At a given temperature and pressure the equilibrium constant values for the equilibria are given bel

Question

At a given temperature and pressure the equilibrium constant values for the equilibria are given below. \ $ \begin{aligned} & 3 A_2+B_2 ightleftharpoons 2 A_3 B, K_1 \ & A_3 B ightleftharpoons \frac{3}{2} A_2+\frac{1}{2} B_2, K_2 \end{aligned} $ \ The relation $K_1$ and $K_2$ is

Professor PC Thomas Classes · Answer

(d) $: K_1=\frac{\left[A_3 Bight]^2}{\left[A_2ight]^3\left[B_2ight]}$ $ K_2=\frac{\left[A_2ight]^{3 / 2}\left[B_2ight]^{1 / 2}}{\left[A_3 Bight]} \ $ Taking square root on both sides in eq. (i), we get $ \begin{aligned} & \sqrt{K_1}=\frac{\left[A_3 Bight]}{\left[A_2ight]^{3 / 2}\left[B_2ight]^{1 / 2}} \ & \Rightarrow\left[A_3 Bight]=\sqrt{K_1}\left[A_2ight]^{3 / 2}\left[B_2ight]^{1 / 2} \end{aligned} $ \ Putting the value of $\left[A_3 Bight]$ in eq. (ii), we get $ K_2=\frac{1}{\sqrt{K_1}} $