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Derivation of Kp and Kc

A mixture of ...

Question

A mixture of $3$ moles of ${S O}_{2}$ , $4$ moles of ${N O}_{2}$ and $4$ moles of $N O$ is placed in a $2.0 L$ vessel.
$S O_{2} (g) + {N O}_{2} (g) ⇌ {S O}_{3} (g) + N O (g)$ .
At equilibrium, the vessel is found to contain $1$ mole of $S O_{2}$ . Calculate the value of $K_{c}$ .

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Solution

Reaction:
$S O_{2} (g) + {N O}_{2} (g) ⇌ {S O}_{3} (g) + N O (g)$

Initial Moles 3 4 0 4
At equilibrium 3-2=1 4-2=2 2 4+2=6

So, $K_{c} = \frac{[S O_{3}] [N O]}{[S O_{2}] [N O_{2}]} = \frac{2 \times 6}{1 \times 2} = 6$

The correct answer is 6

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