54. A prescription calls for 30 mL of a 5% w/v solution. How many grams of active ingredient are required?
Answer: B
1.5 grams of active ingredient are required.
To prepare a 30 mL solution at a 5% w/v concentration, 1.5 grams of the active ingredient is necessary. This is calculated based on the percentage concentration of the solution and the total volume prescribed.
A) 0.15
This option is incorrect because 0.15 grams would represent only 0.5% of the total volume. To achieve a 5% w/v solution, much more active ingredient is required.
B) 1.5
This option is correct as it accurately represents the amount of active ingredient needed. A 5% w/v solution means there are 5 grams of solute per 100 mL of solution. Therefore, for 30 mL, the calculation is (5 g/100 mL) * 30 mL = 1.5 grams.
C) 15
This option is incorrect because 15 grams exceeds the requirement for a 5% solution. A 5% concentration in 30 mL would only necessitate 1.5 grams, not 15 grams.
D) 150
This option is also incorrect as it vastly overestimates the amount of active ingredient needed. A 5% w/v solution does not require such a large quantity; 150 grams would be far beyond the necessary dosage for 30 mL.
Conclusion
The calculation for a 5% w/v solution clearly shows that 1.5 grams of the active ingredient is required for 30 mL. Other options fail to meet this requirement, either underestimating or dramatically overestimating the necessary amount of active ingredient needed for the specified volume and concentration.