Guldberg and Waage proposed that "The rate at which a substance reacts is directly proportional to its active mass and rate of a elementary chemical reaction is directly proportional to product of active masses of reactants each raised to a power equal to corresponding stoichiometric coefficient appearing in the balanced chemical equation :

For dilute solutions active mass is equal to concentration. Taking the example of the reaction

`N_2(g) + 3H_2(g) ⇋ 2NH_3(g)`

We can write,

Rate of forward reaction `r_f prop [N_2] [H_2]^3` rate of reverse reaction `r_r` a `[NH_3]^2`

thus, for the forward reaction :

`A + B -> C+ D`

Rate of disappearance of `A, (-d[A])/(dt) prop [A]`

rate of disappearance of `B, (-d[B])/(dt) prop [B]`

and rate of the forward reaction

`((dx)/(dt))_f prop [A] [B]`

`((dx)/(dt))_f = k_f [A] [B]`

and similarly for the backward reaction

`C+ D->A+B`

`((dx)/(dt))_b = k_b [C] [D]`

where `k_f` and `k_b` are rate constant of the forward and backward reactions respectively. At dynamic equilibrium

`((dx)/(dt))_f = ((dx)/(dt))_b`

`k_f [A] [B]= k_b [C] [D]`


`k_c = k_f/k_b = ([C][D])/([A][B])`

where `K_c` is called equilibrium constant. For a general reversible reaction

`aA + bB ⇋ cC + dD`

`k_c = ([C]^c[D]^d)/([A]^a[B]^b)`

This represents equilibrium equation and is also known as the law of mass action. As usual, square brackets [A], indicate the molar concentration of the substance (say A) within brackets

`[A] = (text(mol))/(text(litre)) (text(mol) L^(-1))`

The equilibrium constant `K_c` is the number obtained by multiplying the equilibrium molar concentrations of all the products and dividing by the equilibrium molar concentrat ion of all the reactants, with the concentration of each substance raised to the power of its coefficient in the balanced chemical equation.

The form of the equilibrium constant expression and the numerical value of the equilibrium constant depend on the form of the balanced chemical equation. Thus for the chemical equation in the reverse direction.

`cC +dD -> aA + bB`

`k_c^' = ([A]^a[B]^b)/([C]^c[D]^d) = 1/k_c`

(i) Variation of the concentration of the reactants and products.

(ii) Dynamic equilibrium stage in a reversible reaction.