Question

Derive specific reaction rate units for a reaction of order n.

Answer 1

The units of the specific reaction rate or rate constant k for a reaction of order n are derived from the rate law expression:

Rate = k[concentration]ⁿ

Since the rate of reaction has units of mol L⁻¹ s⁻¹ and concentration has units of mol L⁻¹, we substitute into the equation to isolate the units of k:

\[\ce{k = \frac{Rate}{[concentration]^n}}\]

= \[\ce{\frac{mol L^{-1} s^{-1}}{(mol L^{-1)^n}}}\]

= mol¹⁻ⁿ Lⁿ⁻¹ s⁻¹

Thus, the units of the rate constant for a reaction of order n are mol¹⁻ⁿ Lⁿ⁻¹ s⁻¹.