For the equilibrium $2H_2O \rightleftharpoons H_3O^{+} + OH^{-}$,the value of $\Delta G^o$ at $298 \ K$ is approximately ....... $kJ \ mol^{-1}$.

Assuming complete dissociation,which of the following aqueous solutions will have the same $pH$ value?

The moles of $H^{+}$ from $H_2O$ alone in a $1 \ L$,$\sqrt{5} \times 10^{-7} \ M$ $HCl$ solution at $25 \ ^\circ C$ is ( $\sqrt{5} = 2.23$ )

What is the $[OH^{-}]$ in the final solution prepared by mixing $20.0 \ mL$ of $0.050 \ M \ HCl$ with $30.0 \ mL$ of $0.10 \ M \ Ba(OH)_2$? $...... \ M$

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:

Which $pH$ value is higher in the following pairs?
$(a)$ $0.1 \ M \ HCl$ and $0.1 \ M \ NaOH$
$(b)$ $0.1 \ M \ HCl$ and $0.01 \ M \ HCl$
$(c)$ $0.1 \ M \ NaOH$ and $0.01 \ M \ NaOH$