Concept:
Unit of rate constant depends on order of reaction.
General relation:
\[
\text{Rate} = k[A]^n
\]
Step 1: Unit of rate.
\[
\text{Rate} = \text{mol dm}^{-3}\text{s}^{-1}
\]
Step 2: For zero order reaction.
\[
k = \text{rate}
\]
So unit of \(k\):
\[
\text{mol dm}^{-3}\text{s}^{-1}
\]
Step 3: Conclusion.
\[
\text{Order = 0}
\]