CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 372
Solution
We first determine the molalities of the ions from the specification and from the material balance.
We obtainmH+= 0. 004 , mCa2+= 0. 002 , mCl−= 0.004 + 2× 0 .002 = 0. 008 mol kg−^1.We calculate the ionic strength of the solution from (11.41)I=
1
2
(
0. 004 × 12 + 0. 002 × 22 + 0. 008 × 12)
= 0. 01 mol kg−^1.The activity coefficients of the ions will be calculated from (11.43)γH+= 0. 889 , γCa2+= 0. 624 , γCl−= 0. 889.The mean activity coefficients of HCl and CaCl 2 will be calculated from the results for the ions
activity coefficients and from relation (11.40)γ±,HCl= (0. 889 × 0 .889)^1 /^2 = 0. 889 ,γ±,CaCl 2 =(
0. 624 × 0. 8892) 1 / 3
= 0. 790.11.4.5 Activity coefficients at higher concentrations
Several semiempirical expansions of equation (11.45) have been suggested for the range of higher
values of the ionic strength, e.g.
lnγ±=−A z+z−√
I
1 +
√
I
+B z+z−I , (11.46)whereBdepends on the nature of both the solvent and the ions.