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Derivation of Kp and Kc

For a reactio...

Question

For a reaction $F e O (s) + C O (g) ⇌ F e (s) + C O_{2} (g)$ the value of $K_{ρ}$ at $1373 K$ is $0.505$ .If the reaction mixture has $1$ mole eaach of $F e$ and $F e O, 1.5$ atm $C O$ and $0.6$ atm $C O_{2}$ ,in which direction will the reaction go?

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Solution

$F e O (s) + C O (g) ⇋ F e (s) + C O_{2} (g)$
As, $Δ n =$ (Number of moles of products) $-$ (Number of moles of reactants) $= 1 - 1 = 0$
So, $K_{p} = K_{c} (R T)^{Δ n}$
$⟹ K_{p} = K_{c}$ ;
$K_{p} = \frac{P_{C O_{2}}}{P_{C O}}$
$K_{c} = \frac{[C O_{2}]}{[C O]}$
Given, $K_{p} = 0.505$
$Q = \frac{P_{C O_{2}}}{P_{C O}} = \frac{0.6}{1.5} = \frac{2}{5} = 0.4$
As, $Q < K_{p}$ so reaction will proceed to increase $C O_{2}$ . So, reaction proceeds forward.

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