When $1$ mole of $\mathrm{A}$ $\left(\mathrm{g}\right)$ is introduced in a closed rigid $1$ litre vessel maintained at constant temperature the following equilibria are established.

$\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{B}\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{g}\right):{\mathrm{K}}_{{\mathrm{c}}_1}$

$\mathrm{C}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{D}\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right):{\mathrm{K}}_{{\mathrm{C}}_2}$

The pressure at equilibrium is twice the initial pressure. Calculate the value of $\frac{{\mathrm{K}}_{{\mathrm{C}}_2}}{{ \mathrm{K}}_{{\mathrm{C}}_1}}$ if $\frac{[\mathrm{C}{]}_{\text{eq }}}{[\mathrm{B}{]}_{\text{leq }}}=\frac{1}{5}$

Boric acid is a weak monoprotic acid. It ionizes in water as

$\mathrm{B}{\left(\mathrm{OH}\right)}_3+{\mathrm{H}}_2\mathrm{O}\leftrightharpoons \mathrm{B}{\left(\mathrm{OH}\right)}_4^{-}+{\mathrm{H}}^{+} : {\mathrm{K}}_{\mathrm{a}}=5.9\times {10}^{-10}$

Calculate $\mathrm{pH}$ of $0.3\mathrm{M}$ boric acid.

A vessel contains three gases $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ in the equilibrium $\mathrm{A}\rightleftharpoons 2\mathrm{B}+\mathrm{C}$

At equilibrium, the concentration of $\mathrm{A}$ was $3 \mathrm{M}$ and that of $\mathrm{B}$ was $4 \mathrm{M}$. On doubling the volume of the vessel, the new equilibrium concentration of $\mathrm{B}$ was $3 \mathrm{M}$ Calculate ${\mathrm{K}}_{\mathrm{c}}$ and the initial equilibrium concentration of $\mathrm{C}$.

The density of an equilibrium mixture of ${\mathrm{N}}_2{\mathrm{O}}_4$ and ${\mathrm{NO}}_2$ at $1 \mathrm{atm}$ and $346 \mathrm{K}$ is $\frac{1.8 \mathrm{g}}{\mathrm{L}}.$ Calculate ${\mathrm{K}}_{\mathrm{c}}$ for the reaction.

${\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$

At $1200°\mathrm{C}$, the following equilibrium is established between chlorine atoms & molecule.

${\mathrm{Cl}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{Cl}\left(\mathrm{g}\right)$

The composition of equilibrium mixture may be determined by measuring the rate of effusion of the mixture through a pin hold. It is found that at $1200°\mathrm{C}$ and $1$ atm pressure the mixture effuses $1.16$ times as fast as krypton effuses under the same condition. Calculate the equilibrium constant ${\mathrm{K}}_{\mathrm{c}}$.