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Characteristics of Equilibrium Constant

What is the r...

Question

What is the relation between the equilibrium constants $K$ , $K_{1}$ and $K_{2}$ for the following reactions?
$N_{2} + 2 O_{2} ⇋ 2 N O_{2}, K$
$N_{2} + O_{2} ⇋ 2 N O, K_{1}$
$2 N O + O_{2} ⇋ 2 N O_{2}, K_{2}$

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Solution

$K = \frac{[N O_{2}]^{2}}{[N_{2}] [O_{2}]^{2}},$
$K_{1} = \frac{[N O_{2}]^{2}}{[N_{2}] [O_{2}]}, K_{2} = \frac{[N O_{2}]^{2}}{[N O]^{2} [O_{2}]}$
Here $K_{1} K_{2} = \frac{[N O_{2}]^{2}}{[N_{2}] [O_{2}]^{2}} = K$
$∴ K = K_{1} K_{2}$

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x y z

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