Observe the given graph. What will be the unit for the rate constant?

The correct answer is Option (3) → s⁻¹

The graph is a straight line through the origin for log([R]₀/[R]) against time, with slope k/2.303. This is the integrated rate equation of a first order reaction:

    \( \displaystyle \log\frac{[R]_0}{[R]} = \frac{k}{2.303}\,t \)

For order n the unit of k is (mol L⁻¹)¹⁻ⁿ s⁻¹; with n = 1 this is s⁻¹.

Why the other options are incorrect

• Option (1) mol L⁻¹ s⁻¹ — Incorrect. Unit for a zero order reaction.

• Option (2) mol⁻¹ L s⁻¹ — Incorrect. Unit for a second order reaction.

• Option (4) mol⁻² L² s⁻¹ — Incorrect. Unit for a third order reaction.

NCERT (2026-27 edition):
First Order Reactions – “… If we plot a graph between log [R]₀/[R] vs t, (Fig. 3.5), the slope = k/2.303.”