61 16
VOl. 74
NOTES
his calculated hydrolysis constants that complexing of by halide ions occurs in such solutions. We have systematically interpreted his data on the assumption of equilibria (1) and ( 2 )
+
+
In+a H20 = InOH+2 11’ Inf3 X - = InX+*
+
(1) (2)
X- stands for C1-, Br- or I- in the appropriate cases. We may write the equilibrium constants for these reactions in terms of concentrations (moles/liter) of the various species K, = (InOH+) (H +)/(In ; K Z= (InX + z ) / (In ( X -) . If we denote the total concentration of indium (111)by m, i t follows that m = (In+3)
+ (InOH+2) -/3nz
(I1lXcz), (InX t 2 )
-
constants we have calculated (H+) for various values of m. These calculated values of (Hi) together with the experimental values of Moeller are presented in Table I1 for several dilute solutions of each of the indium halides. TABLE I1 Solution
n1
x
(H+) 10’
Calcd.
- (H+) =
=
(X-), and (InOHt2) = (II+)
3m IC2/&
1
1
__ I+ (KB(H+)Z/KI) ’ K1
(3)
Assuming that Kz(I-I+) ”Kl is sinall compared to unity equation (4) results.
From the experimental data,3 the quantity nz (H+)/(H+)zwas calculated for various valucs of m, in the range 5.10-4 to 4.10-? 1117,and plotted as a function of m. I n accordance with equation (4) this plot was linear in dilute solutions. From the slope and intercept of this line values of K1 and Kz were calculated. An analytical treatment of the data using the interpolation formula of Lagrange4 was also made. The values of K l and K z thus obtained agreed quite well with those found by the graphical method. Actually the graphical extrapolation is, to a certain extent, subjective and the agreement with the analytical procedure provides some justification for the graphical valucs. 121though corrections involving the activity coefficients of the several species might be expected to d e c t the values of K1 and Kz by as much as 2 0 5 , we have not incorporated such Corrections in our treatment since the graphical values (presumably pertaining to infinite dilution) and the analytical values (which are, in a sense, averages over a range of concentrations) arc in accord. Table I gives the values of IC1and IC2 obtained by the analytical method. These values bear out the validity of the ussuinption that K 2 ( H f)?/Ki is Solutloll
‘r’wI’1: I Kl x IO’
:x
InC13 IuBra
1
Ill13
1.46
1 ax
irr
223 1XI 95 5
small compared to unity since ( H i ) is of the order M in the solutions upon which the above of calculations are based. K1 is independent of the anion, and the halide complexing constants decrease with increasing anion radius as might be expected for electrostatically bonded complexes. Equation (3) may be solved for (H+) in terms of m, K1 and Kz. Inserting the above values for these (4) See for example, H. Margenau a n d G L i Murphy, “The Mathcmatics of Physics arid C h c m i s t i r r , ” D. Van Nustraii(l Co , InL , K e n Y c r k , U Y 1$23
10‘
1.8 4.1 4.7 3.0 3.5 4.8 R.0 17.0 1. 3 5.4 6.5 7.5
Coiiibining these re1;ttions me obtain cquation (3) 111
x
Exptl
1.8 4 .0 4.5 3 ,7
3.8 4.7 6.0 7.9 4.3 5, 3 6.6 8.1
The agreement of the experimental and calculated values of (H+) provides substantiation of the original assumption of equilibria (1) and ( 2 ) and also of the tabulated values of K1 and Kz. From the magnitude of the values given in Table I for K 1 and KZ it may be seen that in concentrated solutions the hydrolysis reaction becomes InX+2
+ H20= InOH+*+ H + + X-
(5)
since reaction ( 2 ) is virtually complete. Designating the equilibrium constant of reaction ( 5 ) as 1
