${\mathrm{p}}^{\mathrm{H}}$ of a mixture containing 100 ml of 0.1 M HCl and 200 ml of 0.05 M NaOH at 298K

$$\begin{gathered} {\mathrm{V}}_{\mathrm{a}}{\mathrm{N}}_{\mathrm{a}}=\frac{100\left(0.1\right)}{1000}={10}^{-2} \\ {\mathrm{V}}_{\mathrm{b}}{\mathrm{N}}_{\mathrm{b}}=\frac{200\left(0.05\right)}{1000}={10}^{-2} \\ \because {\mathrm{V}}_{\mathrm{a}}{\mathrm{N}}_{\mathrm{a}}={\mathrm{V}}_{\mathrm{b}}{\mathrm{N}}_{\mathrm{b}} \end{gathered}$$

The solution is neutral,  ${\mathrm{p}}^{\mathrm{H}}$ = 7