Question

(3) What affect does the charge of the ion in solution have on the activity coefficient? How does this effect change as a function of the ionic strength (u)? (4) Does the activity coefficient depend on whether the ion is a cation or an anion?

Answer 1

for any ionic solution ,ionic strength $\mu$ is given by the summation of product of molality and (charge )²of the ith ion

suppose for example

AB₂$\rightleftharpoons$ A²⁺ +2B^-

if m is the molailty of AB₂ ,then the molatily of A²⁺ will be m and B^-1 would be 2m since two ions of B is produced

charge of A is +2 and B is -1

so

$\mu = 1/2 \sum m_{i}Z_{i}^{2}$

where m =molality and Z =charge

for the above case

$\mu = 1/2 (m_{A}Z_{A}^{2}+m_{B}Z_{B}^{2})$

$\mu = 1/2 (m*2^{2}+2m*1^{2})$

$\mu = 1/2 (4m+2m)$

$\mu = 1/2 (6m)$

$\mu = 3m$

thus ionic strength is $\mu \propto Z^{2}$ so if charge increases ionic strength increases or vice versa

from the Debye Huckel limiting law

mean ionic activity is related to ionic strength as

^{$-log\gamma_{i}=A \left | Z_{i}^{2 \right |\sqrt{\mu }$}

^{A = constant}

^{3a) if charges increases then activity decreases or vice versa}

^{B)$-log\gamma_{i}\propto \sqrt{\mu }$}

if ionic strength increases then activity coefficient decreases as seen from the above relation

4) mean ionic activity does not depend whether it is cation or anion because what ever be the charge of the cation or anion , the charges will be squared and also we consider the mod value of the charges even if have  1 cation or anion (product of negative value and positive value is always negative value but the mod of negative value will always be positive.)