Question

The equilibrium constant $K$ for the reaction $HA+B\rightleftharpoons B{H}^{+}+A^{-}$ is $100$. If the rate constant for the forward reaction is ${10}^5$, then the rate constant for the reverse reaction is:

• A. ${10}^{-3}$
• B. ${10}^5$
• C. ${10}^{-7}$
• D. ${10}^3$

Answer 1

The correct option is D ${10}^3$

Given a reaction : $HA+B\to B{H}^{+}+A^{-}$

The equilibrium constant for the reaction is $K$.
According to the law of mass action, we have $K=\frac{K_f}{K_r}$, where $K_f$ is the rate constant for the forward reaction and $K_r$ is the rate constant for the reverse reaction.
Therefore, $100=\frac{{10}^5}{K_r}$ $⟹K_r$ $={10}^3$

Hence, the rate constant for backward reaction is ${10}^3$.