# Effect of Temperature and Catalyst on the Rate Constant

Let us now consider the effect of increase in temperature on the number of effective collisions. Fig. 20.16. Energy distribution at different temperatures

On the basis of probability consideration Fig. 20.16 is drawn to give the energy distribution curves at temperatures T1 and T2 (where T 2 = T 1 + 1 0). Now as we know that the rise in temperature increases the kinetic energy of molecules ( ·: K.E. T) therefore, the energy distribution curve gets flattened and shifts towards higher energy region. A close examination of the curves in the graph clearly reveals that the function of molecules possessing higher kinetic energy, i.e., energy greater than threshold energy, as indicated by shaded portion becomes almost double and therefore the rate of reaction almost doubles for 10 rise of temperature. Thus, increase in the rate of reaction with increase in temperature is mainly due to increase in number of collisions which are energetically effective.

Temperature Dependence of Rate Constant

Arrhenius developed the mathematical relation between temperature and the rate constant on the basis of the observations from the large number of experiments. This temperature dependence of the rate constants is expressed algebraically as

K = A e-E a /RT

Equation (20.1) is called Arrhenius equation. Here A is pre exponential factor and is called frequency factor, Ea is the energy of activation and Tis the temperature in kelvin scale.

The term e -Ea I RT in the above equation is also called as Boltzmann Factor. Both A and E0 are characteristic of the reaction. Another form of the equation which is more useful for calculations is obtained by taking logarithm of Eqn. (20.1), therefore,

Log k2 / k1 = Ea / 2.303 R [ 1/T1 – 1 / T2]

Here k2 and k1 are rate constant at temperature T1 and T2 respectively Ea is activation energy and R is universal gas constant.

EFFECT OF CATALYST ON RATE OF REACTION

A catalyst is a substance that alters the rate of chemical reaction without itself being permanently chemically changed. Never state things like “it doesn’t react, just speeds it up”. It must take part in the reaction and it must change chemically, albeit on a temporary basis. A catalyst provides a different ‘pathway’  ormechanism that makes the bond breaking processes (or other electronic changes in the reactants) occur more readily. In general,

• A catalyst speeds up a reaction, but it must be involved ‘chemically’, however temporarity, in some way,_ and is continually changed and reformed as the reaction proceeds.

• Catalysts work by providing an alternative reaction pathway of lower activation energy.

Thus, the function of a catalyst is thus to lower down the activation energy. In sample words, greater the decrease in the activation energy caused by the catalyst, higher will be the reaction rate. In the presence of a catalyst, the reaction follows a path of lower activation energy. Under this condition, a large number of reacting molecules are able to cross-over the energy barrier and thus the rate of reaction increases. The energy profile diagram for the catalysed and uncatalysed reactions are as shown in the Fig. 20.17. Where dotted curve represents the progress of uncatalysed reaction and solid curve represents:- the catalysed reaction. Fig. 20.17. Potential energy curves for catalysed and uncatalysed reactions.

For a general reaction of the type A + B à AB the course of uncatalysed and catalysed reaction may be represented as:

(a) Uncatalysed reaction: (b) Catalysed reaction: Though the catalyst increases the rate of the reaction, yet it does not effect the state of equilibrium in case of reversible reactions. It is because the activation energy for the forward reaction and backward reaction is reduced to the same extent