A 70 kg woman was administered 1000 mg of the drug as i.v. bolus. After its uniform distribution in the body, the plasma concentration of the drug was found to be 50 mg/L. What is its volume of distribution?
- 70L
- 500L
- 20L
- 0.1L
The Correct Option is C
Solution and Explanation
To determine the volume of distribution (\(V_d\)) of a drug, we use the relationship between the dose administered, the plasma concentration, and the volume of distribution. The formula for calculating the volume of distribution is:
\(V_d = \frac{Dose}{C_0}\)
Where:
- \(V_d\) is the volume of distribution (L)
- Dose is the amount of drug administered (mg)
- \(C_0\) is the plasma drug concentration at time zero (initial concentration) (mg/L)
In the given problem:
- Dose = 1000 mg
- \(C_0 = 50 \, \text{mg/L}\)
Substituting these values into the formula, we get:
\(V_d = \frac{1000}{50} = 20 \, \text{L}\)
Thus, the volume of distribution of the drug is 20 liters. This means that the initial drug concentration was evenly distributed in a volume of 20 liters in the body.
Conclusion: The correct answer is 20L.
This calculation helps in understanding how extensively a drug disperses into body tissues compared to the blood. A larger volume of distribution indicates more extensive distribution into tissues.
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