FPGEE for National Association of Boards of Pharmacy (NABP) Practice Exam

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What equation is used to determine half-life based on volume of distribution and clearance?

  1. Half-life (hours) = 0.693 x (Vd / CL)

  2. Half-life (hours) = Vd / (0.693 x CL)

  3. Half-life (hours) = CL / (0.693 x Vd)

  4. Half-life (hours) = (0.693 x Vd) / CL

The correct answer is: Half-life (hours) = 0.693 x (Vd / CL)

The correct equation to determine half-life based on volume of distribution (Vd) and clearance (CL) is derived from the pharmacokinetic principles that govern drug elimination. The half-life of a drug is the time it takes for the concentration of the drug in the plasma to reduce by half. This relationship can be mathematically represented as: Half-life (t1/2) = (0.693 x Vd) / CL. The half-life is proportional to Vd, meaning that a larger volume of distribution indicates that the drug is more widely distributed throughout the body, resulting in a longer half-life. Conversely, it is inversely proportional to clearance. If clearance is high, the drug is eliminated more quickly, leading to a shorter half-life. Thus, the correct answer illustrates that the half-life of a drug can be calculated by multiplying the volume of distribution by 0.693 (which is the natural logarithm of 2, crucial for half-life calculations) and then dividing by the clearance. This highlights the relationship between these three pharmacokinetic parameters effectively. The other choices do not reflect the proper relationship among these variables, leading to incorrect formulations for determining the half-life.