Dopamine Concentration
1. **State the problem:** We need to find the percent concentration of dopamine HCl in an intravenous infusion after diluting one vial of dopamine HCl injection into 250 mL of 5% dextrose injection.
2. **Given data:**
- Volume of one vial = 5 mL
- Concentration in vial = 40 mg/mL
- Volume of diluent (5% dextrose) = 250 mL
3. **Calculate the total amount of dopamine HCl in one vial:**
$$\text{Total dopamine HCl} = 40 \text{ mg/mL} \times 5 \text{ mL} = 200 \text{ mg}$$
4. **Calculate the total volume after dilution:**
$$\text{Total volume} = 5 \text{ mL} + 250 \text{ mL} = 255 \text{ mL}$$
5. **Calculate the concentration in mg/mL after dilution:**
$$\text{Concentration} = \frac{200 \text{ mg}}{255 \text{ mL}} \approx 0.7843 \text{ mg/mL}$$
6. **Convert mg/mL to percent concentration:**
Percent concentration means grams per 100 mL. First convert mg/mL to g/mL:
$$0.7843 \text{ mg/mL} = 0.0007843 \text{ g/mL}$$
Then convert to grams per 100 mL:
$$0.0007843 \text{ g/mL} \times 100 = 0.07843 \%$$
7. **Final answer:** The percent concentration of dopamine HCl in the infusion is approximately
$$0.0784 \%$$
This means the infusion contains about 0.0784 grams of dopamine HCl per 100 mL of solution.