An esterase enzyme is used to hydrolyze a specific ester substrate, resulting in the formation of a product. In a laboratory experiment, $0\mathrm{.}1$ mL of the enzyme solution is added to a reaction mixture containing $1$ mL of substrate solution. After incubation, the concentration of product formed is measured to be $0\mathrm{.}05$ mmol. If the enzyme solution has a protein concentration of $0\mathrm{.}2$ mg$/$mL$,$ calculate the specific activity of the esterase enzyme in units per mg of protein.