Integrated rate law expression provides the predicted temporal evolution in reactant and product concentrations for reactions having an assumed order dependence.
Consider the following elementary reaction
For zero-order reaction, the rate law is
k is rate constant.
⇒ –d[A] = k dt
If at t = 0, the initial concentration is [A]0 and the concentration at t = t, is [A], then integration yields
⇒ [A]0 – [A] = kt
This is an integrated rate equation for a zero-order reaction in terms of reactant.
= k d[P] = k dt
at t = 0, [P] = 0
and at t = t, [P] = [P]
then integration yields
[P] = kt
This is an integrated rate law equation for a zero-order reaction in terms of product.
i.e. [A]0 – [A] = kt = [P]
[A]0 – [A] = kt
[A] = –kt + [A]0
y = mx + c
[P] = kt
y = mx
[A]0 – [A] = 2kt …(i)
When t = 0 then [P] = 0 and t = t then [P] = [P]
[P] = 3kt …(ii)
Problem. Find the integrated rate law expression for an elementary zero-order reaction given below.
The rate law of the above elementary reaction is given below
⇒ – [[A] – [A]0] = kt
[A]0 – [A] = kt …(i)
[P] = kt …(iii)
From equation (i), (ii) & (iii) we get