For the reaction, \(\mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2…

For the reaction, \(\mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\), the equilibrium constant is \(\mathrm{K}_1\). The equilibrium constant is \(\mathrm{K}_2\) for \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_2(\mathrm{~g})\). What is K for the reaction \(\mathrm{NO}_2(\mathrm{~g}) \rightleftharpoons \frac{1}{2} \mathrm{~N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) ?\)
  1. \(\frac{1}{\left(K_1 K_2\right)}\)
  2. \(\frac{1}{\left(2 K_1 K_2\right)}\)
  3. \(\frac{1}{\left(4 K_1 K_2\right)}\)
  4. \(\left(\frac{1}{K_1 K_2}\right)^{1 / 2}\)

Solution

$\begin{aligned} & \mathrm{N}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{NO}(g) ; K_1 \\ & \frac{2 \mathrm{NO}(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{NO}_2(g) ; K_2}{\mathrm{~N}_2(g)+2 \mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{NO}_2(g) ; K=K_1 \times K_2} \cdots \\ & \therefore \text { For } \mathrm{NO}_2(g) \rightleftharpoons \frac{1}{2} \mathrm{~N}_2(g)+\mathrm{O}_2(g) ; \\ & K^{\prime}=\left[\frac{1}{K_1 K_2}\right]^{1 / 2} \end{aligned}$

Asked in: NEET 2011 (Screening)

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