Equilibrium constants $\mathrm{K}_1$ and $\mathrm{K}_2$ for the following equilibria: are related as:

Equilibrium constants $\mathrm{K}_1$ and $\mathrm{K}_2$ for the following equilibria: are related as:
  1. $\mathrm{K}_2=1 / \mathrm{K}_1{ }^2$
  2. $\mathrm{K}_2=\mathrm{K}_1{ }^2$
  3. $\mathrm{K}_2=1 / \mathrm{K}_1$
  4. $\mathrm{K}_2=\mathrm{K}_1 / 2$

Solution

$\mathrm{K}_1=\frac{p_{\mathrm{NO} 2}}{p_{\mathrm{NO}} \cdot\left(\mathrm{p}_{\mathrm{O} 2}\right)^{1 / 2}}$ $\mathrm{K}_2=\frac{\left(p_{\mathrm{NO}}\right)^2 \cdot p_{\mathrm{O} 2}}{\left(\mathrm{p}_{\mathrm{NO} 2}\right)^2}$ takin square root on both sides in eq. 2. $\begin{aligned} & \Rightarrow \sqrt{\mathrm{K}_2}=\frac{p_{\mathrm{NO}} \cdot\left(p_{\mathrm{O} 2}\right)^{1 / 2}}{p_{\mathrm{NO} 2}} \\ & \Rightarrow \sqrt{\mathrm{K}_2}=\frac{1}{\mathrm{~K}_1} \Rightarrow \mathrm{K}_2=\frac{1}{\mathrm{~K}_1^2} \end{aligned}$

Asked in: NEET 2005

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