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

First Order Reaction

A first-order reaction is one in which the rate of reaction is directly proportional to the concentration of one reactant. As the concentration decreases with time, the reaction rate also decreases. First-order kinetics is one of the most important topics in chemical kinetics and is frequently asked in CBSE, NEET and JEE examinations.

Definition

A reaction is called a first-order reaction when its rate depends on the first power of the concentration of a single reactant.

General Reaction

A → Products

Rate Law

Rate = k[A]

where

• Rate = Rate of reaction
• k = Rate constant
• [A] = Concentration of reactant

Integrated Rate Equation

After integrating the rate law,

ln([A]₀/[A]) = kt

or

k = (2.303/t) log([A]₀/[A])

where

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

Half-Life of First Order Reaction

The half-life is the time required for the concentration of the reactant to become half of its initial value.

t_1/2 = 0.693/k

An important feature of a first-order reaction is that the half-life is independent of the initial concentration.

Characteristics

• Rate depends on reactant concentration.
• Rate decreases continuously with time.
• Half-life remains constant.
• Integrated equation contains logarithms.
• Unit of rate constant is s^-1.

Graphical Representation

• Concentration vs Time → Exponential decay curve.
• log[A] vs Time → Straight line with slope = −k/2.303.
• ln[A] vs Time → Straight line with slope = −k.

Examples

• Radioactive decay.
• Decomposition of N₂O₅.
• Decomposition of hydrogen peroxide (under suitable conditions).
• Isomerization reactions.

Applications

• Nuclear chemistry.
• Pharmaceutical drug degradation.
• Environmental chemistry.
• Chemical industries.

Exam Tip:
If the half-life remains constant throughout the reaction, it is most likely a first-order reaction.

Summary

Property	First Order Reaction
Rate Law	Rate = k[A]
Integrated Equation	ln([A]₀/[A]) = kt
Half-Life	0.693/k
Unit of k	s⁻¹
Depends on Concentration	Yes
Half-Life Depends on Initial Concentration	No
Graph	Exponential decay

Conclusion

First-order reactions are among the most common chemical reactions. Their constant half-life, logarithmic integrated rate equation, and exponential decrease in concentration make them easy to identify experimentally. Understanding first-order kinetics is essential for mastering chemical kinetics and solving numerical problems in competitive examinations.