QJEEM21Ch5c1d: JEE Main 2021 Chemistry - Class 11 JEEM21Ch5c1d Solution: The equilibrium constant for the reaction A(s) M(s) + O 2 (g)…

In the given equilibrium, the solid substances do not contribute to the equilibrium constant expression since their activities are considered to be 1.

For the reaction:

$\text{A(s)} \rightleftharpoons \text{M(s)} + \frac{1}{2}\text{O}_2(\text{g})$

The equilibrium constant, $K_p$ , is given by:

$K_p = P_{\text{O}_2}^{n}$

where $P_{\text{O}_2}$ is the partial pressure of $\text{O}_2$ and $n$ represents the stoichiometric coefficient of $\text{O}_2$ in the balanced chemical reaction, which is $\frac{1}{2}$ . Therefore, the expression for $K_p$ becomes:

$K_p = \left( P_{\text{O}_2} \right)^{\frac{1}{2}}$

Given that $K_p = 4$ , substituting into the equation gives:

$4 = \left( P_{\text{O}_2} \right)^{\frac{1}{2}}$

To find $P_{\text{O}_2}$ , square both sides of the equation:

$4^2 = P_{\text{O}_2}$

$16 = P_{\text{O}_2}$

Thus, the partial pressure of $\text{O}_2$ at equilibrium is $\boxed{16}$ atm.