Temperature Dependence of the Rate of a Reaction

Temperature Dependence of the Rate of a Reaction

For every 10°C rise in temperature, the rate of reaction becomes double, It can be explained by Arrhenius equation.

Temperature coefficient is the ratio of rate constant of a reaction at two temperatures differing by 10.

Temperature coefficient = kT+10/kT ≈ 2 to 3

Arrhenius equation

Arrhenius equation is a mathematical expression to give a quantitative relationship between rate constant and temperature, and the expression is

The effect of temperature on rate is given by Arrhenius law
k = A.e–Ea/RT

K = rate constant ,Ea = Activation energy , R = Gas constant, T = Absolute Temp.,

A = Frequency factor (Arrhenius Constant)

Taking log an both order

On comparing with the equation of line

From the above equation it is clear that when T → ∞ then k becomes A.i.e. Arrhenius constant is that value of rate constant at infinite temperatures.
Now on comparing Arrhenius equation with the equation of a straight line, we have

Pre exponential factor

The effect of temperature on rate of reaction at two different temperature T1& T2 can be calculated by the Arrhenius law.

Activated complex (or transition state)

Activated complex is the highest energy unstable intermediate between the reactants and products and gets decomposed immediately (having very short life), to give the products. In this state, bonds of reactant are not completely broken while the bonds of products are not completely formed.

Threshold energy (ET) The minimum amount of energy which the reactant must possess in order to convert into products is known as threshold energy.

Activation energy (Ea) The additional amount of energy, required by the reactant so that their energy becomes equal to the threshold value is known as activation energy.

Ea = ET – ER (ET is threshold energy , ER is energy of reaction )

Lower the activation energy, faster is the reaction.

(i) If k2 and k1 are rate constant at temperature T2 and T1; then

ii) Fraction of molecules with energy equal to or greater than the activation energy is called Boltzmann factor and is given by

(iii) Ea is constant for a particular reaction.

(iv) Ea does’t depend on temperature, volume, pressure, etc., but gets affected by catalyst.

In the Arrhenius equation, when T → ∞ then k= Ae° = A

when Ea = 0,k = A  and the rate of reaction becomes independent temperature.

Catalysis of kinetic

A catalyst is a chemical substance which alters the rate of a reaction WIthout itself undergoing any permanent chemical change.

Properties of catalyst

·         In the chemical reactions, catalyst provides an alternate pathway or reaction mechanism by reducing the activation energy between reactants and products and hence. lowering the potential energy barrier as shown.

In the presence of catalyst, activation energy decreases and hence , rate of reaction increases

·        A catalyst does not change the enthalpy (∆rH) , Gibb’s energy (∆G) of reaction and equilibrium constant of a reaction .

·        It only helps in attaining the equilibrium faster

Collision Theory of Chemical Reactions

The number of collisions between the reacting molecules taking place per second per unit volume is known as collision frequency (ZAB

But only those collisions in which the colliding species are associated with certain minimum amount of energy and collide in proper orientation result in the product formation, such collisions are called fruitful collisions or effective collision.

rate = ZABe-Ea/RT

where, ZAB represents the collision frequency of reactants, A and B, e-Ea/RT represents the fraction of molecules with energies equal to or greater than Ea.

So, to account for effective collisions, another factor, P called the probability or steric factor is introduced.

rate = PZABe-Ea/RT

For example, formation of methanol from bromoethane depends upon the orientation of reactant molecules. The proper orientation of reactant molecules lead to bond formation whereas improper orientation makes them simply bounce back and no products are formed.

Diagram showing molecules having proper and improper orientation

To account for effective collisions, another factor P, called the probability or steric factor is introduced. It takes into account the fact that in a collision, molecules must be properly oriented i.e.,

Thus, in collision theory activation energy and proper orientation of the molecules together determine the criteria for an effective collision and hence the rate of a chemical reaction.