To determine how many milliliters of sterile water should be added to a vial containing 5 μg/mL of a drug to prepare a solution containing 1.5 μg/mL of the drug, follow these steps:
1. Initial setup:
- Initial concentration of the drug, [tex]\(C_1\)[/tex]: 5 μg/mL
- Desired final concentration of the drug, [tex]\(C_2\)[/tex]: 1.5 μg/mL
- Volume of the initial solution, [tex]\(V_1\)[/tex]: 1 mL (Assume 1 mL for simplicity)
2. Using the dilution formula:
The dilution formula is given by:
[tex]\[
C_1 \times V_1 = C_2 \times V_2
\][/tex]
where [tex]\(V_2\)[/tex] is the final volume of the solution.
3. Solving for the final volume, [tex]\(V_2\)[/tex]:
[tex]\[
V_2 = \frac{C_1 \times V_1}{C_2}
\][/tex]
Substituting the known values:
[tex]\[
V_2 = \frac{5 \, \text{μg/mL} \times 1 \, \text{mL}}{1.5 \, \text{μg/mL}}
\][/tex]
[tex]\[
V_2 \approx 3.3333 \, \text{mL}
\][/tex]
4. Calculating the volume of sterile water to be added:
The volume of sterile water to be added, [tex]\(V_{\text{add}}\)[/tex], is the difference between the final volume and the initial volume:
[tex]\[
V_{\text{add}} = V_2 - V_1
\][/tex]
Substituting the values:
[tex]\[
V_{\text{add}} \approx 3.3333 \, \text{mL} - 1 \, \text{mL}
\][/tex]
[tex]\[
V_{\text{add}} \approx 2.3333 \, \text{mL}
\][/tex]
Therefore, you should add approximately 2.3333 milliliters of sterile water to the vial.
