$A$ solution of formic acid is half-neutralized by the addition of a $KOH$ solution. If $K_a (HCOOH) = 2 \times 10^{-4}$,what is the $pH$ of the solution? (Given: $\log 2 = 0.3010$)

At $298 \text{ K}$, a certain buffer solution contains equal concentrations of $X^-$ and $HX$. The $K_b$ for $X^-$ is $10^{-10}$. What is the $pH$ of this buffer solution?

$20 \, mL$ of $0.2 \, M \, HCN$ is mixed with $10 \, mL$ of $0.2 \, M \, NaOH$. Calculate the $pH$ of the resulting mixture. The $pKa$ value of $HCN$ is $5$.

One litre buffer solution was prepared by adding $0.10 \ mol$ each of $NH_3$ and $NH_4Cl$ in deionised water. The change in $pH$ on addition of $0.05 \ mol$ of $HCl$ to the above solution is $............ \times 10^{-2}$ ($Nearest$ $integer$) ($Given$: $pK_b$ of $NH_3 = 4.745$ and $\log_{10} 3 = 0.477$)

Aqueous solutions of $HNO_3$,$KOH$,$CH_3COOH$,and $CH_3COONa$ of identical concentrations are provided.
The pair$(s)$ of solutions which form a buffer upon mixing is(are):
$A$. $HNO_3$ and $CH_3COOH$
$B$. $KOH$ and $CH_3COONa$
$C$. $HNO_3$ and $CH_3COONa$
$D$. $CH_3COOH$ and $CH_3COONa$

Derive the equation for the calculation of $pH$ of an acidic buffer solution.