The formula in textbooks for t_ frac12 of a drug following first order elimination is generally given as t_ frac12= frac ln(2).V_dCl where V_d is the volume of distribution and Cl is the clearance. Assuming first order kinetics of elimination, the rate of elimination (R) would be proportional to the plasma concentration (Cp). R = Cp . k. For calculation of t_ frac12, since this is a first order elimination, t_ frac12 = ln(2)/k. Substituting, t_ frac12 = frac ln(2).CpR. Since Cl = R/Cp, substituting would give, t_ frac12 = ln(2)/Cl. Since both the formulae don't match (this one doesn't have a V_d term at all!), where have I gone wrong? Also then how is Cl different from k? According to the correct formula, k=Cl/V_d. How is that so? Volume of distribution is the apparent volume of blood the drug takes up and is given by V_d = frac DosePc. Clearance is the volume of blood that has been cleared of the drug in unit time and is given by Cl = R/Cp. Correct me if the basic definitions themselves are wrong.