Question

Using activities, find $\left[{\mathrm{Ag}}^{+}\right]$in $\mathbf{0}\mathbf{.}\mathbf{060}\mathbf{MKSCN}$saturated with$\mathbf{AgSCN}\left(s\right)$

Short answer

The concentration of ${\mathrm{Ag}}^{+}$ion in 0.060MKSCN is$2.9\times {10}^{-11}\mathrm{M}$

Step-by-step solution

Define the formula for activity species.

Any species' activity value is calculated by multiplying its concentration by its activity coefficient.

For a species C, the activity is given by

${\mathbf{A}}_{\mathbf{c}}\mathbf{=}\left[C\right]{\mathbf{\gamma }}_{\mathbf{c}}$

where,

A - Activity

[c] - Concentration

- Activity coefficient.

Calculate the activity species.

Given

$0.060{\mathrm{MKSCN}}^{-1}$saturated with ${\mathrm{AgSCN}}_{\left(\mathrm{s}\right)}$

The ionic strength $\left(\mu \right)$is $0.060\mathrm{M}$from KSCN,

The solubility product expression

$$\begin{gathered} \mu =0.060M \\ {\mathrm{K}}_{\mathrm{SP}}=\left[{\mathrm{Ag}}^{+}\right]{\gamma }_{{\mathrm{Ag}}^{+}}\left[{\mathrm{SCN}}^{-}\right]{\gamma }_{\mathrm{SCN}}=1.1\times {10}^{-12}\mathrm{At}\mathrm{and}{\mathrm{\gamma }}_{\mathrm{SCN}}=0.80 \\ {\gamma }_{A{g}^{-}}=0.79 \end{gathered}$$

Substitute the values of concentration and activity coefficients into the solubility product expression

$$\begin{gathered} {\mathrm{K}}_{\mathrm{SP}}=\left[{\mathrm{Ag}}^{+}\right]\left(0.79\right)\left[0.060\right]\left(0.80\right) \\ =1.1\times {10}^{-12}\left[{\mathrm{Ag}}^{+}\right] \end{gathered}$$

The concentration of${\mathrm{Ag}}^{+}$ion in$0.060\mathrm{MKSCN}\mathrm{is}2.9\times {10}^{-11}\mathrm{M}$