For a reaction of order n, the unit of the rate constant is :

Solution

Chemistry ma’am · 4 steps

Make the units of k[A]ⁿ match the units of rate, then solve for the units of k.

1. Write the rate law. For order n, rate = k[A]ⁿ. Rate has units mol L⁻¹ s⁻¹ and concentration has units mol L⁻¹.

   k = rate/[A]ⁿ = (mol L⁻¹ s⁻¹)/(mol L⁻¹)ⁿ = (mol L⁻¹)¹⁻ⁿ s⁻¹

2. Open the bracket. Raise each unit inside to the power 1-n. Moles give mol¹⁻ⁿ, and litres give L⁻⁽¹⁻ⁿ⁾ = Lⁿ⁻¹.
3. Quick check. For n = 1 this gives s⁻¹, and for n = 0 it gives mol L⁻¹ s⁻¹. Both are the familiar units.
4. So. The unit of k is mol¹⁻ⁿ Lⁿ⁻¹ s⁻¹, which is option (c).

The idea to keep. Units of k are always (mol L⁻¹)¹⁻ⁿ s⁻¹. The litre sits in the denominator, so its power flips sign: Lⁿ⁻¹.

Answer from the NTA final answer key. Solution by PrepWiser.