The Arrhenius theory of rate of reaction states that for reactants to form products, the colliding particles (or molecules) of the reactants must possess a certain amount of energy so as to overcome the reaction barrier. This energy is the activation energy(E_a).

\[ k = A \ e^{-\frac{E_a}{RT}} \]

• k is the rate constant of the reaction.
• A is the pre-exponential factor (frequency factor).
• E_a is the activation energy.
• R is the gas constant.
• T is the absolute temperature in Kelvin.

According to this equation, the rate constant k depends on the temperature T and the activation energy E_a. It shows how increasing the temperature can increase the rate of a chemical reaction.

The rate law in chemistry is a mathematical expression that describes the rate of a chemical reaction. It shows the relationship between rate of reaction and concentration. It is typically represented as:

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

Where:

• Rate: Represents the reaction rate.
• k: Is the rate constant, specific to the reaction and dependent on factors like temperature.
• [A] and [B]: Denote the concentrations of the reactants A and B.
• x and y: Are the reaction orders, determined experimentally, showing how concentration affects the rate.

The reaction rate is directly proportional to [A]^x and [B]^y, and the values of x and y tell us how the concentrations influence the rate.

The sum of the exponents x and y gives the overall order of the reaction.

Example 1: If the reaction is second order with respect to A (x = 2) and first order with respect to B (y = 1), and the rate constant k is found to be 0.05 M^-1s^-1, calculate the rate of the reaction when [A] = 0.2 M and [B] = 0.1 M.

The rate law is given as:

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

Substitute the given values:

Rate = (0.05)(0.2)²(0.1)¹

Calculating:

Rate = 0.0002 M^-1s^-1

So, the rate of the reaction when [A] = 0.2 M and [B] = 0.1 M is 0.0002 M^-1s^-1.

Example 2: A kinetic study of the reaction
A + B = C
was carried out at different concentrations of the reactants at 25⁰c. The results obtained are summarized in the table below

No	[A] moldm-3	[B] mol/dm³	Reaction rate MS-1
I	0.10	0.10	2 × 10 -5
II	0.10	0.20	8 × 10-5
III	0.20	0.10	4 × 10-5

Determine

1. The overall order of the reaction
2. The specific rate law of the equation