The units of the rate constant $k$ for a FIRST-ORDER reaction are

1. Use $\text{rate} = k[A]^n$ with $n = 1$ for first order. 2. Rearrange: $k = \dfrac{\text{rate}}{[A]} = \dfrac{\text{mol L}^{-1}\,\text{s}^{-1}}{\text{mol L}^{-1}} = \text{s}^{-1}$. 3. So for first order, $k$ has units of inverse time only. This is why first-order half-life $t_{1/2} = 0.693/k$ has units of time, as expected. 4. Option A is the unit of RATE itself, not the rate constant. Option C is for second-order reactions ($n = 2$). Option D would imply $n = 1$ but rate also dimensionless, which is wrong. 5. General formula: $[k] = \text{mol}^{1-n}\,\text{L}^{n-1}\,\text{s}^{-1}$. Plug $n = 1$ → $\text{s}^{-1}$. _Source: NCERT Class 12 Chemistry Part 1, Ch 3, §3.2.3 (Order of a Reaction) + Units of rate constant table, p. 7–8._