# Chemical Kinetics

The branch of chemistry, which deals with the study of reaction rates and their mechanisms, is called chemical kinetics.

## Rate of Chemical Reaction

The change in concentration of a reactant or a product in unit time is called rate of reaction. It can be expressed in following terms:

- The rate of decrease in concentration of any one of the reactants.
- Or the rate of increase in concentration of any one of the products.

Let us assume a hypothetical reaction in which volume of the system remains constant.

`R→P`

In this reaction, one mole of reactant R produces one mole of product P. If [R]_{1} and [P]_{1} are the concentrations of R and P at time t_{1} and [R]_{1} and [P]_{1} are their concentrations at time t_{1} then,

`Δt=t_2-t_1`

`&Delta[R]=[R]_2-[R]_1`

`Δ[P]=[R]_2-[P]_1`

Rate of disappearance of R = (Decrease in concentration of R) ÷ (Time taken)

`=-(Δ[R])/(Δt)` ………(1)

Rate of appearance of P = (Increase in concentration of P) ÷ (Time taken)

`=+(Δ[P])/(Δt)` ……….(2)

Equations (1) and (2) give average rate of reaction (r_{av}).

Since Δ[R] is a negative quantity, it is multiplied with -1 to make the rate of the reaction a positive quantity.

### Units of rate of reaction

Units of rate of reaction are concentration time^{-1}. So, if concentration is in mol L^{-1} and time is in second, then unit for rate of reaction will be mol L^{-1} s^{-1}. But, in gaseous reactions, when concentration of gases is expressed in terms of their partial pressure, the units of rate will be atm ^{-1}.

Let us consider the following reaction:

`Hg + Cl_2→Hg\Cl_2`

In this reaction, the stoichiometric coefficients of the reactants and products are same. In this case, rate of reaction is given as follows:

`r=-(&Delta[Hg])/(Δt)``=-(Δ[Cl_2])/(Δt)``=(Δ[Hg\Cl_2])/(Δt)`

Let us consider following reaction:

`2HI→H_2+I_2`

In this reaction, the stoichiometric coefficients of reactants or products are not equal to one. In this case, the rate of disappearance of any of the reactants, or the rate of appearance of any of the products is divided by their respective stoichiometric coefficients.

`r=-1/2(Δ[HI])/(Δt)``=(Δ[H_2])/(Δt)``=(Δ[I_2])/(Δt)`

### Factors Affecting Rate of Reaction

Rate of reaction depends upon the following factors:

- Concentration of reactants
- Temperature
- Catalyst

## Dependence of Rate on Concentration:

For a given temperature, the rate of a chemical reaction may depend on the concentration of one or more reactants and products. The representation of rate of reaction in terms of concentration of the reactants is known as **rate law** or **rate equation** or **rate expression**.

### Rate Expression and Rate Constant

Let us consider the following reaction:

`aA+bB→cC+dD`

Here, a, b, c and d are stoichiometric coefficients of reactants and products.

The rate expression for this reaction is

Rate ∝ `[A]^x[B]^y`

Or, Rate `=k[A]^x[B]^y`

Or, `-(d[R])/(dt)=k[A]^x[B]^y` ………. (1)

This equation is known as differential rate equation, where k is called the rate constant. This equation is alsoe called rate law or rate expression. *Rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power. The power may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.*

Rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation, i.e. theoretically. But it must be determined experimentally.

## Order of a Reaction

The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.

Rate `=k[A]^x[B]^y`

Here, `x+y` = Order of reaction

Order of the reaction can be 0, 1, 2, 3 and even a fraction. In a zero order reaction, the rate of reaction is independent of the concentration of reactants.

#### Units of rate constant:

Let us consider the equation for rate of reaction given above. This equation can also be written as follows:

`k=text(Rate)/([A]^x[B]^y)`

`=text(concentration)/text(time)xx1/(text(concentration)^n)`

If SI units of concentration is mol L^{-1} and that of time is s, then units of k for different order are as follows:

Zero order reaction:

`(mo\l L^(-1))/(s)xx1/((mo\l L^(-1))^0)=mo\l L^(-1)s^(-1)`

First order reaction:

`(mo\l L^(-1))/(s)xx1/((mo\l L^(-1))^1)= s^(-1)`

Second order reaction:

`(mo\l L^(-1))/(s)xx1/((mo\l L^(-1))^2)=mo\l^(-1) Ls^(-1)`