$\mathrm{K}_{1}$ and $\mathrm{K}_{2}$ are equilibrium constant for reactions (1) and (2)…

$\mathrm{K}_{1}$ and $\mathrm{K}_{2}$ are equilibrium constant for reactions (1) and (2)
$\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) ightleftharpoons 2 \mathrm{NO}(\mathrm{g})$ ... (1)
$\mathrm{NO}(\mathrm{g}) ightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})$ ... (2)
Then,
  1. $\mathrm{K}_{1}=\left(\frac{1}{\mathrm{~K}_{2}}ight)^{2}$
  2. $\mathrm{K}_{1}=\mathrm{K}_{2}^{2}$
  3. $\mathrm{K}_{1}=\frac{1}{\mathrm{~K}_{2}}$
  4. $\mathrm{K}_{1}=\left(\mathrm{K}_{2}ight)^{0}$

Solution

$\mathrm{N}_{2}+\mathrm{O}_{2}=2 \mathrm{NO} \quad \ldots \mathrm{K}_{1}$
$2 \mathrm{NO} ightleftharpoons \mathrm{N}_{2}+\mathrm{O}_{2} \quad \ldots \quad \frac{1}{\mathrm{~K}_{1}}$
$\mathrm{NO} ightleftharpoons \frac{1}{2} \mathrm{~N}_{2}+\mathrm{O}_{2} \quad ...\mathrm{~K}_{2}=\left(\frac{1}{\mathrm{~K}_{1}}ight)^{1 / 2}$
$\mathrm{K}_{2}=\left(\frac{1}{\mathrm{~K}_{1}}ight)^{1 / 2} \quad \mathrm{or} \quad \mathrm{~K}_{2}^{2}=\frac{1}{\mathrm{~K}_{1}}$
$\mathrm{K}_{1}=\frac{1}{\left(\mathrm{~K}_{2}ight)^{2}}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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