The units of rate and rate constant for a certain reaction are same. The order of reaction is:
Unit of rate of the reaction=mol L−1 s−1
For zero-order, the unit of the rate constant=mol L−1 s−1
For first-order, the unit of the rate constant=s−1
For second-order, the unit of the rate constant=mol−1 L s−1
For third-order, unit of the rate constant=mol−2 L2 s−1
Hence, for a zero order reaction, the units of rate and rate constant will be same.