# Effect of Temperature on the Reaction Rate

## (Arrhenius Theory) :

Temperature has very marked effect on the reaction rate. It has been found that the rate of most homogeneous reactions are nearly doubled or tripled by 10° rise in temperature.

$\large \frac{k_{t+10}}{k_t} = 2 \; or \;3 (nearly)$

The ratio of the rate constants of a reaction at two different temperatures differing by 10°

i.e. kt+10 / kt is known as temperature coefficient of reaction rate.

This ratio also depends upon temperature and two temperatures generally selected are 25°C and 35°C. If a reaction has a temperature coefficient of reaction rate equal to 3, then by raising its temperature from 25°C to 65°C, the rate will increase by nearly 3 × 3 × 3 × 3 i.e. 81 times.

In order to explain the effect of temperature on the reaction rate.

Arrhenius proposed a theory of reaction rate which states as follows :

(i) A chemical reaction takes place by collision between the reactant molecules, and collision to be effective the colliding molecules must posses some certain minimum energy called threshold energy of the reaction.

(ii) Reactant molecules having energy equal or greater than the threshold are called active molecules and those having energy less than the threshold are called passive molecules.

(iii) At a given temperature there exists a dynamic equilibrium between active and passive molecules. The process of transformation from passive to active molecules being endothermic, increase of temperature increases the number of active molecules and hence the reaction.
Passive molecules <—-> Active molecules, ΔH = +ve

(iv) Concept of energy of activation (Ea)
The extra amount of energy which the reactant molecules (having energy less than the threshold) must acquire so that their mutual collision may lead to the breaking of bond(s) and hence the reaction, is known as energy of activation of the reaction. It is denoted by the symbol Ea. Thus,

Ea = Threshold energy − Actual average energy

Ea is expressed in kcals mole−1 or kJ mole−1

The essence of Arrhenius Theory of reaction rate is that there exists an energy barrier in the reaction path between reactant(s) and product(s) and for reaction to occur the reactant molecules must climb over the top of the barrier which they do by collision. The existence of energy barrier and concept of Ea can be understood from the following diagram.

ΣHR = Summation of enthalpies of reactants

ΣHP = Summation of enthalpies of products

ΔH = Enthalpy change during the reaction

Ea1 = Energy of activation of the forward reaction (FR)

Ea2 = Energy of activation of the backward reaction (BR)

Notable Points

(i) ΔH = Energy activation of FR − Energy of activation of BR

(ii) In the diagram mentioned above, FR is exothermic (ΔH is −ve) while BR is endothermic (ΔH is +ve). The minimum activation energy of FR i.e. any exothermic reaction will be zero while minimum activation energy for BR i.e. any endothermic reaction will be equal to ΔH

(iii) Greater the height of energy barrier, greater will be the energy of activation and more slower will be the reaction at a given temperature.

(iv) Rate = Collision frequency × fraction of the total number of collision which is effective.

or ,

= Collision frequency × fraction of the total number of collisions in which K.E. of the colliding molecules equals to Ea or exceeds over it.

Collision frequency is the number of collisions per unit volume per unit time. It is denoted by the symbol Z. Z is directly proportional to √T. By 10° rise in temperature. So, it is the fraction of the total number of effective, collisions that increases markedly by 10° rise in temperature resulting into marked increase in the reaction rate.