For a one-compartment IV bolus with Vd = 50 L and Cl = 5 L/h, what are the elimination rate constant k and the half-life t1/2?

• A. k = 0.1 h^-1; t1/2 ≈ 6.93 h
• B. k = 0.01 h^-1; t1/2 ≈ 69.3 h
• C. k = 0.5 h^-1; t1/2 ≈ 1.386 h
• D. k = 0.2 h^-1; t1/2 ≈ 3.47 h

Answer: (A)

In a one‑compartment IV bolus, the elimination rate constant k is determined by k = Cl / Vd, and the half-life is t1/2 = 0.693 / k. With Cl = 5 L/h and Vd = 50 L, k = 5/50 = 0.1 h^-1. Then t1/2 = 0.693 / 0.1 = 6.93 h. So the elimination constant is 0.1 h^-1 and the half-life is about 6.93 hours. This pair directly reflects the given clearance and volume of distribution; other numerical choices would imply different Cl/Vd ratios and thus different k and t1/2.