At 298 K Based on above equilibria, the equilibrium constant of the reaction, is ________ (Nearest integer). [2023]

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Solution

Q.
At 298 K

$N_{2} (g) + 3 H_{2} (g) ⇌ 2 {NH}_{3} (g), K_{1} = 4 \times 10^{5}$

$N_{2} (g) + O_{2} (g) ⇌ 2 NO (g), K_{2} = 1.6 \times 10^{12}$

$H_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ H_{2} O (g), K_{3} = 1.0 \times 10^{- 13}$

Based on above equilibria, the equilibrium constant of the reaction, $2 {NH}_{3} (g) + \frac{5}{2} O_{2} (g) ⇌ 2 NO (g) + 3 H_{2} O (g)$ is ________ $\times 10^{- 33}$ (Nearest integer). [2023]

Ans.
(4)

$Target equation = eq(2) - eq(1) + 3 eq(3)$

$K = \frac{K_{2} \times {(K_{3})}^{3}}{K_{1}} = \frac{1.6 \times 10^{12} \times {(1 \times 10^{- 13})}^{3}}{4 \times 10^{5}}$

$= \frac{16 \times 10^{11} \times 10^{- 39}}{4 \times 10^{5}} = 4 \times 10^{- 33} = 4$

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