Question

For which one of the following reactions $K_p =K_c?$

• A. $PCl_5 \rightleftharpoons PCl_3 + Cl_2$
• B. $N_2 +O_2 \rightleftharpoons 2NO $
• C. $N_2 + 3H_2 \rightleftharpoons 2NH_3 $
• D. $2SO_3 \rightleftharpoons 2SO_2 + O_2 $

Answer 1

Answer: (B)

$K_p=K_c(RT)^{\Delta n_g}$
$ K_p = K_c$ only when $(RT)^{\Delta n}=0$
(a) $PCl_5 \rightleftharpoons PCl_3+Cl_2$
$ \Delta n_g=n_p-n_g$
$ = 2-1$
$ = 1 $
$\therefore \Delta K_p \ne K_c$
(b) $N_2 +3O_2 \rightleftharpoons 2NO$
$ \Delta n_g=2-2$
$ = 0$
$\therefore K_p = K_c $
(c) $N_2 +3H_2 \rightleftharpoons 2NH_3 $
$ \Delta n_g=2-4$
$ = -2$
$\therefore K_p \ne K_c$
(d) $2SO_3 \rightleftharpoons 2SO_2 + O_2$
$ \Delta n_g=3-2=1$
$\therefore K_p \ne K_c$