Rate of disappearance of reaction of reactants is equal to the $\frac{\mathrm{d}\left[\mathrm{R}\right]}{\mathrm{dt}}$.

Concentration has the unit $\mathrm{M}$. Time has the unit of second.

Hence, unit of rate of disappearance is $\mathrm{M}{ \mathrm{s}}^{-1}$.

Rate of reaction is equal to the concentration per unit time. So, the unit of rate of reaction is $\mathrm{M}{ \mathrm{s}}^{-1}$.

The unit of rate constant k depends upon order of reaction. Each order of reaction has the different unit of rate constant.

The unit of rate constant k for a first order reaction is ${\mathrm{s}}^{-1}$.

Hence, the incorrect statement is the unit of rate constant k for a first order reaction is $\mathrm{M}{ \mathrm{s}}^{-1}$.