If the equilibrium constant for the reaction $2 A B ightleftharpoons A_2+B_2$ is 49 , what is the…
If the equilibrium constant for the reaction $2 A B ightleftharpoons A_2+B_2$ is 49 , what is the equilibrium constant for $A B ightleftharpoons \frac{1}{2} A_2+\frac{1}{2} B_2 ?$
7
$\frac{1}{7}$
24.5
49
Solution
$\begin{array}{r}2 A B ightleftharpoons A_2+B_2 \\ K_c=\frac{\left[A_2ight]\left[B_2ight]}{[A B]^2}\end{array}$
again, $\quad \begin{aligned} A B & ightleftharpoons \frac{1}{2} A_2+\frac{1}{2} B_2 \\ K_c{ }^{\prime} & =\frac{\left[A_2ight]^{1 / 2}\left[B_2ight]^{1 / 2}}{[A B]} \\ K_c & =\left(K_c{ }^{\prime}ight)^2\end{aligned}$
or $\quad K_c{ }^{\prime}=\sqrt{K_c}=\sqrt{49}=7$