Answer: X < Z < Y
For X: $2SO_2 + O_2 \rightleftharpoons 2SO_3$
$\Delta n_g = -1$
$\therefore \frac{K_p}{K_c} = (RT)^{-1} = (0.0821 \times 300)^{-1} = \frac{1}{24.63}$
For Y : $PCl_5 \rightleftharpoons PCl_3 + Cl_2$
$\Delta n_g = 2 - 1 = 1$
$\therefore \frac{K_p}{K_c} = RT = 24.63$
For Z : $2HI \rightleftharpoons H_2 + I_2$
$\Delta n_g = 0$
$\therefore \frac{K_p}{K_c} = (RT)^0 = 1 $
Clearly, $\frac{K_p}{K_c}$ increases in the order X < Z < Y