What is the formula for half-life t1/2 in first-order kinetics, and what factors influence it?

• A. t1/2 = 0.693 / k
• B. t1/2 = 0.693 × CL / Vd
• C. t1/2 = 0.693 × Vd / CL
• D. t1/2 = 1.386 × Vd / CL

Answer: (C)

In first-order elimination, the half-life reflects how fast the drug is cleared relative to how much it is distributed in the body. The formula t1/2 = 0.693 × Vd / CL captures this relationship: a larger volume of distribution (Vd) means the drug is more spread out into tissues and takes longer to reduce in the plasma, while greater clearance (CL) means the body removes it faster, shortening the half-life. The same idea can be written as t1/2 = 0.693 / k, where k is the elimination rate constant; since k = CL / Vd, both forms are equivalent. The half-life is independent of dose and changes only if clearance or distribution changes. Factors influencing t1/2 include liver and kidney function (affecting CL), drug interactions that alter metabolism or excretion, body composition or age (affecting Vd), and conditions that change protein binding or tissue distribution. In short, increasing Vd lengthens t1/2, while increasing CL shortens it.