The $pH$ of a solution at $25\,^oC$ containing $0.10\,M$ sodium acetate and $0.03\,M$ acetic acid is ($pK_a$ for $CH_3COOH = 4.57$)

The Henderson-Hasselbalch equation for an acidic buffer is given by $pH - pK_a = 5$. This condition holds true when:

$A$ litre of buffer solution contains $0.1 \ mol$ of each of $NH_3$ and $NH_4Cl$. On the addition of $0.02 \ mol$ of $HCl$ by dissolving gaseous $HCl$,the $pH$ of the solution is found to be $...... \times 10^{-3}$ (Nearest integer).
Given: $pK_b(NH_3) = 4.745$,$\log 2 = 0.301$,$\log 3 = 0.477$,$T = 298 \ K$.

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?

What would be the $pH$ of a solution obtained by mixing $5 \ g$ of acetic acid and $7.5 \ g$ of sodium acetate and making the volume equal to $500 \ mL$? $(K_a = 1.75 \times 10^{-5}, pK_a = 4.76)$

$pH$ of a mixture of $1 \ M \ HA$ $(pK_a = 4.2)$ and $1 \ M \ NaA$ is $4.5$. In $300 \ mL$ of buffer,the volume of $HA$ is $....... \ mL$ $[\log \ 2 = 0.3]$