Chemistry MECHANISM OF THE REACTION

Reaction Mechanism and Rate Determining Step :

To understand what is order of reaction, based on mechanism consider the reaction :

`2NO(g) + 2H_2(g) -> N_2(g) + 2H_2O(g)`

Kinetic experiment carried out at `1100` `K` upon this reaction has shown following rate data : See Table.

From the Expt. No.1 and 2, it is evident that rate increases `4` fold when concentration of `NO` is doubled keeping the concentration of `H_2` constant i.e.

Rate `prop [NO]^2`, when `[H_2]` is constant.

Again from Expt. No.2 and 3, it is evident that when concentration of `H_2` is doubled keeping the concentration of `NO` constant, the rate is just doubled i.e.

Rate `prop [H_2]`, when `[NO]` is constant.

From Expt. (1) and Expt. (3), the rate increases `8`-fold when concentrations of both `NO` and `H_2` are doubled simultaneously i.e.

Rate `prop [NO]^2 [H_2]`

This is the rate-law of reaction as observed experimentally. In the rate law, the power of nitric oxide concentration is `2` while that of hydrogen concentration is `1`. So, order of reaction w.r.t. `NO` is `2` and that w.r.t. `H_2` is `1` and overall order is `2 + 1` i.e. `3`.

Catalyst :

A catalyst is a substance which increases the rate of a reaction without itself being consumed at the end of the reaction and the phenomenon is called catalysis. There are some catalysts which decrease the rate of reaction and such catalysts are called negative catalyst. Obviously, the catalyst accelerating the rate will be positive catalyst. However, the term positive is seldom used and catalyst itself implies positive catalyst. Catalyst are generally foreign substances but sometimes one of the product formed may act as a catalyst and such catalyst is called auto catalyst and the phenomenon is called auto catalysis. Thermal decomposition of `KClO_3` is found to be accelerated by the presence of `MnO_2`. Here `MnO_2` (foreign substance) acts as a catalyst.

`2KClO_3+ [MnO_2] -> 2KCl + 3O_2 + [MnO_2]`

`MnO_2` can be received in the same composition and mass at the end of the reaction. In the permanganate titration of oxalic acid in the presence of bench `H_2SO_4` (acid medium), it is found that, in the beginning of titration there is slow discharge of the colour of permanganate solution but after sometime the discharge of the colour become faster. This is due to the formation of `MnSO_4` during the reaction which acts as a catalyst for the same reaction. Thus, `MnSO_4` is an auto catalyst for this reaction. This is an example of auto
catalysis.

`2KMnO_4 + 2H_2SO_4 + 5H_2C_2O_4-> K_2SO_4 + 8H_2O + 10CO_2 + 2MnSO_4`

General Characteristics of Catalyst :

i) A catalyst does not initiate the reaction. It simply fastens it.

ii) Only a small amount of catalyst can catalyse the reaction.

iii) A catalyst does not alter the position of equilibrium i.e. magnitude of equilibrium constant and hence `DeltaG^0`. It simply lowers the time needed to attain equilibrium.This means if a reversible reaction in absence of catalyst completes to go to the extent of `75%` till attainment of equilibrium, and this state of equilibrium is attained in `20` minutes then in presence of a catalyst also the reaction will go to `75%` of completion before the attainment of equilibrium but the time needed for this will be less than `20` minutes.

iv) A catalyst drives the reaction through a different route for which energy barrier is of short height and hence `E_a` is of lower magnitude. That is, the function of the catalyst, to lower down the activation energy.

`E_a =` Energy of activation in absence of catalyst.

`E'_a =` Energy of activation in presence of catalyst.

`E_a - E'_a =` lowering of activation energy by catalyst.

If `k` and `k_(cat)` be the rate constant of a reaction at a given temperature `T`, and `E_a` and `E'_a` are the activation energies of the reaction in absence and presence of catalyst, respectively, then

`k_text(cat)/k = (Ae^(-E_a//RT))/(Ae^(-E_a//RT))` `=>` `k_text(cat)/k = Ae^((E_a-E'_a)//RT)`

Since `E_a- E'_a` is +ve so `k_(cat) > k`. the ratio `(k_text(cat))/k` gives the number of times the rate of reaction will increase by the use of catalyst at a given temperature and this depends upon `E_a - E'_a`. Greater the value of `E_a - E'_a` , higher is the value of `(k_(cat))/k`.