For a reaction $2{\mathrm{A}}_{\left(\mathrm{g}\right)}\rightleftharpoons 2{\mathrm{B}}_{\left(\mathrm{g}\right)}+{\mathrm{C}}_{\left(\mathrm{g}\right)},{\mathrm{K}}_{\mathrm{c}}=3.75\times {10}^{-6}$ at $1069 \mathrm{K}$. The approximate value of ${\mathrm{K}}_{\mathrm{p}}$ for this reaction at the same temperature is $\left(\mathrm{R}=0.082 \mathrm{L}\right.\mathrm{bar}\left.{\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}\right)$

Equilibrium constant in terms of concentration $\left({\mathrm{K}}_{\mathrm{c}}\right)$ and in terms of partial pressure $\left({\mathrm{K}}_{\mathrm{p}}\right)$ are related as,

${\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}(\mathrm{RT}{)}^{∆\mathrm{n}}$

$\mathrm{\Delta n}=$ number of gaseous moles of product $-$ number of gaseous moles of reactant

$∆\mathrm{n}=3-2=1$

Hence,

${\mathrm{K}}_{\mathrm{p}}=3.75\times {10}^{-6}\times \left[0.082\times 1069\right]$

$=3.28\times {10}^{-4}$

$\approx 3.3\times {10}^{-4}$