Arrhenius theory of reaction rate

It was developed by max Trautz and William lewis.

It gives insight in to the energetics and mechanistic aspects of reactions.

It is based upon kinetic theory of gases.   

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

A chemical reaction takes palce due to the collision among reactant molecules. The number of collisions taking place per second per unit volume of the reaction mixture is known as collision frequency (Z).

Every collision does not bring a chemical change. The collision that actually produce the products are effective collision. For a collision to be effective the following two barriers are to be effective the following two barriers are to be cleared.

Energy barrier :

The minimum amount of energy which the colliding molecules must posses as to make the chemical reaction to occur is known as threshold energy.

“The minimum amount of extra energy required by reactant molecules to pariticipate in a reaction is called activaiton energy (Ea)”

Orientation barrier :

Energy alone does not determine the effectiveness of the collision. The reacting molecules must collide in proper direction to make collision effective. Following diagrams can explain importance of suitable direction for collision.

Collision to be effective the colliding molecules must posses some certain minimum energy called threshold energy of the reaction.

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.

Concept of energy of activation (Ea)

he 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 energy 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.

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 . By 10ºC rise in temperature, so it is the fraction of the total number of effective collision that increases markedly resulting into marked increase in the reaction rate.

Arrhenius equation                        

Integrating equation 4 assuming Ea to be constant we get,

lnk = –         or       ln = –  or       k = 

This is integrated form of Arrhenius equation.

Where, Constant A = pre–exponential factor it is a constant for a given reaction.

From this equation it is evident that as T ® ¥, k ®  A. Thus, the constant A is the rate constant of reaction at infinity temperature. The rate constant goes on increasing with temperature.

So, when T approaches inifinty, k will be maximum. That is to say, A is the maximum rate constant of a reaction.

The expontential term i.e. e–Ea/RT measures the fraction of total number of molecules in the activated state or fraction of the total number of effective collisions.

 

Where  

nEa  =  no. of molecules of reactant in the activated state   

n = total no. of molecules of the reactant in the reaction

From Arrhenius Equation we have,     

log k = 

So from this it is evident that a plot of log k versus  will be a straight line of the slope equal to and intercept equal to log A as shown below :

Thus, from this plot Ea and A both can be determined accurately.

If k1 and k2 be the rate constant of a reaction at two different temperature T1 and T2 respectively, then we have

log k1 =    and

log k2 = 

Subtracting we get