The unit of the rate constant for a reaction of order \( n \) is given by:
\[
k = \left( \text{mol}^{1-n} \, \text{dm}^{3(n-1)} \, \text{s}^{-1} \right)
\]
For a zero-order reaction:
\[
k = \text{mol} \, \text{dm}^{-3} \text{s}^{-1}
\]
which matches the given unit. Thus, the correct answer is zero.