Question

A young child weighing 20 kg was given a drug in the dose 100 mg/kg body weight. The plasma concentration of the drug is 2 mg/dl and the clearance is 200 ml/hr. What is the time required to reach steady state plasma concentration?

• A. 10 hrs
• B. 20 hrs
• C. 30 hrs
• D. 40 hrs

Hint:

Find Vd, then half-life from 0.693 x Vd / CL, then multiply by about 5.5.

Answer 1

The Correct Option is B

Step 1: First find the total dose. Total dose = dose per kg x body weight = \(100 \times 20 = 2000\) mg.

Step 2: Calculate the volume of distribution. \(V_d = \dfrac{\text{total dose}}{\text{plasma concentration}} = \dfrac{2000\ \text{mg}}{2\ \text{mg/dl}} = 1000\) dl. In matching units this corresponds to 1000 dl, used directly below.

Step 3: Calculate the half-life. \(t_{1/2} = \dfrac{0.693 \times V_d}{CL} = \dfrac{0.693 \times 1000}{200} = 3.5\) hours.

Step 4: Steady state is reached after about 5.5 half-lives. Time = \(5.5 \times 3.5 = 19.25\) hours, which rounds to the closest option, 20 hours.