Whether a reaction is of first order or not can be verified by using the analytical methods based on the rate equations. The reagents are allowed to react, the change of concentration is measured at different time intervals. For a first order reaction:
(i) Plot of log [A0]/[A] versus t gives a straight line passing through the origin.
(ii) Plot of log[A] versus t gives a straight line with an intercept log [A]0 and a slope = – k /2.303.
(iii) Plot of [A] versus t is exponential.
(iv) The value of k calculated by using kt = 2.303 log [A]0 / [A] for different time intervals come out to
(v) The half life period is independent of the initial concentration of the reactant.
This reaction follows second order kinetics.
So that, the rate equation for this reaction will
Rate, R = k[X]2 .............(1)
Let initial concentration is x mol L−1,
Plug the value in equation (1)
Rate, R1 = k .(a)2
Given that concentration is increasing by 3 times so new concentration will 3a mol L−1
Plug the value in equation (1) we get
Rate, R2 = k (3a)2
We have already get that R1 = ka2 plus this value we get
R2 = 9 R1
So that, the rate of formation will increase by 9 times.
Rate = k[A]2
If concentration of X is increased to three times,
Rate = k[3A]2
or Rate = 9 k A2
Thus, rate will increase 9 times.