The question is regarding enzyme specific activity. Is well established that the equation (Delta Abs/time(minutes))/Epsilon(M-1*cm-1)*Pathlength (cm) times the volume (here is the "problem") is used to calculate the substrate/product over time (dS/dT or dP/dT). The outcome is usually expressed in U/ml or micromol*min-1*ml.
Using the outcome in micromol*min-1*ml, dividing this value by the final concentration of the protein in mg/ml , we will have the specific activity, in U/mg or micromol*min-1*mg-1.
The volume used sometimes is just the volume of the reaction, however, some biochemists use a ratio between the reaction volume and the volume of protein inside the reaction. Which one is the most appropriate?