Question

What is the correct unit for the rate constant in a first-order reaction?

• A. Moles per litre per second
• B. Per second
• C. Litre per mole per second
• D. Moles squared per litre squared per second

Hint:

For first-order reactions, the unit of the rate constant k is always s⁻¹.

Answer 1

The Correct Option is B

Step 1: Understanding the rate law.
For a first-order reaction, the rate law is r = k[A], where k is the rate constant and [A] is the concentration of reactant A. The rate r is measured in units of concentration/time (mol L⁻¹ s⁻¹).

Step 2: Unit analysis.
Rearranging the rate law: k = r ÷ [A]. Since r has units mol L⁻¹ s⁻¹ and [A] has units mol L⁻¹, dividing gives: k's unit = (mol L⁻¹ s⁻¹) ÷ (mol L⁻¹) = s⁻¹.

Step 3: Conclusion.
Therefore, the correct unit for the rate constant k in a first-order reaction is s⁻¹, which corresponds to option (B).

Answer 2

Quick shortcut: For a reaction of order n, the unit of the rate constant k is (mol/L) raised to power (1−n), multiplied by s⁻¹.

This is a first-order reaction, so n = 1, and the power becomes (1−1) = 0.

(mol/L)⁰ = 1, so it cancels out completely.

What's left is just s⁻¹, i.e. "per second" — option (B).

Answer 3

Elimination approach: For a first-order reaction, the half-life \( t_{1/2} = \frac{0.693}{k} \) does not depend on the initial concentration at all -- it stays the same no matter how much reactant you start with. That's only possible if \( k \) itself carries no concentration units, i.e. its dimension is purely inverse time. This rules out any option carrying a mole/litre term in any power, including the litre per mole per second option. The only choice left with no concentration dependence at all is per second, option (B).