Calculate the $pH$ of a mixed solution containing $10 \ mL$ of $0.2 \ M$ $Ca(OH)_2$ and $25 \ mL$ of $0.1 \ M$ $HCl$.

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:

From an aqueous solution of $ZnSO_4$,normal zinc carbonate may be precipitated by

Order of solubility of solid $AgCl_{(s)}$ in given cases.
$(i)$ In pure water
$(ii)$ In presence of $0.1 \ M$ $AgNO_3$
$(iii)$ In presence of $2 \ M$ $aq.$ solution of $KCN$
$(iv)$ In presence of $1 \ M$ $aq.$ solution of $Ca(CN)_2$
$(v)$ In presence of $2 \ M$ $aq.$ solution of $NH_3$
(Assuming $100 \%$ dissociation of $AgNO_3$,$KCN$ and $Ca(CN)_2$ and complex formation with $NH_3$ and $CN^{-}$ will take place.)

The dissociation constant of a weak acid is $1 \times 10^{-4}$. The equilibrium constant of its reaction with a strong base is:

What is ionic equilibrium? Discuss the relation of types of substances and ionic equilibrium in solution.