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Derivation of Kp and Kc

In which of t...

Question

In which of the following equilibrium, $K_{c}$ and $K_{p}$ are not equal?

2 C (s) + O_{2} (g) ⇌ 2 C O (g)

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2 N O (g) ⇌ N_{2} (g) + O_{2} (g)

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S O_{2} (g) + N O_{2} (g) ⇌ S O_{3} (g) + N O (g)

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H_{2} (g) + I_{2} (g) ⇌ 2 H I (g)

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Solution

The correct option is A $2 C (s) + O_{2} (g) ⇌ 2 C O (g)$
In the equilibrium $2 C (s) + O_{2} (g) ⇌ 2 C O (g)$ , $K_{c}$ and $K_{p}$ are not equal as $Δ n \neq 0$ . $Δ n$ is the difference in the number of moles of gaseous products and gaseous reactants.
$K_{p} = K_{c} (R T)^{Δ n}$
Now,
$Δ n = 2 - 1 = 1$
$K_{p} = K_{c} (R T)^{1}$
$∴ K_{p} \neq K_{c}$

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