Question

The value of $K_p/K_C$ for the following reactions at $300K$ are, respectively :(At $300K,RT=24.62$ $d{m}^3$ atm $mo{l}^{-1}$)
$N_2(g)+O_2(g)\leftrightharpoons 2NO(g)$
$N_2{O}_4(g)\leftrightharpoons 2N{O}_2(g)$
$N_2(g)+3H_2(g)\leftrightharpoons 2N{H}_3(g)$

• A. $1,24.62d{m}^{3}atmmo{l}^{-1},$ $606.0d{m}^{6}at{m}^{2}mo{l}^{-2}$
• B. $1,4.1\times 10^{-2}d{m}^{-3}at{m}^{-1}mo{l}^{-1},$ $606.0d{m}^{6}at{m}^{2}mo{l}^{-2}$
• C. $606.0d{m}^{6}at{m}^{2}mo{l}^{-2},$ $1.65\times 10^{-3}d{m}^{3}at{m}^{-2}mo{l}^{-1}$
• D. $1,24.62d{m}^{3}atmmo{l}^{-1},$ $1.65\times 10^{-3}d{m}^{-6}at{m}^{-2}mo{l}^2$

Answer 1

Answer: (D)

We know that, the relationship between $K_p$ and $K_C$ of a chemical equilibrium state (reaction) is
$K_p=K_C(RT{)}^{\Delta n_g}$
$\Rightarrow \frac{K_p}{K_C}=(RT{)}^{\Delta n_g}$
where, $\Delta n_g=\Sigma n_{\text{Products }}-\Sigma n_{\text{Reactants }}$
(i) $N_2(g)+O_2(g)\rightleftharpoons 2NO(g)$
$\Rightarrow (RT{)}^{2-(1+1)}=(RT{)}^0=1$
(ii) $N_2{O}_4(g)\rightleftharpoons 2N{O}_2(g)$
$\Rightarrow (RT{)}^{2-1}=RT=24.62d{m}^{3}atmmo{l}^{-1}$
(iii) $N_2(g)+3H_2(g)\rightleftharpoons 2N{H}_3(g)$
$\Rightarrow (RT{)}^{2-(3+1)}=(RT{)}^{-2}$
$=\frac{1}{{\left(24.62d{m}^{3}atmmo{l}^{-1}\right)}^2}$
$=1.649\times 10^{-3}d{m}^{-6}at{m}^{-2}mo{l}^2$