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Derivation of Kp and Kc

Assume that t...

Question

Assume that the decomposition of $H N O_{3}$ can be represented by the following equation: $4 H N O_{3} (g) ⇌ 4 N O_{2} (g) + 2 H_{2} O (g) + O_{2} (g)$ .
The reaction approaches equilibrium at 400 K temperature and 30 atm pressure. At equilibrium, the partial pressure of $H N O_{3}$ is 2 atm.
The value of $K_{c}$ ( $(m o l / L)^{3}$ ) at 400 K is:(Use $: R = .08 a t m - L / m o l e - K$ )

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Solution

$P_{t o t a l} = P_{H N O_{3}} + P_{N O_{2}} + P_{O_{2}} + P_{H_{2} O}$

$∴ P_{N O_{2}} = 4 P_{O_{2}} a n d P_{H_{2} O} = 2 P_{O_{2}}$

$∴ P_{t o t a l} = P_{H N O_{3}} + 7 P_{O_{2}}$

$\Rightarrow 30 - 2 = P_{O_{2}} \times 7$

$\Rightarrow P_{O_{2}} = \frac{28}{7} = 4$ atm

$K_{p} = \frac{P_{N O_{2}}^{4} P_{H_{2} O} P_{O_{2}}}{P_{H N O_{3}}^{4}}$

$K_{p} = K_{c} (R T)_{g}^{Δ n} = K_{c} (0.08 \times 400)^{3}$

$\Rightarrow K_{c} = \frac{2^{20}}{(32)^{3}} = 32$ .

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