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Chemistry Question 54 – JEE-MAIN 2025

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Half life of zero order reaction A → product is 1 hour, when initial concentration of reactant is 2.0 mol L−1. The time required to decrease concentration of A from 0.50 to 0.25 mol L−1 is:

For a zero-order reaction, the rate of reaction is independent of the reactant concentration.

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Ninja Strategy•Zero Order Half-Life Proportionality

Recognize that for a zero-order reaction, the half-life is directly proportional to the initial concentration. Since the initial concentration for the desired change (0.50 mol L−1) is much lower than the given initial concentration (2.0 mol L−1), the time taken should be significantly less than the given half-life of 1 hour, quickly eliminating options 1 and 4.

Step 1: Determine the rate constant (k)✦ Active

For a zero-order reaction, the half-life is given by the formula t1/2=[A]02k. We are given t1/2=1 hour when the initial concentration [A]0=2.0 mol L−1.

1 hour=2.0 mol L−12k

Solving for k:

k=2.0 mol L−12×1 hour=1.0 mol L−1 hour−1
Step 2: Calculate the time for the concentration change○ Expand

The integrated rate law for a zero-order reaction is [A]t=[A]0−kt. We need to find the time t for the concentration to decrease from [A]0=0.50 mol L−1 to [A]t=0.25 mol L−1.

0.25 mol L−1=0.50 mol L−1−(1.0 mol L−1 hour−1)t

Rearranging and solving for t:

t=0.50−0.251.0 hour=0.25 hour
Step 3: Convert time to minutes○ Expand

To match the options, convert the time from hours to minutes:

t=0.25 hour×60 min/hour=15 min
💡 Teacher's Secret Hint

Always check the units of the options before finalizing the answer.

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