Recall, equilibrium is dynamic and is the result of the forward and reverse reaction rates being equal to one another. In a previous study guide, we related the rate constants for a one step reaction to the equilibrium constant.

For the general reaction:

The rates of the forward and reverse reaction are written as:

$\displaystyle rate_f=k_f[A]^a[B]^b$     $\displaystyle rate_r=k_r[C]^c[D]^d$

At equilibrium, the rates of the forward and reverse reaction are equal. Below, we set the rates equal.

$\displaystyle k_f[A]^a[B]^b=k_r[C]^c[D]^d$
 

Rearranging the equation:

$\displaystyle \frac{k_f}{k_r}=\frac{[C]^c[D]^d}{[A]^a[B]^b}$
 
We see that $\displaystyle \frac{k_f}{k_r}$ is equal to the equilibrium constant, Kc. Now we can write,

$\displaystyle \frac{k_f}{k_r}=K_c$