What are the units of the rate constant for a third order reaction? A mol dm⁻³ s⁻¹ B mol⁻¹ dm³ s⁻¹ C mol² dm⁻³ s⁻¹ D mol⁻² dm³ s⁻¹ - AQA - A-Level Chemistry - Question 33 - 2020 - Paper 3

For a third order reaction, the general rate equation can be expressed as:

$$ext{Rate} = k[A]^3$$

Where:

• Rate has units of concentration per unit time, which is mol dm⁻³ s⁻¹.

Given that the concentration of reactant A is raised to the power of 3, the units of k (the rate constant) need to compensate for this.

Thus, the units for the rate constant k can be derived as follows:

$$[k] = \frac{\text{Rate}}{[A]^3} = \frac{\text{mol dm}^{-3} s^{-1}}{(\text{mol dm}^{-3})^3} = \frac{\text{mol dm}^{-3} s^{-1}}{\text{mol}^3 \text{dm}^{-9}} = \text{mol}^{-2} \text{dm}^6 s^{-1}$$

However, to express k in a more usable form we simplify the expression:

$[k] = \text{mol}^{-2} \text{dm}^{6} s^{-1}$

This means the correct answer is:

D mol⁻² dm³ s⁻¹