Question

You are supplied with a pain-relieving drug (MW 300) formulation at 5 mg/ml. A patient with a plasma volume of 2.5 L needs an initial dose of 20 $\mu$M for immediate relief. How much solution do you need to inject to the patient?

• A. 1 ml
• B. 2 ml
• C. 3 ml
• D. 4 ml

Hint:

Steps: $\mu M \rightarrow$ moles $\rightarrow$ mass $\rightarrow$ volume Always convert units carefully!

Answer 1

The Correct Option is C

Concept: We use:
• Molarity = moles volume
• Convert required concentration into total moles, then into mass, and finally into volume using given drug concentration

Step 1: Convert required concentration.
\[ 20 \ \mu M = 20 \times 10^{-6} \ \text{mol/L} \]

Step 2: Find total moles required.
\[ \text{Moles} = 20 \times 10^{-6} \times 2.5 = 50 \times 10^{-6} = 5 \times 10^{-5} \ \text{mol} \]

Step 3: Convert moles to mass.
\[ \text{Mass} = 5 \times 10^{-5} \times 300 = 0.015 \ \text{g} = 15 \ \text{mg} \]

Step 4: Find required volume.
Given concentration = $5 \ \text{mg/ml}$ \[ \text{Volume} = \frac{15}{5} = 3 \ \text{ml} \]

Step 5: Final conclusion.
Thus, required volume is: \[ 3 \ \text{ml} \]