Question

Find the activity coefficient of each ion at the indicated ionic strength:

$$\begin{gathered} \mathbf{\left(}\mathbf{a}\mathbf{\right)}{{\mathbf{SO}}_{\mathbf{4}}}^{\mathbf{2}\mathbf{-}}\mathbf{\to }\mathbf{(}\mathbf{\mu }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{01}\mathbf{M}\mathbf{)} \\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}{\mathbf{Sc}}^{\mathbf{3}\mathbf{+}}\mathbf{\to }\mathbf{(}\mathbf{\mu }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{005}\mathbf{M}\mathbf{)} \\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}{\mathbf{Ec}}^{\mathbf{3}\mathbf{+}}\mathbf{\to }\mathbf{(}\mathbf{\mu }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{M}\mathbf{)} \\ \mathbf{\left(}\mathbf{d}\mathbf{\right)}{\mathbf{\left(}{\mathbf{CH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{\right)}}_{\mathbf{3}}{\mathbf{NH}}^{\mathbf{+}}\mathbf{\to }\mathbf{(}\mathbf{\mu }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{M}\mathbf{)} \end{gathered}$$

Short answer

Thus the activity coefficient of each ion with indicated ionic strength is

$$\begin{gathered} {{\mathrm{SO}}_4}^{2-}\to (\mathrm{\mu }=0.01\mathrm{M})\Rightarrow 0.660 \\ {\mathrm{Sc}}^{3+}\to (\mathrm{\mu }=0.005\mathrm{M})\Rightarrow 0.540 \\ {\mathrm{Ec}}^{3+}\to (\mathrm{\mu }=0.1\mathrm{M})\Rightarrow 0.180 \\ {\left({\mathrm{CH}}_3{\mathrm{CH}}_2\right)}_3{\mathrm{NH}}^{+}\to (\mathrm{\mu }=0.05\mathrm{M})\Rightarrow 0.830 \end{gathered}$$

Step-by-step solution

Formula for finding the activity coefficient.

An activity coefficient is a factor used to account for deviations from ideal behavior in a solution.

It is calculated by the formula,

$\log \gamma =-0.5\times {\mathrm{z}}^2\times \sqrt{\mathrm{\mu }}$

where, z is the charge of the ions and$\mathrm{\mu }$ is the ionic strength.

Identifying the Activity coefficient for each ion with its indicated ionic strength.

By using the below table, we can identify the activity coefficient of each ion,

Thus the activity coefficient of each ion with indicated ionic strength is

$$\begin{gathered} {{\mathrm{SO}}_4}^{2-}\to (\mathrm{\mu }=0.01\mathrm{M})\Rightarrow 0.660 \\ {\mathrm{Sc}}^{3+}\to (\mathrm{\mu }=0.005\mathrm{M})\Rightarrow 0.540 \\ {\mathrm{Ec}}^{3+}\to (\mathrm{\mu }=0.1\mathrm{M})\Rightarrow 0.180 \\ {\left({\mathrm{CH}}_3{\mathrm{CH}}_2\right)}_3{\mathrm{NH}}^{+}\to (\mathrm{\mu }=0.05\mathrm{M})\Rightarrow 0.830 \end{gathered}$$