Question

Which of the following curve represents the first order reaction?

• A. A
• B. B
• C. C
• D. D

Hint:

General relation for half-life: \( t_{1/2} \propto [R]_0^{(1-n)} \), where \( n \) is the order of reaction. For \( n=1 \), \( t_{1/2} \propto [R]_0^0 \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A first-order reaction has a rate that is directly proportional to the concentration of one reactant and a half-life that is constant regardless of initial concentration.
Step 2: Detailed Explanation:
According to the formula \( t_{1/2} = \frac{0.693}{k} \), the half-life of a first-order reaction is independent of the initial concentration \( [R]_0 \).
Thus, a plot of \( t_{1/2} \) versus \( [R]_0 \) will be a straight line parallel to the x-axis (Horizontal).
Option (A) is for a zero-order reaction where \( t_{1/2} \propto [R]_0 \).
Option (C) is for a zero-order reaction where the rate is independent of concentration.
In first-order, the rate vs concentration graph should be a straight line passing through the origin.
Step 3: Final Answer:
Graph (B) correctly represents a first-order reaction as the half-life remains constant.