Math Problem Statement

A pharmacy bulk package bottle of vancomycin 10 g is reconstituted with 95 mL of sterile water for injection to a final concentration of 500 mg/5 mL. The label for the compounded sterile preparation reads 'Vancomycin 1.25 g/D5W 500 mL.' What volume of medication should be withdrawn from the pharmacy bulk package bottle to fill the order?

Solution

The question asks how much volume should be withdrawn from a bulk vancomycin solution based on given details.

Information provided:

  • The bulk package contains 10 g of vancomycin reconstituted with 95 mL of water, yielding a concentration of 500 mg/5 mL.
  • The label on the compounded solution indicates 1.25 g of vancomycin in 500 mL of D5W.

Step-by-Step Approach:

  1. Concentration in the bulk package:

    • The reconstituted solution contains 10 g of vancomycin in 95 mL of water.
    • 10g=10,000mg10 \, \text{g} = 10,000 \, \text{mg}.
    • Therefore, the concentration of the bulk package is: Concentration=10,000mg95mL=105.26mg/mL\text{Concentration} = \frac{10,000 \, \text{mg}}{95 \, \text{mL}} = 105.26 \, \text{mg/mL}
  2. Amount required:

    • The label reads 1.25 g (or 1,250 mg) of vancomycin in the final preparation.
    • To find the volume needed to get 1,250 mg from the bulk package (with concentration 105.26mg/mL105.26 \, \text{mg/mL}): Volume=1,250mg105.26mg/mL11.87mL\text{Volume} = \frac{1,250 \, \text{mg}}{105.26 \, \text{mg/mL}} \approx 11.87 \, \text{mL}

The closest answer to this value from the provided options is D. 12.5 mL.


Do you need further clarification or details? Here are five questions to further explore this concept:

  1. How do you calculate the concentration of a medication in solution?
  2. What steps are involved in converting grams to milligrams?
  3. How can you verify if a reconstituted solution has the correct concentration?
  4. What are the typical dilution methods used in compounding medications?
  5. How would changes in reconstitution volume affect the concentration of a drug?

Tip: Always ensure you’re clear on whether units need to be converted (e.g., grams to milligrams) before performing calculations.

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Math Problem Analysis

Mathematical Concepts

Concentration calculations
Unit conversion
Proportions

Formulas

Concentration = (Amount of drug in mg) / (Volume in mL)
Required Volume = (Desired amount in mg) / (Concentration in mg/mL)

Theorems

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Suitable Grade Level

Advanced Pharmacy/Medical Calculations (Undergraduate level)