A 500-mg dose of a drug has therapeutic efficacy for 6 h. If the half- life of the drug is 8 h, for how long would a 1gm dose be effective
**Core Concept**
The half-life of a drug is a critical pharmacokinetic parameter that determines its duration of action. It is the time required for the plasma concentration of a drug to decrease by half, and it is influenced by factors such as metabolism, excretion, and distribution. In this question, we are asked to calculate the duration of action of a drug based on its half-life and the dose administered.
**Why the Correct Answer is Right**
The duration of action of a drug is directly proportional to its dose and inversely proportional to its clearance. Since the half-life is a constant 8 hours, we can use the principle of first-order kinetics to calculate the duration of action. The formula for calculating the duration of action is: time = dose / clearance. Since the clearance is not given, we can use the half-life to estimate it. The half-life is related to clearance by the formula: half-life = 0.693 / clearance. Rearranging this formula, we get: clearance = 0.693 / half-life. Plugging in the values, we get: clearance = 0.693 / 8 = 0.0866. Now, we can calculate the duration of action for the 1-gm dose: time = dose / clearance = 1 / 0.0866 = 11.55 hours.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not take into account the dose administered. The duration of action is directly proportional to the dose.
**Option B:** This option is incorrect because it assumes that the half-life is directly proportional to the dose, which is not true. The half-life is a constant parameter that is independent of the dose.
**Option C:** This option is incorrect because it assumes that the clearance is directly proportional to the dose, which is not true. The clearance is a constant parameter that is independent of the dose.
**Clinical Pearl / High-Yield Fact**
When calculating the duration of action of a drug, remember that the half-life is a constant parameter that is independent of the dose. However, the clearance, which is related to the half-life, can be affected by factors such as liver or kidney function, which can alter the drug's duration of action.
**Correct Answer: A. 11.55 hours**