Questions: A pharmacist adds 10 mL of a 20 %(w / v) solution of a drug to 500 mL of D5W for parenteral infusion. What is the percentage strength of the drug in the infusion solution? (a) 2 % v / v (b) 2 % w / v (c) 1.96 % w / v (d) 0.39 % w / v

Solution Steps

The original solution is a \(20\% \, (\mathrm{w}/\mathrm{v})\) solution, which means there are 20 grams of drug per 100 mL of solution. Since the pharmacist adds 10 mL of this solution, we calculate the amount of drug as follows:

\[ \text{Amount of drug} = \left(\frac{20 \, \text{g}}{100 \, \text{mL}}\right) \times 10 \, \text{mL} = 2 \, \text{g} \]

The total volume of the infusion solution is the sum of the volume of the drug solution and the volume of the D5W:

\[ \text{Total volume} = 10 \, \text{mL} + 500 \, \text{mL} = 510 \, \text{mL} \]

The percentage strength of the drug in the infusion solution is calculated as the weight of the drug per volume of the total solution, expressed as a percentage:

\[ \text{Percentage strength} = \left(\frac{2 \, \text{g}}{510 \, \text{mL}}\right) \times 100\% = 0.3922\% \, (\mathrm{w}/\mathrm{v}) \]

Final Answer