First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Physical Chemistry

Created by: Asf Institute

Chemistry : First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

The document First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev is a part of the Chemistry Course Physical Chemistry.
All you need of Chemistry at this link: Chemistry

(2)  First-order reaction

Consider the following elementary reaction
A  → P
If the reaction is first order with respect to [A], the rate law expression is

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev 

k is rate constant
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
If t = 0, the init ial concentration is [A]0 and the concentration at t = t, is [A], then integrating yields

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

[A] = [A]0 e–kt…(i)
orFirst-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev …(ii)

Using this idea, the concentration of product with time for this first-order reaction is :

[P] + [A] = [A]0
[P] = [A]0 – [A]
[P] = [A]0 – [A]0 e–kt 
[P] = [A]0 (1 – e–kt) ….(iii)

Graph representation of first order reaction

[A] = [A]0 e–kt

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Plot of concentration vs time.

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
ln [A] = –kt + ln [A]0

  First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Plot of log [A] vs time.

t1/2 i.e. half life t ime of first order reaction

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

when t = t1/2; then [A] =

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
ln 2 = kt1/2

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Problem. The half life for the first order decomposition of N2O5 is 2.05 � 10s. How long will it take for a sample of N2O5 to decay to 60% of its initial value?

Sol. We know that,

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

The time at which the sample has decayed to 60% of its initial value then

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

T = 1.51 x 104 s
Problem. Find the t3/4 i.e. 3/4 life time of first order reaction.

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Sol.

Integrated rate law expression is

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

when t = t3/4 than              First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

then         
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

ln 4 = kt3/4

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

(3)  Second-order reaction: (Type I) 

Consider the following elementary reaction,

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

If the reaction is second order with respect to [A], the rate law expression is rate =

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

k is rate constant

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

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

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev…(i)

The concentration of product with time for second order reaction

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
or First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
then        First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev…(ii)

t1/2 i.e. Half-life t ime of second order reaction (type I)

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

when t = t1/2 then

⇒  First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Second-order reaction (Type II) 

Second order reactions of t ype II invo lves two different reactants A and B, as fo llows

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Assuming that the reaction is first order in both A and B, the reaction rate is

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

If t = 0 then the init ial concentration are [A]0 & [B]and the concentration at t = t, are [A] & [B].

The loss of reactant i.e. the formation of product is equal to

[A]0 – [A] = [B]0 – [B] = [P]
[B]0 – [A]0 + [A] = [B]
then

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

the integration yield

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

let Δ = [B]0 – [A]
The solution to the integral involving [A] is given by

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Using this so lut ion to the integral, the integrated rate law expressio n beco mes

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
⇒ First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

 Graph representation of second order reaction of type I

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Y = mx + C

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Plot of concentration vs time 

(4)  nth order reaction where n ≥ 2 :

An nth order reaction may be represented as

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

the rate law is, First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

where k is rate constant for nth order reaction

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

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

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Let

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev…(1)
t1/2 i.e. Half life time of nth order reaction

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Where t = t1/2 then First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev …(2)

i.e.  First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev…(3)

Thus we can say that t1/2 of the reaction is inversely proportional to the init ial concentration of reactant, except first order reaction.

So, for a first order reaction (n = 1), t1/2 is independent on [A]0 for a second order reaction (n = 2), t1/2 is dependent on [A]0

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

for a nth order reaction 

 First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Note : For the elementary reaction, the order of reaction is equal to the molecularity of the reaction.

Problem. Find the rate law for the following reaction.

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Sol.

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Rate law is 

Problem. Find the rate law for the following reaction.

Sol.  

 (1)  First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev


(2) First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

  
(3) First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev= k1[A] + k2[A] = (k1 + k2)[A]

Problem. Find the rate law for the following reaction

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Sol. 

(1) First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
(2) First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev = k1[A] – k2[B] – k3[B]
               = k1[A] – (k2 + k3) [B]
(3) First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev
 (4) First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Dynamic Test

Content Category

Related Searches

Important questions

,

shortcuts and tricks

,

mock tests for examination

,

ppt

,

Free

,

Previous Year Questions with Solutions

,

video lectures

,

pdf

,

Sample Paper

,

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

,

Summary

,

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

,

MCQs

,

First-Order & Second Order Reaction - Chemical Kinetics Chemistry Notes | EduRev

,

Objective type Questions

,

Exam

,

Extra Questions

,

Semester Notes

,

past year papers

,

practice quizzes

,

Viva Questions

,

study material

;