What is the relationship between $K_{p}$ and $K_{c}$ when $\Delta n = 0$,$\Delta n > 0$,and $\Delta n < 0$?
The relationship is given by the equation $K_{p} = K_{c}(RT)^{\Delta n}$.
$1$. If $\Delta n = 0$,then $K_{p} = K_{c}(RT)^{0} = K_{c}$.
Example: $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,where $\Delta n = 2 - (1+1) = 0$.
$2$. If $\Delta n > 0$,then $K_{p} = K_{c}(RT)^{\text{positive value}}$,which implies $K_{p} > K_{c}$.
Example: $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,where $\Delta n = (1+1) - 1 = +1$.
$3$. If $\Delta n < 0$,then $K_{p} = K_{c}(RT)^{\text{negative value}}$,which implies $K_{p} < K_{c}$.
Example: $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,where $\Delta n = 2 - (1+3) = -2$.
$1$. If $\Delta n = 0$,then $K_{p} = K_{c}(RT)^{0} = K_{c}$.
Example: $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,where $\Delta n = 2 - (1+1) = 0$.
$2$. If $\Delta n > 0$,then $K_{p} = K_{c}(RT)^{\text{positive value}}$,which implies $K_{p} > K_{c}$.
Example: $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,where $\Delta n = (1+1) - 1 = +1$.
$3$. If $\Delta n < 0$,then $K_{p} = K_{c}(RT)^{\text{negative value}}$,which implies $K_{p} < K_{c}$.
Example: $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,where $\Delta n = 2 - (1+3) = -2$.
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MediumAIEEE 2005
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