How many mL of a 1:60 stock solution of Ephedrine Sulphate would be needed to make 30 mL of a product to treat nasal congestion containing 0.25 % Ephedrine Sulphate?单项选择题
A
a. 2.5 mL
B
b. 3.5 mL
C
c. 4.0 mL
D
d. 4.5 mL
E
e. 5.0 mL

Question

How many mL of a 1:60 stock solution of Ephedrine Sulphate would be needed to make 30 mL of a product to treat nasal congestion containing 0.25 % Ephedrine Sulphate?

BlackTom AI · Accepted Answer

Using the dilution equation C1V1 = C2V2, where C1 is the stock concentration, V1 the volume of stock needed, C2 the desired final concentration, and V2 the final volume.

1) Relevant concepts
- A 1:60 stock solution means 1 part drug in 60 parts total, i.e. concentration = 1/60 = 0.0166667 (fraction) = 1.6667% (w/v).
- Percent concentrations and volumes must be in consistent units; here percent and mL are compatible when using C1V1 = C2V2.

2) Step-by-step reasoning and intermediate calculations
- C1 = 1/60 = 0.0166667 → C1 = 1.6667%
- C2 = 0.25%
- V2 = 30 mL
- Apply C1V1 = C2V2 → V1 = (C2 × V2) / C1
- Substitute numbers: V1 = (0.25% × 30 mL) / 1.6667%
- Compute numerator: 0.25 × 30 = 7.5 (percent·mL)
- Divide: V1 = 7.5 / 1.6667 = 4.5 mL

3) Why the correct answer is correct
Because 4.5 mL of the 1:60 (1.6667%) stock contains exactly the amount of ephedrine needed so that, when diluted to a total volume of 30 mL, the final concentration is 0.25% (check: (1.6667% × 4.5 mL) / 30 mL = 0.25%).

4) Why the other choices are incorrect
- a. 2.5 mL → final C = (1.6667% × 2.5)/30 = 0.1389% (too low)
- b. 3.5 mL → final C = (1.6667% × 3.5)/30 = 0.1944% (too low)
- c. 4.0 mL → final C = (1.6667% × 4.0)/30 = 0.2222% (slightly low)
- e. 5.0 mL → final C = (1.6667% × 5.0)/30 = 0.2778% (too high)

Conclusion: The required volume of the 1:60 stock is 4.5 mL, which matches the provided correct answer (d. 4.5 mL).

How many mL of a 1:60 stock solution of Ephedrine Sulphate would be needed to make 30 mL of a product to treat nasal congestion containing 0.25 % Ephedrine Sulphate?单项选择题

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