Which of the following statements is/are correct for the first-order reaction: A → P?

I. The concentration of A decreases linearly with time.
II. The rate of reaction is constant.
III. A plot of ln[A] versus time is a straight line with the slope equal to -k.

Question

Which of the following statements is/are correct for the first-order reaction: A → P?

I.	The concentration of A decreases linearly with time.
II.	The rate of reaction is constant.
III.	A plot of ln[A] versus time is a straight line with the slope equal to -k.

BlackTom AI · Accepted Answer

To analyze the first-order reaction A → P, we recall the characteristic behaviors of a first-order process.
Option I: The statement that [A] decreases linearly with time is incorrect. In a first-order reaction, the concentration declines exponentially according to [A] = [A]0 e^(-kt), not a straight line. A linear decrease would imply a zero-order process where the rate is constant regardless of [A].
Option II: The claim that the rate of reaction is constant is false for a first-order step. The rate equals k[A], meaning it depends on the current concentration of A and thus changes over time as [A] changes.
Option III: The assertion that a plot of ln([A]) versus time is a straight line with slope -k is true. Starting from [A] = [A]0 e^(-kt), taking natural logs gives ln([A]) = ln([A]0) - kt, which is a linear relation with slope -k and intercept ln([A]0).
In summary, I and II describe linear or constant-rate behavior that does not fit first-order kinetics, while III correctly captures the linear ln([A]) vs time relationship for a first-order process.

Which of the following statements is/are correct for the first-order reaction: A → P? I. The concentration of A decreases linearly with time. II. The rate of reaction is constant. III. A plot of ln[A] versus time is a straight line with the slope equal to -k.

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