Question

Find the activity coefficient of ${\mathbf{H}}^{\mathbf{+}}$in a solution containing $\mathbf{0}\mathbf{.}\mathbf{010}\mathbf{}\mathbf{}\mathbf{M}\mathbf{}\mathbf{}\mathbf{HCI}$plus $\mathbf{0}\mathbf{.}\mathbf{040}\mathbf{}\mathbf{}\mathbf{M}\mathbf{}\mathbf{}{\mathbf{KCIO}}_{\mathbf{4}}$ . What is the pH of the solution?

Short answer

Thus the activity coefficient of ${\mathrm{H}}^{+}$is $\gamma \left({\mathrm{H}}^{+}\right)=0.86$and pH of role="math" localid="1654858154412" ${\mathrm{H}}^{+}$ is 2.07

Step-by-step solution

Step 1:Finding the activity coefficient of solution H+

In this problem, we need to find the activity coefficient of ${\mathrm{H}}^{+}$in a solution containing $0.010\mathrm{M}\mathrm{HCI}$plus $0.040\mathrm{M}{\mathrm{KCIO}}_4$ and also we need to find the pH value of the solution.

First, we need to find the activity coefficient of ${\mathrm{H}}^{+}$by calculating the ionic strength $\left(\mathrm{\mu }\right)$,

$\mathrm{\mu }\left(\mathrm{HCI}\right)+\mathrm{\mu }\left({\mathrm{KCIO}}_4\right)=0.001\mathrm{M}+0.04\mathrm{M}=0.05\mathrm{M}$

From the Table $8-1$we can see that the activity coefficient of localid="1654858360555" ${\mathrm{H}}^{+}$is

$\gamma \left({\mathrm{H}}^{+}\right)=0.86$when$0.05\mathrm{M}$

Calculating the pH value of the solution H+.

The pH value of the solution can be calculated by,

$$\begin{gathered} \mathrm{pH}=-\mathrm{log\mu }\left({\mathrm{H}}^{+}\right)\gamma \left({\mathrm{H}}^{+}\right) \\ \mathrm{pH}=-\log \left(0.01\times 0.86\right) \\ \mathrm{pH}=2.07 \end{gathered}$$

Thus the activity coefficient of ${\mathrm{H}}^{+}$is $\gamma \left({\mathrm{H}}^{+}\right)$and pH of ${\mathrm{H}}^{+}$is 2.07