J O U R N A L OF THE AMERICAN CHEMICAL SOCIETY (Registered in U. S. Patent Office) (Copyright, 1955, by the American Chemical Society)
VOLUME
NUMBER 18
SEPTEMBER 27, 1955
77
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTION NO. 1287 FROM THE DEPARTMENT O F CHEMISTRY O F YALE UPZIVERSITY]
The Activity Coefficient of Hydrochloric Acid in Concentrated Aqueous Higher Valence Type Chloride Solutions at 25 '. 111. The System Hydrochloric Acid-Aluminum Chloride BY HERBERTS.HARNEDAND ROBERTGARY RECEIVED APRIL 1, 1955 The activity coefficient of hydrochloric acid in solutions of aluminum chloride has been determined a t 1, 3, 5 total ionic strengths by measurements of the electromotive forces of suitable cells. The rule of the linear variation of the logarithm of the activity coefficient of the acid a t constant total ionic strength is closely obeyed. The thermodynamics of the system is developed by the use of the Gibbs-Duhem and cross-differentiation equations.
Electromotive force measurements of cells of the type Hz IHCl(mi), MCldmz) I AgCl-Ag
have been made by Harned and and Mason and Kellam3 on systems containing aluminum and cerium chlorides] respectively. Following the procedure adopted by us4 in studying the cells containing barium and strontium chlorides, a precise and extensive series of results have been obtained which form the basis for a thorough exposition of the thermodynamics of the system hydrochloric acid-aluminum chloride-water a t high ionic strengths. Experimental Data.-Table I contains the observed electromotive forces of the cells designated. Each result is the mean of three measurements which agreed to within 0.05 mv. Activity Coefficients and the Linear Variation of their Logarithms at 1,3,5 Constant Ionic Strengths. -Table I1 contains the activity coefficients of hydrochloric acid computed by the equation
TABLE I ELECTROMOTIVE FORCES IN ABSOLUTE VOLTSOF THE CELLS: HZ(1 ATM.)I HCl (PI = m l ) , AlCl, ( p ~1 AgC1-Ag ) AT 25' AT 1 , 3 , 5 TOTAL IONIC STRENGTHS ml
1.0 0.9 .8 .7 .6 .5 .4 .3 .2 .1
p = 1
r = 3
E
mi
E
0.23322 ,23799 ,24321 ,24869 ,25499 ,26207 ,27024 ,28039 ,29349 . 31433
3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6 0.3
0.15813 ,15841 ,16484 ,17183 ,17959 ,18810 ,19794 .....
,22429 ,24688
f i = 5 ml
5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5
E
0.09519 .lo290 ,11108 ,11968 ,12897 ,13901 ,15036 ,16334 ,17988 ,20383
of the table were used to test the validity of the linear variation rule. Since 0.1% in y1 correspond to about 0.05 mv., the magnitudes of the deviations, Ayll indicate that the linear equations represent the observed results within narrow limits. E = E" - 0.1183 log ~ / ~ I ~ W Z I ( W Z I3~22) (1) A possible exception occurs with the results a t 5 As in our earlier calculation^,^ the value of 0.22246 total ionic strength and low acid concentration absolute volt for E o was used. The molalities of the where the observed results seem to fall below the acid and salt are represented by ml and m2, respec- calculated ones. At 1 p the formula used by Hartively. The numerical equations given a t the top ned and Mason' was: log y1 = -0.0900 - 0.0605 p (1) H.S. Harned and C. M . Mason, THISJ O U R N A L , 63, 3377 (1931). which agrees closely with the equation employed (2) H. S. Harned and B. B. Owen, "The Physical Chemistry of by us. Electrolytic Solutions," Reinhold Publ. Corp., New York, N. Y., 1950, Thermodynamic Considerations.-Following the p. 458. procedure adopted in our earlier communications, (3) C. M. Mason and D B. Kellam, J . P h y s . Chem., SB, 689 (1934). (4) H. S . Harned and R. Gary, THISJOURNAL, 76, 5924 (1954): the assumption is made that the linear variation 77, 1991 (1955). rule holds within narrow limits for the activity co4695
+
HERBERT S. HARNED AND ROBERT GARY
4696
VOl. 77
TABLE I1 OBSERVEDAND CALCULATED ACTIVITY COEFFICIENTS OF HYDROCHLORIC ACID = y I (0bs.j - y1 (calcd.) /A = 1; log yi = -0.09091 - 0.0611 ~2 Eq. used for calm. U , = 3; log yl = 0.11915 - ,0629 ,U2 = 5 ; log 71 0.37676 - ,0631 1.12 1-
=
-p
i
-
~
__-.
~ - p
Yl
AYl
mi
Yl
1.0 0.9 .8
0.8111 .7994 ,7870 .7781 ,7664
-0.0003 . 0000 - ,0012 .0010 .0002 .0000
3.0 2.7 2.4 2.1
1.318 1.284 1.205 1.157 1,108 1.062 1.015 .... 0.9286 8872
i
+ + + ,0009 - ,0009 + .0005
. ----
G .5 .4 .3 .2 1
iOJJ
,7458 ,7335 ,7246 ,7135
1.8
1.5 1.2 0 .9 .6 3
- ,0005
eficients of both electrolytic components. Thus log Y1 = log Yl(0) log Y2 = log YZ(0) P = ,Ul
+
- a12p2 - azlpl
(2) (3) (4)
P2
I n these expressions ~ I ( o ) ,yz(o)are the activity coefficients of the acid and salt in water, yl, yz their activity coefficients in the mixtures, p1 and 1.12, their concentrations expressed as ionic strengths and a12 and a21 are constants a t each total ion strength. If the constant a12is known and equations 2 and 3 are valid, then azl may be computed by the equation QZ1 ZZ+ZZ-
2 2.3 /*
a12 ZI+ZI-
z+x
+
...... ,0008
-
- ,0026
x (zI+z~-
+
p =
J -
71
371
5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1 .o 0 . ;i
2.380 2.216 2.059 1.916 1.780 1,657 1.537 1.431 1.322 1 225
-0.001 ,002 ,000 ,002 ,000 ,002 - ,002 . 0 00 - ,009 - .013
+ + +
of the data of Stokes6 and Robinson and Stokes.' I n the second part of the table, similar quantities for the system hydrochloric acid-cerium chloridewater obtained from the data of Mason and Kellam3are recorded. The values of cyl2 for the cerium chloride mixtures were obtained from measurements of the activity coefficient of the acid a t 0.01 M in the cerium chloride solutions and, consequently, are not the result of as comprehensive a study as the present one. TABLE I11 DATAEMPLOYED IN EQUATIONS $1
Pi2
an
12au
+ 4a2l
= 2 = 3 p = 5
(1) HCl-A1C13-H2O8 0.831 0.0614 -0.0636 - ,099 0.905 ,062 1.007 ,0629 - ,1113 1.272 ,0631 - ,1179
0.482 ,348 ,310 ,286
= 1 p = 2 p = 3
(2) HC1-CeC13-H20 1.039 0.795 0.0870 - ,0177 1.188 ,847 ,0908 - ,0426 1.348 ,914 ,0918 - ,0510
0.973 .919 ,898
1
From the knowledge of alz and azl, the osmotic coefficient, &, in the mixture may be computed by the equation
+2
+ + + +
~~
IN1
S =
where zl+, z1-, z2+, 2 2 - are the valences of the ions and 41 and 42 are the osmotic coefficients of the two electrolytes in the pure solvent. If the subscripts one and two represent hydrochloric acid and aluminum chloride, respectively, then ZZ+ = 3, 22- = z1+ = 21- = 1 and this equation reduces to
~
,002 - ,006 - ,001 ,002 ,002 ,003 ,001
+I
(G-- G)]( j )
zl+z2-
+o
Z~+ZZ-
1
2 2.3 p
A71
[ ( A - A-) ZI+ZI-
---
--.
= 3--
mi
,U
1.1 p
p
=
1 1.039 1.118 1.318 1.680
We have shown that equation 2 expresses within narrow limits the variation of the logarithm of activity coefficient of hydrochloric acid a t constant total ionic strength. Since no experimental method is available for determining the activity coefficient of aluminum chloride in these mixtures, we have assumed that its variation is expressed by equation 3. Following a procedure suggested by Glueckaufg which involves fundamental cross differentiation equations, we have shown that, if both equations 2 and 3 are valid, the quantity S = vlka12 vzja21 must be a constant, independent of the total ionic strength, p . For systems containing a uniunivalent and a triunivalent electrolyte, S = 12a12 4~x21. Values of S are recorded in the last column of Table 111. The behavior of S for these acid-triunivalent salt mixtures follows the pattern found for the acid-bi-
z ) (1
XI
(7)
where v 1 and v2 are the number of ions into which the electrolytes dissociate and the valence factors j and k are defined by the relations p l = jm,, pz = km2. The activity of water and subsequently the water vapor pressure can be obtained by the equation Table I11 contains the measured values of cy12 and values of azlcalculated by equation 6. The osmotic coefficients, qbl and &, were obtained from plots ( 5 ) A typographical error in sign occurs in these last two equations as printed in our earlier communication (ref. 4). The minus sign should be plus in the right hand parentheses in both these equations. This error does not affect any of the calculations.
+
+
(6) R.H.Stokes, T r a m . F a r a d a y Soc., 44, 295 (1948). (7) R. A. Robinson and R . H. Stokes, ibid., 45, 612 (1919). (8) The result a t 2 p was computed from the data of Harned and hlason (reference 1). (9) E. Glueckauf, H.A. C. McKay and A. R . Mathieson, J . Chem. SOL.S. 299 (1949); T r a n s . F a r a d a y Soc., 47, 428 (1931).
Sept. 20, 1955
univalent chloride systems. S appears to decrease rapidly in the more dilute solutions and to approach constancy a t the higher concentrations. When the sensitivity of this test is taken into account, i t appears that equations 2 and 3 yield a close approximation to the actual behaviors of these mixtures. For purposes of future comparison, we record in Table IV the hypothetical osmotic coefficients of
-
TABLE IV OSMOTICCOEFFICIENTS AND VAPORPRESSURES AT 25” THE SYSTEM HCl-A1Cls-H20 -p
7
= -1
-p
7
m
mx
P
ml
1.0 0.9 .8 .7 .6 .5 .4 .3 .2 .1
1.039 1.026 1.013 1.OOL; 0.985 .968 .950 ,929 ,904 ,872 831
22.88 22.96 23.02 23.09 23.15 23.22 23.28 23.34 23.48 23.49 23.52
3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 .6
.o
4697
MECHANISM OF COMPLEX ELECTRODE REACTIONS
= Qx
1.348 1.327 1.306 1.282 1.257 1.230 1.199 1.164 1.123 . 3 1.072 . o 1.006
[CONTRIBUTION FROM
h-OYES
-p
P
mi
20.54 20.79 21.03 21.27 21.51 21.76 21.99 22.22 22.46 22.69 22.91
5.0 4.5 4.0 3.6 3.0 2.5 2.0 1.5 1.0 0.5 0.1
OF
= 5-
P
QX
1.680 1.651 1.622 1.592 1.560 1.526 1.488 1.447 1.399 1.343 1.272
17.55 18.00 18.44 18.89 19.33 19.78 20.23 20.67 21.12 21.57 22.01
the mixtures and the water vapor pressure of the solutions as calculated by equations 7 and S.
Conclusions (1) Equation 2 represents within narrow limits the variation of the logarithm of the activity coefficient of hydrochloric acid in aluminum chloride solutions. The values of a12change little with ionic strength in these solutions. A like behavior is found for hydrochloric acid-cerium chloride-water systems. ( 2 ) The calculated values of the quantity ~ Z I , vary with ionic strength, and consequently S = 12aI2 4azl is found to decrease with increasing concentration. The magnitude of this decrease indicates that in these concentrated solutions, small deviations from results calculated by equation 3 will occur. This contribution was supported in part by the Atomic Energy Commission under Contract AT(30-1)1375.
+
NEW HAVEN,CONN.
LABORATORY, DEPARTMENT OF CHEMISTRY AND CHEMICAL ENGINEERING, UNIVERSITY O F ILLINOIS]
Mechanism of Complex Electrode Reactions BY K. B. OLDHAM RECEIVEDFEBRUARY 21, 1955 Several possible mechanisms may be envisaged to explain any complex electrode reaction. By assuming a single step to be rate determining, any postulated mechanism may be reduced to an “equivalent reaction pair,” which embodies all the kinetic properties of the mechanism. Account is taken of concentration polarization by including transport processes in the treatment. The procedure is easily extended to cover cases of mixed rate determination. From the equivalent reaction pair, current-voltage relationships can be derived in which it is possible to recognize regions of specific control. The converse operation, the determination of the reaction mechanism from current-voltage curves, is subject to severe limitation. The most direct method, examination of the regions of specific control, is applicable only for intermediate values of the rate constant. Under favorable conditions, experimental data will enable the equivalent reaction pair t o be constructed, from which possible mechanisms may be inferred. Mechanisms yielding the same equivalent pair are kinetically indistinguishable.
Analysis of conditions a t an electrode surface is greatly simplified if one variable, time, can be ignored; hence steady-state conditions only will be treated here. A steady-state electrode system is one in which the activities of all substances present, both a t the electrode surface and in the bulk, do not vary appreciably with time, a t any potential within the experimental range. Constancy of current is a necessary, though not a sufficient, criterion of steady-state conditions. The term “electrode reaction” will here denote those processes intimately coiicerned in the transfer of electrons between an electrode and substances in solution. An electrode reaction may thus involve, in addition t o the actual electron transfer, many other reactions, all occurring within a few molecular diameters of the electrode surface. It is convenient to consider the volume in which electrode reactions occur as a zone in which concentrations are uniform and to refer to the activities of substances in this reaction zone as activities “at” the electrode surface. It must be borne in mind that the reaction zone is also occupied by the electrical double layer, but no further mention will be made of this layer on the assumption that any effect of i t
will be nullified by an excess of indifferent electrolyte, the presence of which will be assumed throughout.
Reaction Rates Any electrode reaction can be represented by a pair of opposed reactions over-all reactants
+ Ne- _r over-all products
(1)
expressing the over-all stoichiometry of the reaction. Only for very simple electrode reactions, such as TI+ eTI, however, can i t be hoped that (1) will depict the mechanism of the process. For a more complex reaction the most likely mechanism is a sequence of a number, say m,of pairs of opposed reactions
+ +
__ __
(2: 1)
initial reactants initial products second reactants )r second products penultimate reactants
final reactants
(2:2)
penultimate products
- 1) (2:m)
(2:m
final products
all proceeding a t the electrode surface. The possibility of parallel reaction paths is considered in an
