Chemistry - Mole Concept Question with Solution | TestHub

Given ,$2\mathrm{P}\mathrm{Q}\rightleftharpoons {\mathrm{P}}_2+{\mathrm{Q}}_2;$
${\mathrm{K}}_1=\frac{\left[{\mathrm{P}}_2\right]\left[{\mathrm{Q}}_2\right]}{[\mathrm{P}\mathrm{Q}{]}^2}=2.5\times 10^5$
$\mathrm{P}\mathrm{Q}+1/2{\mathrm{R}}_2\rightleftharpoons \mathrm{P}\mathrm{Q}\mathrm{R};$
${\mathrm{K}}_2=\frac{\left[\mathrm{P}\mathrm{Q}\mathrm{R}\right]}{\left[\mathrm{P}\mathrm{Q}\right][{\mathrm{R}}_2{]}^{1/2}}$
$=5\times 10^{-3}$
For the required equilibrium
$1/2{\mathrm{P}}_2+1/2{\mathrm{Q}}_2+1/2{\mathrm{R}}_2\rightleftharpoons \mathrm{P}\mathrm{Q}\mathrm{R};$
${\mathrm{K}}_3=\frac{\left[\mathrm{P}\mathrm{Q}\mathrm{R}\right]}{\left[{\mathrm{P}}_2{]}^{1/2}\right[{\mathrm{Q}}_2{]}^{1/2}[{\mathrm{R}}_2{]}^{1/2}}$
${\mathrm{K}}_3={\mathrm{K}}_2\times \sqrt{\frac{1}{{\mathrm{K}}_1}}$
$=5\times 10^{-3}\times \sqrt{\frac{1}{2.5\times 10^5}}=\frac{5\times 10^{-3}}{0.5\times 10^3}$
$=1\times 10^{-5}$