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Derivation of Kp and Kc

The value of ...

Question

The value of $\frac{K_{p}}{K_{c}} \frac{i n a t m}{i n M}$ for the reaction,
$S O_{2} {C l}_{2} (g) ⇌ {S O}_{2} (g) + {C l}_{2} (g)$ at temperature 365.4 K is $3 \times 10^{a}$ . The value of $a$ is:

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Solution

$K_{P} = K_{c} (R T)^{△ n g}$
$\frac{K_{P}}{K_{c}} = (R T)^{△ n g}$
For the reaction, $S O_{2} C l_{2} (g) ⇌ S O_{2} (g) + C l_{2} (g) △ n g = 1 + 1 - 1 = 1$
$∴ \frac{K_{P}}{K_{C}} = (R T)^{△ n g} = R T = 0.821 \times 365.4$
$∴ \frac{K_{P}}{K_{C}} = 30 = R T = 3 \times 10^{1} ⟹ a = 1$

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