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Derivation of Kp and Kc

For the react...

Question

For the reaction, $N_{2} (g) + 3 H_{2} (g) ⇌ 2 N H_{3} (g)$ , equilibrium constant $K_{C}$ is:

\frac{(n_{N H_{3}})^{2}}{(n_{N_{2}}) (n_{H_{2}})^{3}} V

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\frac{(n_{N H_{3}})^{2}}{(n_{N_{2}}) (n_{H_{2}})^{3}} V^{2}

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\frac{(n_{N H_{3}})^{2}}{(n_{N_{2}}) (n_{H_{2}})^{3}} V^{3}

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\frac{(n_{N H_{3}})^{2}}{(n_{N_{2}}) (n_{H_{2}})^{3}}

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Solution

The correct option is B $\frac{(n_{N H_{3}})^{2}}{(n_{N_{2}}) (n_{H_{2}})^{3}} V^{2}$
$N_{2} + 3 H_{2} ⇌ 2 N H_{3} K_{c} = \frac{(n_{N H_{3}} / V)^{2}}{(n_{N_{2}} / V) (n_{H_{2}} / V)^{3}} = \frac{(n_{N H_{3}})^{2}}{n_{N_{2}}) (n_{H_{2}})^{3}} V^{2}$

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