Second Order Reaction - Definition, Rate Law, Integrated Rate Equation and Half-Life

Second Order Reaction

A second-order reaction is a chemical reaction whose rate depends on the square of the concentration of a single reactant or on the product of the concentrations of two different reactants. Second-order kinetics is an important topic in chemical kinetics and is frequently asked in CBSE, NEET, and JEE examinations.

Definition

A reaction is called a second-order reaction when the overall order of the reaction is equal to two.

General Rate Laws

For one reactant:

Rate = k[A]²

For two reactants:

Rate = k[A][B]

where

• Rate = Rate of reaction
• k = Rate constant
• [A], [B] = Concentrations of reactants

Integrated Rate Equation

For the reaction:

A → Products

The integrated rate equation is:

1/[A] = 1/[A]₀ + kt

where

• [A]₀ = Initial concentration
• [A] = Concentration after time t
• k = Rate constant
• t = Time

Half-Life of Second Order Reaction

The half-life of a second-order reaction is given by:

t_1/2 = 1/k[A]₀

Unlike a first-order reaction, the half-life of a second-order reaction depends on the initial concentration. As the initial concentration increases, the half-life decreases.

Characteristics

• Rate depends on the square of concentration or two reactant concentrations.
• Rate decreases as concentration decreases.
• Half-life depends upon initial concentration.
• Integrated equation contains reciprocal concentration.
• Unit of rate constant is L mol^-1 s^-1.

Graphical Representation

• Concentration vs Time → Curved decreasing graph.
• 1/[A] vs Time → Straight line.
• Slope of the straight line = k.
• Intercept = 1/[A]₀.

Examples

• Dimerization reactions.
• Reaction between potassium iodide and persulphate ions.
• Saponification of ethyl acetate with sodium hydroxide.
• Many bimolecular reactions.

Applications

• Chemical manufacturing.
• Polymerization reactions.
• Environmental chemistry.
• Industrial process design.
• Reaction mechanism studies.

Exam Tip:
If a plot of 1/[A] versus time gives a straight line, the reaction follows second-order kinetics.

Summary

Property	Second Order Reaction
Rate Law	Rate = k[A]2 or k[A][B]
Integrated Equation	1/[A] = 1/[A]₀ + kt
Half-Life	1/k[A]₀
Unit of Rate Constant	L mol-1 s-1
Depends on Concentration	Yes
Half-Life Depends on Initial Concentration	Yes
Linear Plot	1/[A] vs Time

Conclusion

Second-order reactions play an important role in understanding reaction mechanisms involving two reacting species. The integrated rate equation, dependence of half-life on initial concentration, and the linear relationship between 1/[A] and time are key characteristics that help identify second-order kinetics. Mastering these concepts is essential for success in CBSE Class 12 Chemistry, NEET, JEE, and other competitive examinations.