Question

Assuming complete dissociation of the salts, calculate the ionic strength of

(a)$\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{mM}\mathbf{}\mathbf{K}\mathbf{}{\mathbf{NO}}_{\mathbf{3}}$

(b)$\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{mM}\mathbf{}{\mathbf{Cs}}_{\mathbf{2}}\mathbf{}{\mathbf{CrO}}_4$

(c) $\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{m}\mathbf{}{\mathbf{MMgCl}}_2$plus$\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{mM}\mathbf{}{\mathbf{AlCl}}_{\mathbf{3}}$

Short answer

(a) The ionic strength of 0.2m MKNO is 0.2mM

(b) The ionic strength of$0.2\mathrm{mM}{\mathrm{Cs}}_2{\mathrm{CrO}}_4$ is 0.6mM

(c) The ionic strength of$0.2\mathrm{m}{\mathrm{MMgCl}}_2$ plus$0.3\mathrm{mM}{\mathrm{AlCl}}_3$ is 2.4mM

Step-by-step solution

Define the ionic strength

The ionic strength of a solution is the amount of ion concentration in it. It's written in the form of I. It has an impact on ion activity. The ion interaction with water and other ions in the solution is marked. The ionic strength formula is used to calculate half of each ionic species' total concentration.

The formula for ionic strength is as follows:

$I=\frac{1}{2}\sum _1^n{C}_i{Z}_j^2$

Calculate the ionic strength of KNO3

The given data is

0.2mM solution of${\mathrm{KNO}}_3$

Calculate the ionic strength by using the ionic strength calculation formula

$$\begin{gathered} \mathrm{\mu }=\frac{1}{2}\left[\left[{\mathrm{K}}^{+}\right]{\left(+1\right)}^2+\left[{{\mathrm{NO}}_3}^{-}\right]{\left(-1\right)}^2\right] \\ =\left(\frac{1}{2}\left[\left[0.2\right]{\left(+1\right)}^2+\left[0.2\right]{\left(-1\right)}^2\right]\right)\mathrm{mM} \\ =\left(\frac{1}{2}\left[0.4\right]\right)\mathrm{mM} \\ =0.2\mathrm{mM} \end{gathered}$$

The ionic strength of 0.2mM KNO is 0.2mM.

Calculate the ionic strength of Cs2 CrO4

The given information is

0.2mM solution of${\mathrm{C}}_{{\mathrm{s}}_2}{\mathrm{CrO}}_4$

Calculate the ionic strength by using the ionic strength calculation formula

$$\begin{gathered} \mathrm{\mu }=\frac{1}{2}\left[2\left[C{s}^{+}\right]{\left(+1\right)}^2+\left[Cr{O}_{{}_3}^{2-}\right]{\left(-2\right)}^2\right] \\ =\left(\frac{1}{2}\left[\left(0.4\right){\left(+1\right)}^2+\left[0.2\right]{\left(-2\right)}^2\right]\right)\mathrm{mM} \\ =\left(\frac{1}{2}\left[1.2\right]\right)\mathrm{mM} \\ =0.6\mathrm{mM} \end{gathered}$$

The ionic strength of 0.2mM ${\mathrm{Cs}}_2{\mathrm{CrO}}_4$is 0.6mM.

Calculate the ionic strength of 0.2m MMgCl2

The given data is

$0.2\mathrm{m}{\mathrm{MMgCl}}_2$plus$0.3\mathrm{mM}{\mathrm{AlCl}}_3$

Calculate the ionic strength by using the ionic strength calculation formula

$$\begin{gathered} \mathrm{\mu }=\frac{1}{2}\left[2\left[M{g}^{2+}\right]{\left(+2\right)}^2+2\left[C{l}^{-}\right]{\left(-1\right)}^2+\left[A{l}^{3+}\right]{\left(3\right)}^2+3\left[C{l}^{-}\right]{\left(-1\right)}^2\right] \\ =\left(\frac{1}{2}\left[\left(0.2\right){\left(+2\right)}^2+\left[0.4\right]{\left(-1\right)}^2+\left[0.3\right]{\left(3\right)}^2+\left[0.9\right]{\left(-1\right)}^2\right]\right)\mathrm{mM} \\ =\left(\frac{1}{2}\left[0.8+0.4+2.7+0.9\right]\right)\mathrm{mM} \\ =2.4\mathrm{mM} \end{gathered}$$