A chemical reaction is at equilibrium when

Every reversible reaction consists of one pair of reactions, one is forward and the other is a backward reaction. At one stage during reversible reactions, two reactions, i.e., forward and backward reactions proceed at the same time with the same rate, the reaction is then said to be in equilibrium.

Consider a chemical reaction,

$\begin{array}{l}\mathrm{A}+\mathrm{B}\rightleftharpoons \mathrm{C}+\mathrm{D}\\ {\mathrm{r}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}[ \mathrm{A}]\left[\mathrm{B}\right]\\ {\mathrm{r}}_{\mathrm{b}}={\mathrm{K}}_{\mathrm{b}}\left[\mathrm{C}\right]\left[\mathrm{D}\right]\end{array}$

So, at equilibrium ${\mathrm{r}}_{\mathrm{f}}={\mathrm{r}}_{\mathrm{b}}$

Thus,

$$\begin{gathered} {\mathrm{K}}_{\mathrm{f}}\left[\mathrm{A}\right]\left[\mathrm{B}\right]={\mathrm{K}}_{\mathrm{b}}\left[\mathrm{C}\right]\left[\mathrm{D}\right] \\ {\mathrm{K}}_{\mathrm{c}}=\frac{{\mathrm{K}}_{\mathrm{f}}}{{\mathrm{K}}_{\mathrm{b}}}=\frac{\left[\mathrm{C}\right]\left[\mathrm{D}\right]}{\left[\mathrm{A}\right]\left[\mathrm{B}\right]} \end{gathered}$$

So, ${\mathrm{K}}_{\mathrm{c}}$ is called the equilibrium constant.

Therefore, Rates of forwarding and backward reactions are equal at equilibrium.