Chemical Kinetics

Effect of Temperature on Rate of Reaction

The rate of most of the chemical reactions increases with increase in temperature. The rate constant nearly doubles with rise in temperature by 10° for a chemical reaction.

Arrhenius Equation: This equation shows the dependence of rate of a chemical reaction on temperature.

`k=Ae^(-E_a/RT)`

Here, A is the Arrhenius factor (or frequency factor), R is gas constant and E_a is activation energy.

To understand this equation, let us take example of following reaction.

`H_2(g)+I_2(g)→2HI(g)`

According to Arrhenius, this reaction can take place only when a molecule each of hydrogen and iodine collide to form an unstable intermediate. The intermediate exists for a very short time and then breaks up to form two molecules of hydrogen iodide.

graph showing reaction coordinate vs potential energy

The intermediate is called activated complex (C), and the energy required to form this is called activation energy (E_a). This graph is plotted for potential energy vs reaction coordinate. The reaction coordinate shows the profile of energy change during the course of reaction. Final enthalpy of reaction depends on the nature of reactants and products.

$graph showing reaction kinetic energy vs fraction of molecules$

All the molecules in the reacting species do not have the same kinetic energy. Ludwig Boltzmann and James Clark Maxwell used statistics to predict the behavior of large number of molecules. According to them, the distribution of kinetic energy may be described by plotting the fraction of molecules with a given kinetic energy vs kinetic energy.

Fraction of molecules `=(N_E)/(N_T)`

Here, N_E is the number of molecules with energy E and N_T is the total number of molecules.

$graph showing reaction kinetic energy vs fraction of molecules$

The peak of the curve corresponds to the most probable kinetic energy. Molecules with energies higher or lower than this value are less in number. When we raise the temperature, the maximum of the curve moves to higher energy value and the curve broadens out so that a greater proportion of molecules get much higher energies.

In this graph, slope `=(E_a)/R` and intercept = In A

So we can find E_a and A using these values.

At temperature T₁

`In k_1=-(E_a)/(RT_1)+In A` ……………….. (1)

At temperature T₂

`In k_2=-(E_a)/(RT_2)+In A` ……………….. (1)

Subtracting equation 1 from (2) we get:

`In k_2-In k_1=(E_a)/(RT_1)-(E_a)/(RT_2)`

Or, `In(k_2)/(k_1)=(E_a)/(R)[(1/(T_1)-1/(T_2)]`

Or, `Io\g(k_2)/(k_1)=(E_a)/(2.303R)[(1/(T_1)-1/(T_2)]`

Or, `Io\g(k_2)/(k_1)=(E_a)/(2.303R)[((T_2-T_1)/(T_1T_2)]` ……………..(3)

Effect of Catalyst

A substance which increases the rate of reaction (but itself does not undergo any permanent chemical change) is called a catalyst.

Intermediate Complex Theory: As per this theory, a catalyst forms temporary bonds with reactants to make an intermediate complex. This complex eventually decomposes to yield products and the catalyst.

A catalyst reduces the activation energy and thus lowers the potential energy barrier. Thus, the catalyst provides an alternate pathway for the reaction. A small amount of catalyst can catalyse a large amount of reactants. A catalyst does not alter Gibbs energy. A catalyst catalyses spontaneous reactions but does not catalyse non-spontaneous reactions. Moreover, a catalyst does not change the equilibrium constant, rather helps in attaining the equilibrium faster.

Collision Theory of Chemical Reactions

This theory was developed by Max Trautz and William Lewis in 1916-18. As per this theory, the reactant molecules are assumed to be hard spheres and reaction occurs when molecules collide with each other. The number of collisions per second per unit volume of the reaction mixture is called collision frequency (Z). For a reaction:

`A + B →` Products

Rate `=Z_(AB)e^(-E_a/RT)`

Here, Z_AB is the collision frequency of reactions, and e^-E_a/RT is the fraction of molecules with energies equal to or greater than E_a.

This equation fairly accurately predicts the value of rate constants for reactions which involve atomic species or simple molecules. But significant deviations are observed for complex molecules.

The reason for this could be that all collisions do lead to the formation of products. The collisions in which molecules collide with sufficient kinetic energy and proper orientation, so as to facilitate formation of new bonds, are called effective collisions.

To account for effective collisons, another factor P is introduced. This is called the probability or steric factor. So, the equation now becomes

Rate `=PZ_(AB)e^(-E_a/RT)`