Which of the following statement(s) is/are correct?

(A) The $\mathrm{pH}$ of $1\times {10}^{–8 }\mathrm{M} \mathrm{HCl}$ solution is $8$.

(B) The conjugate base of ${\mathrm{H}}_2{\mathrm{PO}}^{4-}$ is ${\mathrm{HPO}}_4^{2-}$.

(C) ${\mathrm{K}}_{\mathrm{w}}$ increases with increase in temperature.

(D) When a solution of a weak monoprotic acid is titrated against a strong base at half neutralisation point, $\mathrm{pH}=\frac{1}{2}{\mathrm{pK}}_{\mathrm{a}}$. Choose the correct answer from the options given below:

When concentration of ${\mathrm{H}}^{+}$ ion is more than ${10}^{-7}\mathrm{M}$, the proton concentration from water must be considered. Hence, the pH of ${10}^{-8}\mathrm{M} \mathrm{HCl}$ solution is not equal to 8.

$\underset{\mathrm{Acid}}{{\mathrm{H}}_2{\mathrm{PO}}_4^{-}}\stackrel{}{\rightleftharpoons }\underset{\mathrm{Conjugate} \mathrm{base}}{{\mathrm{HPO}}_4^{2-}}+{\mathrm{H}}^{+}$

${\mathrm{K}}_{\mathrm{w}}$ increase with increase in temperature as dissociation of water increases with increase in temperature.

When weak monoprotic acid is titrated against strong base, at half neutralization point, the solution becomes acidic buffer and its $\mathrm{pH}$ is given by

$\mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}+\log \frac{\left[\mathrm{Salt}\right]}{\left[\mathrm{Acid}\right]}$

$\Rightarrow \mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}+0$ as $\left[\mathrm{salt}\right]=\left[\mathrm{acid}\right]$