Question

1- Calculate activity coefficient $\gamma$ of Mg2+ in a 0.0100 M MgCl2 solution.

a - By linear interpolation data in table 7-1

b - By using extended Debye-Huckel equation

Answer 1

a) From the data given we find,

Ionic strength(micro Molar)	Activity coeffcient	-log(activity coefficient)
0.001	0.872	0.059483515
0.005	0.755	0.122053048
0.01	0.69	0.161150909
0.05	0.52	0.283996656
0.1	0.45	0.346787486

Plotting log(activity coefficient), log($\gamma \pm$) versus ionic strength, we get

0.4 0.35 0.3 0.25 -log(yt)0.063 In(lonic strength) +0.474 0.2 R2 - 0.971 Series1 0.15 Log. (Series1) 0.1 0.05 0 0 0.02 0.04 0.06 0.08 0.1 0.12 lonic strength (uM)

Based on the curve fit we find,

log($\gamma \pm$) = 0.063 * Ionic strength + 0.474

At Ionic strength = 0.01M,

log($\gamma \pm$) = 0.063*ln(0.01) + 0.474

= 0.183874

Therefore,

$\gamma \pm$ for Mg2+ from interpolation = exp(-0.183874)

$\gamma \pm$ for Mg2+ from interpolation = 0.83204

b) From Debye-Huckel theory,

log($\gamma \pm$) = - A*z1*z2*I^0.5

where A = 0.509,

z1 is the charge on the ion 1

z1 is the charge of the ion 2

I is the ionic strength given by

I =0.5* $\sum$Cizi^2

For MgCl2,

I = 0.5* (0.01*2^2+0.02*1^2)

= 0.03

log($\gamma \pm$) = - 0.509*2*1*(0.03)^0.5

= - 0.176323

Therefore,

$\gamma \pm$ for Mg2+ from Debye Huckel theory = exp(-0.176323)

$\gamma \pm$ for Mg2+ from Debye Huckel theory = 0.838347