9.2 Law of Mass Action

Guldberg and Waage in 1869 put forward this law. According to this law "The rate at which a substance reacts is directly proportional to its active mass and the rate of a reaction is directly proportional to the product of the active masses of the reacting substances". Generally, an active mass is considered as the molar concentration having units of mol dm $^{- 3}$ , expressed as square brackets [].

For example, consider a reversible reaction of the type

Suppose [A], [B], [C] and [D] are the molar concentrations (mol dm $^{- 3}$ ) of A, B, C and D respectively.

According to the Law of Mass Action:

The rate of the forward reaction $\alpha$$\alpha$ [A][B] $={\mathrm{k}}_{\mathrm{f}}[\mathrm{A}][\mathrm{B}]$$= \mathrm{k}_{\mathrm{f}}[\mathrm{A}][\mathrm{B}]$

Similarly,

where ${\mathsf{k}}_{\mathrm{r}}$$\mathsf{k}_{\mathrm{r}}$ and ${\mathsf{k}}_{\mathrm{r}}$$\mathsf{k}_{\mathrm{r}}$ are the proportionality constant called specific rate constants of the forward and the reverse reactions, respectively.

At equilibrium state:

Where $K_{\mathrm{c}}=\frac{{\mathrm{k}}_{\mathrm{f}}}{{\mathrm{k}}_{\mathrm{r}}}$$K_{\mathrm{c}} = \frac{\mathrm{k}_{\mathrm{f}}}{\mathrm{k}_{\mathrm{r}}}$

Law of Mass Action describes the reationsnip between active masses of the reactants and the rate of a reaction.

Derivation of the Expression for Equilibrium Constant for General Reaction