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Characteristics of Equilibrium Constant

Reaction K ...

Question

Reaction $K$
$\frac{1}{2} N_{2} (g) + O_{2} (g) ⇋ N O_{2}$ $K_{1}$
$2 N O_{2} (g) ⇌ N_{2} O_{4} (g)$ $K_{2}$
Using the above equations, write down expression for $K$ of the following reaction:
$N_{2} O_{4} (g) ⇌ N_{2} (g) + \frac{1}{2} O_{2} (g)$

K_{1} K_{2}

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\frac{K_{2}^{2}}{K_{1}}

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\frac{1}{K_{2} K_{1}^{2}}

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\frac{1}{{K_{1}^{2} K}_{2}}

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Solution

The correct option is C $\frac{1}{{K_{1}^{2} K}_{2}}$
$\frac{1}{2} N_{2} (g) + O_{2} (g) ⇋ N O_{2}$ $K_{1}$ .....(1)
$2 N O_{2} (g) ⇌ N_{2} O_{4} (g)$ $K_{2}$ .....(2)
Multiply equation (1) with 2.
$N_{2} (g) + 2 O_{2} (g) ⇋ 2 N O_{2}$ $K_{3} = K_{1}^{2}$ .....(3)
Reverse equation (3)
$2 N O_{2} ⇋ N_{2} (g) + 2 O_{2} (g)$ $K_{4} = \frac{1}{K_{3}} = \frac{1}{K_{1}^{2}}$ .....(4)
Subtract equation (2) from equation (4)
$N_{2} O_{4} (g) ⇌ N_{2} (g) + \frac{1}{2} O_{2} (g)$
$K = \frac{K_{4}}{K_{2}} = \frac{1}{{K_{1}^{2} K}_{2}}$

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Similar questions

2 N O (g) + O_{2} (g) ⇋ N O_{2} (g); K_{1}

2 {N O}_{2} (g) ⇋ N_{2} O_{4} (g); K_{2}

2 N O (g) + O_{2} (g) ⇋ N_{2} O_{4} (g); K_{3}

K_{1}

K_{2}

N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)

N O (g) ⇌ \frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g)

K_{1}

K_{2}

N_{2} (g) + O_{2} (g) ⇌ 2 N O (g) . . . . . . (1)

N O (g) ⇌ \frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g) . . . . . . . . . (2)

K_{1}

K_{2}

N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)

N O (g) ⇌ \frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g)

N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)

K_{1}

K_{2}

2 N O (g) + O_{2} (g) ⇌ 2 N O_{2} (g)

N O_{2} (g) ⇌ \frac{1}{2} N_{2} (g) + O_{2} (g)

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