Question

A doctor needs to administer 2 mL of a 100 mg/mL solution to a 200 lb. patient. However, the doctor has the solution available only in 20 mg/mL strength. What volume of the 20 mg/mL solution would be needed to administer the desired dose?

a) 10 mL
b) 30 mL
c) 40 mL
d) 20 mL

Answer 1

To administer 2 mL of a 100 mg/mL solution using a 20 mg/mL solution, 0.4 mL of the 20 mg/mL solution would be needed.

Step-by-step explanation:

To find the volume of the 20 mg/mL solution needed to administer the desired dose, we can use the concept of dilution. The concentration of the desired solution is 100 mg/mL, but we have a solution with a concentration of 20 mg/mL. Since the concentration is inversely proportional to the volume, we can set up a proportion to solve for the volume:

(20 mg/mL) / x = (100 mg/mL) / 2 mL

Cross multiplying, we get 20 mg/mL * 2 mL = 100 mg/mL * x

Simplifying, we find that 40 mL = 100 mg/mL * x

Dividing both sides by 100 mg/mL, we find that x = 0.4 mL. Therefore, the volume of the 20 mg/mL solution needed to administer the desired dose is 0.4 mL.