Question

For a first-order reaction, the unit of rate constant is: ____.

• A. mol L⁻¹ s⁻¹
• B. s⁻¹
• C. L mol⁻¹ s⁻¹
• D. mol² L⁻² s⁻¹

Hint:

To quickly find the units for any order, remember that the units of Rate are always mol L⁻¹ s⁻¹. For first order, Rate = $k$[A], so $k$ must simply be "per time" to cancel out the concentration units.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The rate of a reaction is defined as the change in concentration per unit time. The rate constant ($k$) links the rate to the concentrations of the reactants raised to their respective orders.

Step 2: Key Formula or Approach:
General formula for units of $k$: \[ \text{Units} = (\text{mol L}^{-1})^{1-n} \text{ s}^{-1} \] where $n$ is the order of the reaction.

Step 3: Detailed Explanation:
For a first-order reaction, $n = 1$. 1. Substitute $n = 1$ into the general formula: \[ \text{Units} = (\text{mol L}^{-1})^{1-1} \text{ s}^{-1} \] \[ \text{Units} = (\text{mol L}^{-1})^0 \text{ s}^{-1} \] 2. Any term raised to the power of zero is 1. 3. Therefore, the unit is $\text{s}^{-1}$ (per second).

Step 4: Final Answer:
The unit of the rate constant for a first-order reaction is s⁻¹.