Chemical Kinetics: Half Time Period and Collision Theory of Reaction Rate (For CBSE, ICSE, IAS, NET, NRA 2022)

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Half Time Period

The time taken for a reaction to reach the half-way stage i.e.. when half of the starting material has reacted is called half-life period of the reaction.

It is denoted or .

For a first order reaction

When ,

Therefore, we get

Half-life period for a first order reaction is independent of the initial concentration.

Collision Theory of Reaction Rate

  • A reaction would occur only when the reactant molecules collide with one another.
  • The rate of a reaction would depend upon the collision frequency.
  • Not all molecular collisions result in chemical reaction . Only effective collisions can bring about chemical reaction.
  • An effective collision is one in which the combined kinetic energy of colliding molecules is equal to or more than the activation energy of the reaction .
  • For a reaction to occur not only the collision should be energetically effective, the orientation of the colliding molecules should be such which permit formation of new bonds.

Threshold Energy

In order for a chemical reaction to occur, the reacting molecules must collide with each other and they must possess some minimum energy during collision. This energy is called the Threshold Energy.

Activation Energy

  • The extra amount of energy supplied to the molecules so that its energy becomes equals to that of threshold energy.
  • This extra energy is called the activation energy.
  • It is denoted as .

Dependence of Reaction Rate on Temperature

  • The rate of reaction is about doubled, for many reactions, by a 10 degree rise in the temperature.
  • If we increase the temperature, then energy of molecules increases.
  • Thus, more number of molecules possesses the threshold energy and result in the increase of rate of reaction.
  • The change in energy that takes place during the course of a reaction is shown in fig.
Dependence of Reaction Rate on Temperature

The rate of reaction is depend upon the rate constant .

The relationship of rate constant with the activation energy and the absolute temperature , is determined by the Arrhenius equation.

is a proportionality constant and is also known as frequency factor and is the gas constant.

Calculating by Graphical Method

Taking natural logarithm of equation, we get

The plot of in vs gives a straight line whose slope is equal to and whose intercept is In (fig)

Graphical Method

Direct Method to Compute

At , the equation (1)

At , the equation (1)

Dividing by

Taking natural logarithm


Converting into logarithm (base 10)


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