If the solubility product of $\mathrm{PbS}$ is $8\times {10}^{-28}$, then the solubility of $\mathrm{PbS}$ in pure water at $298 \mathrm{K}$ is $\mathrm{x}\times {10}^{-16} \mathrm{mol}{ \mathrm{L}}^{-1}$. The value of $\mathrm{x}$ is____ (Nearest integer) [Given $\sqrt{2}=1.41$]

A litre of buffer solution contains $0.1$ mole of each of ${\mathrm{NH}}_3$ and ${\mathrm{NH}}_4\mathrm{Cl}$. On the addition of $0.02$ mole of $\mathrm{HCl}$ by dissolving gaseous $\mathrm{HCl}$, the $\mathrm{pH}$ of the solution is found to be $\_\_\_\_\_\times {10}^{-3}$ (Nearest integer)

Given: ${\mathrm{pK}}_{\mathrm{b}}\left({\mathrm{NH}}_3\right)=4.745$

$\log 2=0.301$

$\log 3=0.477$

$\mathrm{T}=298 \mathrm{K}]$

Consider the following reaction approaching equilibrium at $27°\mathrm{C}$ and $1$ atm pressure

$\mathrm{A}+\mathrm{B}\underset{{\mathrm{K}}_{\mathrm{r}}={10}^2}{\stackrel{{\mathrm{K}}_{\mathrm{t}}=0^3}{\rightleftharpoons }}\mathrm{C}+\mathrm{D}$

The standard Gibb's energy change $\left({\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}°\right)$ at $27°\mathrm{C}$ is $\left(-\right)$ _____ ${\mathrm{kJmol}}^{-1}$ (Nearest integer).

(Given : $\mathrm{R}=8.3\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ and $\ln 10=2.3$)

Water decomposes at $2300 \mathrm{K}$

${\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)$

The percent of water decomposing at $2300 \mathrm{K}$ and 1 bar is _____ (Nearest integer). Equilibrium constant for the reaction is $2\times {10}^{-3}$ at $2300 \mathrm{K}$