LESSON PLAN
Class – XII
Section – B
Subject – Chemistry
Period – 2nd
Unit – Chemical Kinetics
Topic – Integrated Rate Equations
Date – 11/07/14
Time Allotted – 40 min
Objectives :After studying this Unit, students will be able to
 derive integrated rate equations for the zero and first order reactions;
 determine the rate constants for zeroth and first order reactions;
 solve the numerical problems on zero and first order reactions.
Synopsys of the topic :It is not always convenient to determine the instantaneous rate, as it is measured by determination of slope of
the tangent at point ‘t’ in concentration vs time plot. In order to avoid this difficulty, we can integrate the
differential rate equation to give a relation between concentrations at different times and rate constant. We
shall determine these equations only for zero and first order chemical reactions.
Zero Order Reactions :
d[R]
d[R]
R P
Rate = - dt = k [R]0
=> - dt = k
=> d[R] = – k dt
Integrating both sides
ʃ d[R] = – k ʃ dt
[R] = – k t + I where, I is the constant of integration.
At t = 0, the concentration of the reactant R = [R]0, where [R]0 is initial concentration of the reactant.
=> I = [R]0
Substituting the value of I in the equation
[R] = -kt + [R]0
=> k =
[R]0−[R]
t
First Order Reactions :
R P
Rate = -
d[R]
dt
= k [R]
=>
d[R]
[R]
= -k dt
Integrating both sides
d[R]
ʃ [R] = -k ʃ dt
ln [R] = – k t + I where, I is the constant of integration.
At t = 0, the concentration of the reactant R = [R]0, where [R]0 is initial concentration of the reactant.
=> I = ln [R]0
Substituting the value of I in the equation
[𝑅]𝑜
[𝑅]𝑜
ln [R] = – k t + ln[R]0 => ln[R]0 – ln [R] = kt => ln [𝑅] = kt => 2.303 log [𝑅] = kt
=> t =
𝟐.𝟑𝟎𝟑
𝒌
log
[𝑅]𝑜
[𝑅]
Role definition : Teacher
The teacher will ask to solve the following problem using the concept learned :
Q. A first order reaction has a rate constant 1.15 × 10-3 s-1. How long will 5 g
of this reactant take to reduce to 3 g?
Role definition : Student
The students will solve the above problem with the help of the teacher.
Role definition : Teacher
Q.Plot the graph between ln[R] and t for a first order reaction
Role definition : Student
The students will plot the graph by comparing the equation with
y = mx + c
Role definition : Teacher
The teacher will give an example of numerical problem asked in previous year’s Board Exam
Q1 . The thermal decomposition of HCOOH is a first order reaction with a rate constant of
2.4 × 10 -3 s-1 at a certain temp. Calculate how long will it take to form three-fourth of its initial
quantity of HCOOH to decompose ( log 0.25 = -0.6021 )
(AISSCE-2011)
Q2. A first order reaction has a rate constant of 0.0051 min-1 . If we begin with 0.10 M concentration
of the reactant , what conc of the reactant will be left after 3 hrs ?
(AISSCE-2009)
Role definition : Student
The students will solve these two questions at their home.