Lecture23222

Kinetics: Integrated Rate Laws

Lecture 23

Integrated rate laws

A sample problem

on determining reactant concentration at a given

time.

If we obtain a straight line,

when we plot ln[reactant] vs time, the reaction is first order with respect to that reactant.when we plot 1/ [reactant] vs time, the reaction is second order with respect to that reactant.when we plot [reactant] vs time, the reaction is zero order with respect to that reactant.

Graphical determination of the reaction order: look for a straight line

The half-life (t1/2) of a reaction

is the time required for the reactant

concentration to reach half of its initial

value.

The half-life of a first order reaction

ln([A]0/[A]t)=kt

ln([A]0/0.5[A]0)=kt1/2

ln2=kt1/2 , 0.693=kt1/2

t1/2 = ln2/k = 0.693/k

Half-life in a first order process

In the radioactive decay of elements,decomposition of each

particle in a first order process is independent of the number of particles.

The half-life of a second order reaction

1/[A]t — 1/[A0] = kt

1/0.5[A]0 — 1/[A0] = kt1/2

2/[A]0 — 1/[A0] = kt1/2

1/[A0] = kt1/2

t1/2=1/k[A0]

Half-life in a second order process

The half-life of a zero order reaction

[A]t — [A]0 = —kt0.5[A]0 — [A0] = —kt1/2

—0.5[A]0 = —kt1/2

0.5[A]0 = kt1/2

[A]0 = 2kt1/2

t1/2= [A]0/2k

Half-life in a zero order process

The half-life and reaction order

The half-life of a first-order reaction is a constant, independent of reactant concentration.The half-life of a second-order reaction is inversely proportional to the initial reactant concentration.The half-life of a zero-order reaction is directly proportional to the initial reactant concentration.

A sample problem

on determining the half-life of a first-

order reaction.

THE END