUISMEITES RECEIVED JUNE 16, 1954
-
Arsenic(V) has been found to be polarographically reducible from concentrated hydrochloric acid solutions, giving a double wave which corresponds to the scheme As(V) + As(0) AsHs. New data are presented 011 the polarographic characteristics of arsenic(II1) in hydrochloric acid media.
Introduction Though the polarography of arsenic in hydrochloric acid solutions has been the subject of several studies, notably those by Kacirkoval and Lingane,? the published data are not in agreement on several important features. Kacirkova' recorded polarograms of + 3 arsenic in 1 N hydrochloric acid. These showed two waves, starting at about -0.3 and -0.6 v. vs. S.C.E., which she attributed to a stepwise reduction to elemental arsenic and arsine, respectively. At very (1) K. Kacirkova, Collection Czcchoslov. Chem. Conrmuns., 1, 477 (1929). (2) J. I. Lingane, I n d . Eng. Chem.. A n d . E d . , 15, 583 (1943).
low arsenic concentrations the two waves were of equal height, as one would expect, but when the arsenic concentration was increased above about 1mM the height of the well-defined first wave became substantially independent of the arsenic concentration. The height of the second wave, on the other hand, did continue to increase] but more rapidly than the arsenic concentration. Though the shape of the second wave was very poorly defined in the absence of a maximum suppressor, it was materially improved by the addition of, e.g., 5 X yo methylene blue. Kacirkova explained the peculiar behavior of the first wave height by postulating the formation of a film of adsorbed ar-
