Question
In which of the following equilibrium $${K_c}$$ and $${K_p}$$ are not equal?
A.
$$2NO\left( g \right) \rightleftharpoons {N_2}\left( g \right) + {O_2}\left( g \right)$$
B.
$$S{O_2}\left( g \right) + N{O_2}\left( g \right) \rightleftharpoons S{O_3}\left( g \right) + NO\left( g \right)$$
C.
$${H_2}\left( g \right) + {I_2}\left( g \right) \rightleftharpoons 2HI\left( g \right)$$
D.
$$2C\left( s \right) + {O_2}\left( g \right) \rightleftharpoons 2\,C{O_2}\left( g \right)$$
Answer :
$$2C\left( s \right) + {O_2}\left( g \right) \rightleftharpoons 2\,C{O_2}\left( g \right)$$
Solution :
Key Idea The reaction for which the number of moles of gaseous products $$\left( {{n_p}} \right)$$ is not equal to the number of moles of gaseous reactants $$\left( {{n_R}} \right),$$ has different value of $${K_C}$$ and $${K_p}.$$
$$\eqalign{
& {\text{From the equation,}}\,{K_p} = {K_C} \times {\left( {RT} \right)^{\Delta \,{n_g}}} \cr
& {\text{where, }}\left[ {\Delta {n_g}\,{\text{gaseous}} = {n_p} - {n_R}} \right] \cr
& \left( {\text{a}} \right)\,{n_p} = {n_R} = 2,\,{\text{thus,}}\,{K_p} = {K_C} \cr
& \left( {\text{b}} \right)\,{n_p} = {n_R} = 2,\,{\text{thus,}}\,{K_p} = {K_C} \cr
& \left( {\text{c}} \right)\,{n_p} = {n_R} = 2,\,{\text{thus,}}\,{K_p} = {K_C} \cr
& \left( {\text{d}} \right)\,{n_p} = 2,\,\,{n_R} = 1,\,{\text{thus,}}\,{K_p} \ne {K_C} \cr} $$