At $STP$, the dissociation reaction of water is $H_2O \rightleftharpoons H^{+}(aq.) + OH^{-}(aq.)$, and the $pH$ of water is $7.0$. The change of standard free energy $(\Delta G^{\circ})$ for the above dissociation process is given by

Which of the following statement$(s)$ is/are correct?
$ (A) $ The $pH$ of $1 \times 10^{-8} \ M \ HCl$ solution is $8$.
$ (B) $ The conjugate base of $H_2PO_4^{-}$ is $HPO_4^{2-}$.
$ (C) $ $K_w$ increases with increase in temperature.
$ (D) $ When a solution of weak monoprotic acid is titrated against a strong base at half neutralisation point,$pH = pK_a$.
Choose the correct answer from the option given below.

What will be the $pH$ of a solution formed by mixing $40 \, cm^3$ of $0.1 \, M \, HCl$ with $10 \, cm^3$ of $0.45 \, M \, NaOH$?

The ionization constant of propanoic acid is $1.32 \times 10^{-5}$. Calculate the degree of ionization of the acid in its $0.05 \, M$ solution and also its $pH$. What will be its degree of ionization if the solution is $0.01 \, M$ in $HCl$ also?

By adding $20 \ mL$ $0.1 \ N$ $HCl$ to $20 \ mL$ $0.1 \ N$ $KOH$,the $pH$ of the obtained solution will be

When $50 \ mL$ of $0.1 \ M$ $HCl$ and $50 \ mL$ of $0.2 \ M$ $NaOH$ solutions are mixed,the $pH$ of the resulting solution will be: