Question

For the following gaseous equilibria $X,YandZ$ at $300K$
$X:2S{O}_2+O_2\rightleftharpoons 2S{O}_3$
$Y:PC{l}_5\rightleftharpoons PC{l}_3+C{l}_2$
$Z:2HI\rightleftharpoons H_2+I_2$

The ratio of $K_p$ and $K_c$ in the increasing order will be:

• A. X = Y = Z
• B. X < Y < Z
• C. X < Z < Y
• D. Z < Y < X

Answer 1

The correct option is C X < Z < Y

For $X:2S{O}_2+O_2\rightleftharpoons 2S{O}_3$
$△n_g=-1$
$\therefore \frac{K_p}{K_c}=(RT{)}^{-1}=(0.0821\times 300{)}^{-1}$
$=\frac{1}{24.63}$
For $Y:PC{l}_5\rightleftharpoons PC{l}_3+C{l}_2$
$△n_g=2-1=1$
$\therefore \frac{K_p}{K_c}=RT=24.63$
For $Z:2HI\rightleftharpoons H_2+I_2$
$△n_g=0$
$\therefore \frac{K_p}{K_c}=(RT{)}^0=1$
Clearly, $K_p/K_c$ increases in the order
$X<Z<Y.$