If molar conductance at infinite dilution for $CH_3COO^-$ and $H^+$ ions are $50 \text{ S cm}^2 \text{mol}^{-1}$ and $350 \text{ S cm}^2 \text{mol}^{-1}$ respectively, and the molar conductivity of $5 \times 10^{-2} \text{ M}$ $CH_3COOH$ is $20 \text{ S cm}^2 \text{mol}^{-1}$, what is the hydrogen ion concentration in $\text{mol/dm}^3$ of $CH_3COOH$?

The dissociation constant of pure water at $18\,^oC$ will be .......... (Degree of dissociation of pure water at $18\,^oC = 1.8 \times 10^{-9}$)

The decreasing order of electrical conductivity of the following aqueous solutions is:
$0.1 \ M$ Formic acid $(a)$
$0.1 \ M$ Acetic acid $(b)$
$0.1 \ M$ Benzoic acid $(c)$

In which of the following mixed aqueous solutions, $pH = pK_{a}$ at equilibrium?
$(1)$ $100 \ mL$ of $0.1 \ M \ CH_{3}COOH + 100 \ mL$ of $0.1 \ M \ CH_{3}COONa$
$(2)$ $100 \ mL$ of $0.1 \ M \ CH_{3}COOH + 50 \ mL$ of $0.1 \ M \ NaOH$
$(3)$ $100 \ mL$ of $0.1 \ M \ CH_{3}COOH + 100 \ mL$ of $0.1 \ M \ NaOH$
$(4)$ $100 \ mL$ of $0.1 \ M \ CH_{3}COOH + 100 \ mL$ of $0.1 \ M \ NH_{3}$

Dilution processes of different aqueous solutions with water are given in $LIST-I$. The effects of dilution of the solutions on $[H^{+}]$ are given in $LIST-II$. (Note: Degree of dissociation $(\alpha)$ of weak acid and weak base is $ << 1$; degree of hydrolysis of salt $ << 1$; $[H^{+}]$ represents the concentration of $H^{+}$ ions)

$LIST-I$	$LIST-II$
$P$. ($10 \ mL$ of $0.1 \ M$ $NaOH$ + $20 \ mL$ of $0.1 \ M$ acetic acid) diluted to $60 \ mL$	$1$. The value of $[H^{+}]$ does not change on dilution
$Q$. ($20 \ mL$ of $0.1 \ M$ $NaOH$ + $20 \ mL$ of $0.1 \ M$ acetic acid) diluted to $80 \ mL$	$2$. The value of $[H^{+}]$ changes to half of its initial value on dilution
$R$. ($20 \ mL$ of $0.1 \ M$ $HCl$ + $20 \ mL$ of $0.1 \ M$ ammonia solution) diluted to $80 \ mL$	$3$. The value of $[H^{+}]$ changes to $1/\sqrt{2}$ times of its initial value on dilution
$S$. $10 \ mL$ saturated solution of $Ni(OH)_2$ in equilibrium with excess solid $Ni(OH)_2$ is diluted to $20 \ mL$ (solid $Ni(OH)_2$ is still present after dilution)	$4$. The value of $[H^{+}]$ changes to $\sqrt{2}$ times of its initial value on dilution

Match each process given in $LIST-I$ with one or more effect$(s)$ in $LIST-II$. The correct option is:

The degree of dissociation of a $0.05 \ M$ solution of $NH_3$ having $pH = 11$ at $25 \ ^oC$ is ...............