# Law of Mass Action

C.M.Guldberg and Waage derived this law in 1864. The law of Mass Action helps to determine the concentrations of the reactants and products at the equilibrium.

## Statement of Law of Mass Action:

“This law is stated as “the rate at which the reaction proceeds is directly proportional to the active masses’ product of the reactions.”

### Active Mass:

The term active mass represents the concentration in mole/dm3 of the reactants and the products for a dilute solution.

## Derivation for Equilibrium Constant

Consider the following general reversible reaction.

A+B   ⇆        C+D

The active masses or concentrations for A, B, C, and D are [A], [B], [C], and [D], respectively.

*Symbols/formulas of the reactants and the products written in the squared brackets represent their equilibrium concentration, i.e., their No. of mole/dm3.According to law of mass action:

Rate of forward reaction µ [A] [B]

= Kf [A] [B]    (Kf is the rate constant for forwards reaction)

Rate of backward reaction µ [C] [D]

= Kr [C] [B]   (Kr is the rate constant for reverse reaction)

At equilibrium state:

Rate of forward reaction = Role of backward reaction

Kf [A] [B] = Kr [C] [D]

On rearranging

Kf/Kr=[C] [D]/ [A] [B]

Since

Kf/Kr=Kc

So,

Kc=[C] [D]/ [A] [B]

The above equation is known as equilibrium constant expression.

In general,

Kc=Product of concentration of Products/Product of concentrations of Reactants

Kc is known as equilibrium constant, the value of which does not depend on the reactants’ initial concentrations; however, it depends on the temperature of the reaction.

It has been decided conventionally that the concentration of the products would be written as the numerator. In contrast, those of the reactants would be written as the denominator.

Consider the more general reversible reaction.

aA + bB                     ⇆       cC + dD

In the above equation, a, b, c, and d are the coefficients, i.e., the No. of moles of A, B, C, and D. In equilibrium, constant expression coefficients of reactants and products become the exponents of the concentration in terms of reactants and products.

Kc= [C]c[D]d/ [A]a[B]b