The dissociation constant of acetic acid is $x \times 10^{-5}$. When $25 \ mL$ of $0.2 \ M \ CH_3COONa$ solution is mixed with $25 \ mL$ of $0.02 \ M \ CH_3COOH$ solution,the $pH$ of the resultant solution is found to be equal to $5$. The value of $x$ is $..........$.

Class $XII$ students were asked to prepare one litre of buffer solution of $pH$ $8.26$ by their chemistry teacher. The amount of ammonium chloride to be dissolved by the student in $0.2 \, M$ ammonia solution to make one litre of the buffer is $..... \, g$ (Given $pK_b(NH_3)=4.74$; Molar mass of $NH_3=17 \, g \, mol^{-1}$; Molar mass of $NH_4Cl =53.5 \, g \, mol^{-1}$)

The $pH$ of a buffer solution made by mixing $25 \ mL$ of $0.02 \ M$ $NH_4OH$ and $25 \ mL$ of $0.2 \ M$ $NH_4Cl$ at $25^{\circ}C$ is ($pK_b$ of $NH_4OH = 4.8$).

Which of the following statements is incorrect for a buffer solution?

$A$ 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: $pK_b(NH_3) = 4.745$,$\log 2 = 0.301$,$\log 3 = 0.477$,$T = 298 \ K$.

Which among the following pairs constitutes a buffer?