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Q. At $700 \,K$, the equilibrium constant, $K _{ p }$, for the reaction $2 SO _{3}( g ) \leftrightharpoons 2 SO _{2}( g )+ O _{2}( g )$ is $1.8 \times 10^{-3} atm$. The value of $K _{ c }$ for the above reaction at the same temperature in moles per litre would be

Equilibrium

Solution:

For the reaction,
$\Delta n=1 $
$\therefore K_{p}=K_{c}(R T)^{\Delta n}=K_{c} R T $
$\therefore K_{c}=\frac{K_{p}}{R T}$
$=\frac{1.8 \times 10^{-3} atm }{0.082\, L \,a t m \,K ^{-1} mol ^{-1} \times 700\, K }=3.13 \times 10^{-5}$