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If the equilibrium constant for is K, the equilibrium constant for will be:
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\(\begin{aligned}
& \mathrm{N}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) ; \mathrm{K} \\
& \frac{1}{2} \mathrm{~N}_2(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g}) ; \mathrm{K}^\prime \\
& \mathrm{K}=\frac{\left[\mathrm{NO}^2\right.}{\left[\mathrm{N}_2\right]\left[\mathrm{O}_2\right]} \\
& \mathrm{K}^\prime=\frac{\mathrm{NO}}{\left[\mathrm{N}_2\right]^{1 / 2}\left[\mathrm{O}_2\right]^{1 / 2}} \\
& \therefore \mathrm{K}^\prime=\sqrt{\mathrm{K}}
\end{aligned}\)
& \mathrm{N}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) ; \mathrm{K} \\
& \frac{1}{2} \mathrm{~N}_2(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g}) ; \mathrm{K}^\prime \\
& \mathrm{K}=\frac{\left[\mathrm{NO}^2\right.}{\left[\mathrm{N}_2\right]\left[\mathrm{O}_2\right]} \\
& \mathrm{K}^\prime=\frac{\mathrm{NO}}{\left[\mathrm{N}_2\right]^{1 / 2}\left[\mathrm{O}_2\right]^{1 / 2}} \\
& \therefore \mathrm{K}^\prime=\sqrt{\mathrm{K}}
\end{aligned}\)
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