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Characteristics of Equilibrium Constant

The equilibri...

Question

The equilibrium constant for the given reaction is $100$ .
$N_{2} (g) + O_{2} (g) ⇌ 2 {N O}_{2} (g)$

What is the equilibrium constant for the reaction given below?
${N O}_{2} (g) ⇌ \frac{1}{2} N_{2} (g) + O_{2} (g)$

10

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0.1

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0.01

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Solution

The correct option is C $0.1$
The equilibrium constant for the given reaction is $100$ .

$N_{2} (g) + 2 O_{2} (g) ⇌ 2 {N O}_{2} (g)$

$K_{1} = \frac{[N O_{2}]^{2}}{[N_{2}] [O_{2}]^{2}} = 100$
The equilibrium constant for the reaction:

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

$K_{2} = \frac{\sqrt{[N_{2}]} [O_{2}]}{[N O_{2}]} = \frac{1}{\sqrt{K_{1}}} = \frac{1}{\sqrt{100}} = 0.1$

Hence, option C is correct.

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