Question
For the reaction $$:2N{O_{2\left( g \right)}} \rightleftharpoons 2N{O_{\left( g \right)}} + {O_{2\left( g \right)}},$$
$$\left( {{K_c} = 1.8 \times {{10}^{ - 6}}\,{\text{at}}\,{{184}^ \circ }C} \right)\left( {R = 0.0831\,kJ/\left( {mol.\,K} \right)} \right)$$
When $${K_p}$$ and $${K_c}$$ are compared at $${{{184}^ \circ }C}$$ it is found that
A.
Whether $${K_p}$$ is greater than, less than or equal to $${K_c}$$ depends upon the total gas pressure
B.
$${K_p} = {K_c}$$
C.
$${K_p}$$ is less than $${K_c}$$
D.
$${K_p}$$ is greater than $${K_c}$$
Answer :
$${K_p}$$ is greater than $${K_c}$$
Solution :
$$\eqalign{
& {\text{For the reaction : }}2N{O_2}\left( g \right) \rightleftharpoons 2NO\left( g \right) + {O_2}\left( g \right) \cr
& {\text{Given}}\,\,\,{K_c} = 1.8 \times {10^{ - 6}}\,{\text{at}}\,{184^ \circ }C \cr
& R = 0.0831\,kj/mol.k \cr
& {K_p} = 1.8 \times {10^{ - 6}} \times 0.0831 \times 457 = 6.836 \times {10^{ - 6}} \cr
& \left[ {\because \,\;{{184}^ \circ }C = \left( {273 + 184} \right) = 457k,\,\,\Delta n = \left( {2 + 1 - 2} \right) = 1} \right] \cr
& {\text{Hence it is clear that}}\,\,{K_p} > {K_c} \cr} $$