Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

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Integrated Rate law Expression:

Integrated rate law expression provide the predicted temporal evolution in reactant and product concentrations for reactions having an assumed order dependence.

(1)  Zero-order Reaction: Consider the following elementary reaction

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
For zero-order reaction, the rate law is

Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev 

k is rate constant.

Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

⇒ –d[A] = k dt

If at t = 0, the init ial concentration is [A]0 and the concentration at t = t, is [A], then integrat ion yields

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

⇒ [A]0 – [A] = kt
This is integrated rate equation for a zero-order reaction in terms of reactant.

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

= k d[P] = k dt
at              t = 0,  [P] = 0
and at        t = t, [P] = [P]
then integration yields

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

[P] = kt
This is integrated rate law equation for a zero-order reaction in terms of product.
i.e. [A]0 – [A] = kt = [P]

 Graph representation of zero-order reaction
[A]0 – [A] = kt
[A] = –kt + [A]0
y = mx + c

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

Graph of reactant vs time.

[P] = kt

y = mx

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

Graph of concentration of product vs time.

Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
[A]0 – [A] = 2kt …(i)

When t = 0 then [P] = 0 and t = t then [P] = [P]

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

[P] = 3kt     …(ii)

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev         …(iii)

 

Problem. Find the integrated rate law expression for an elementary zero order reaction given below.

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

Sol.

Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev 

The rate law of above elementary reaction is given below

 Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

⇒ Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

⇒  – [[A] – [A]0] = kt
        [A]0 – [A] = kt                                                                           …(i)


⇒ Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev                                          …(ii)
⇒ Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev
Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

[P] = kt                                                                 …(iii)

From equation (i), (ii) & (iii) we get

Integrated Rate Law Expression Of Zero Order - Chemical Kinetics Chemistry Notes | EduRev

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