Question

The equilibrium constant for the reaction $A\iff B$ is $K$. The equilibrium constant for the reaction $mA\iff mB$ is:

• A. $mK$
• B. $\frac{K}{m}$
• C. $K^m$
• D. $K^{-m}$

Answer 1

The correct option is C $K^m$

Let $K$ is the equilibrium constant for the reaction, $A\iff B$.
Let $K^{\prime }$ be the equilibrium constant for the reaction, $mA\iff mB$.
$K=\frac{B}{A}$ or $B=KA$ and $K^{\prime }=\frac{B^m}{A^m}.$
Substituting $B=KA$ in the expression for $K^{\prime }$, we get
$K^{\prime }=\frac{B^m}{A^m}=\frac{(KA{)}^m}{A^m}=K^m\times \frac{(A{)}^m}{A^m}=K^m.$

Hence, option c is the correct answer.