(i) Define specific reaction rate.
(ii) Define Half-life period of a chemical reaction. Also obtain the expression for half-life period.
Derive the general for of the expression for the half-life of a first order reaction.
(i) Specific reaction rate. This is also called rate constant or velocity constant. Specific reaction rate may be defined as the rate of reaction under specific conditions, when the product of concentration of the reactants is unity.
(ii) Half-life period of a chemical reaction in which the concentration of reactant is reduced to half of the intial value of concentration.
It is denoted by tl/2 or t0.5.
The rate equation for a reaction of first order is expressed as:
On substituting these values, we get
The relation (i) is the required expression for half-life period of first order reaction.
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.