Problem 97 - A Complete Resource Book in Chemistry for JEE Main

Question

The half-life of a chemical reaction at a particular concentration is \(50 \mathrm{~min}\), when the concentration of reactants is doubled, the half-life becomes \(100 \mathrm{~min}\). Find the order. (a) zero (b) first (c) second (d) third

Step-by-Step Solution

Answer

The order of the reaction is second (c).

Step 1: Understanding Half-life and Order Relationship

The half-life of a reaction is the time it takes for the concentration of a reactant to reduce to half. For zero order, half-life is inversely proportional to concentration, for first order, it is constant and independent of concentration, and for second order, it is directly proportional to the initial concentration.

Step 2: Analyzing Given Information

We are given that when the concentration of reactants is doubled, the half-life changes from 50 minutes to 100 minutes. This implies the half-life is directly affected by the concentration.

Step 3: Inferring the Order of Reaction

Since the half-life doubles when the concentration doubles, the reaction cannot be zero or first order. For a reaction where half-life is directly proportional to the concentration, it indicates second order.

Key Concepts

Half-life

Half-life in chemistry refers to the time required for a reactant in a chemical reaction to decrease to half of its initial concentration. It's a simple way to explain how fast a reaction progresses. In first-order reactions, the half-life is constant, meaning it doesn't change no matter the starting concentration.
For zero-order reactions, the half-life is inversely proportional to the concentration, meaning if you increase the concentration, the half-life decreases. In contrast, for second-order reactions, the half-life is directly proportional, so doubling the concentration results in doubling the half-life, as seen in our problem here. Understanding half-life is crucial because it's like reading the 'speedometer' of your reaction's progress.

Chemical Kinetics

Chemical kinetics is the field that explores the rates of chemical reactions and the steps involved. It helps us understand how fast a reaction proceeds and why. Factors such as temperature, concentration, and catalysts can influence these rates.
Chemical reactions occur when molecules collide with sufficient energy, and kinetics studies how likely these collisions lead to reactions. By examining these concepts, you can predict how long it will take for a reaction to reach completion or change based on different conditions. This is essential in everything from pharmacology to industrial manufacturing.

Order of Reaction

The 'order of reaction' tells us how the concentration of reactants affects the speed of a reaction. It can be zero, first, second, or of higher order. Each order has unique characteristics:

• **Zero Order**: The rate is constant and does not depend on the concentration of the reactant.
  
• **First Order**: The rate depends linearly on one concentration, and the half-life remains constant regardless of initial concentration.
  
• **Second Order**: The rate is proportional to the square of the concentration, which means doubling the concentration will affect the rate and often the half-life as well.
  

In the given exercise, doubling the concentration causes the half-life to double, indicating a second-order reaction, where this relationship is key to understanding reaction kinetics.

Concentration Effect

The concentration of reactants can significantly impact the rate and course of a chemical reaction. For different orders of reactions, this impact varies widely. In your given exercise, when concentrations double and the half-life doubles, it's a direct indication of a second-order reaction, where the reaction rate found is proportional to the square of the reactant concentration.
This concentration effect means that higher concentrations can lead to higher reaction rates but can also lead to longer or shorter times for completion, depending on the reaction order. For chemists and engineers, understanding this effect is crucial for controlling reactions in labs and industries efficiently. It's the guide for predicting how changes in concentration alter reaction dynamics.