FIRST ORDER REACTIONS

Let us consider a first order reaction

A⎯⎯→ products

Suppose that at the beginning of the reaction (t= 0), the concentration of A is amoles litre^–1

. If after time t, x moles of A has changed, the concentration of A is a– x. We know that for a first order reaction, the rate of reaction, dx/dt, is directly proportional to the concentration of the reactant. Thus,

where I is the constant of integration. The constant k may be evaluated by putting t= 0 and x= 0.

Thus,  I = – 1n a

Substituting for I in equation (2)

Changing into common logarithms

The value of k can be found by substituting the values of a and (a– x) determined experimentally at time interval t during the course of the reaction.

Sometimes the integrated rate law in the following form is also used :

Where x₁and x₂ are the amounts decomposed at time intervals t₁ and t₂ respectively from the start.