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.
