JEE Main 2025 · 24 January · evening · Single correct · +4 / −1
Given below are two statements :
Statement (I) :
is valid for first order reaction.
Statement (II) :
is valid for first order reaction.
In the light of the above statements, choose the correct answer from the options given below :
- (a) Both Statement I and Statement II are false
- (b) Statement I is true but Statement II is false
- (c) Statement I is false but Statement II is true
- (d) Both Statement I and Statement II are true
Answer and solution
Answer (b) Statement I is true but Statement II is false
Solution
Chemistry ma’am · 4 steps
Check each graph against the first-order equation and watch the sign of the slope in the second one.
- Statement I. For a first-order reaction, t_(1/2) = 0.693/k. It does not depend on [R]₀, so a plot of t_(1/2) against [R]₀ is a horizontal line. Statement I is true.
- First-order law. The integrated rate law, written with common logarithms, is shown below. The concentration falls with time, so [R] < [R]₀ and log[R]/[R]₀ is negative and keeps getting more negative.
log[R]/[R]₀ = -k/2.303 t
- Statement II. So the plot of log[R]/[R]₀ against time is a straight line through the origin going downward, with slope -k/2.303. The graph shows a rising line with slope +k/2.303, which fits log[R]₀/[R], not log[R]/[R]₀. Statement II is false.
- So. Statement I is true and Statement II is false, which is option (b).
The idea to keep. First order: half-life is independent of starting concentration. log[R]/[R]₀ against t slopes down at -k/2.303. Flip the ratio and the slope turns positive.
Answer from the NTA final answer key. Solution by PrepWiser.