Final answer:
After an elimination half-life of 3 hours, a 70 Kg patient would have 15 mg of a drug remaining from an initial 30 mg dose. The elimination rate constant (k) is 0.231 per hour, so the expected elimination rate for the drug would be 3.465 mg/hr.
Step-by-step explanation:
The student's question asks about the expected elimination rate of a drug three hours after administration. The patient weighs 70 Kg and was given 30 mg of a drug with a volume of distribution (Vd) of 5 L/Kg and an elimination half-life of 3 hours. To determine the elimination rate, we need to apply pharmacokinetic equations.
The volume of distribution (Vd) can be calculated by multiplying the patient's body weight by the Vd value:
- Vd (total) = 70 kg * 5 L/kg = 350 L
Since the elimination half-life is 3 hours, after one half-life has passed (which is 3 hours in this case), the drug concentration will have decreased by half. Therefore, half of the initial dose will remain:
- Remaining dose after 3 hours = 30 mg / 2 = 15 mg
The elimination of the drug follows first-order kinetics, where the amount eliminated per unit of time is proportional to the concentration of the drug in the body. The elimination rate constant (k) for first-order kinetics is given by:
- k = 0.693 / elimination half-life
- k = 0.693 / 3 hours = 0.231 per hour
Finally, we can determine the elimination rate by multiplying the remaining dose by the elimination rate constant (k):
- Elimination rate = 15 mg * 0.231/hr = 3.465 mg/hr
Note: This calculation assumes that the concentration of the drug remains constant throughout the entire body volume and doesn't account for changes in drug distribution over time.