A prescription calls for 30 mL of a 5% w/v solution. How many grams of active ingredient are required?

Rationale

1.5 grams of active ingredient are required for a 30 mL of a 5% w/v solution.

To find the amount of active ingredient in grams, we use the formula for weight/volume percentage, which states that a 5% w/v solution contains 5 grams of solute per 100 mL of solution. Thus, for 30 mL, we calculate the amount of solute needed.

A (0.15) YOUR ANSWER

This choice represents a miscalculation of the required grams. A 5% w/v solution has 5 grams of active ingredient per 100 mL, which means for 30 mL, the amount cannot be as low as 0.15 grams. The correct calculation shows that 1.5 grams is needed.

B (1.5) CORRECT

This is the correct calculation. A 5% w/v solution contains 5 grams of the active ingredient in 100 mL. Therefore, for 30 mL, the calculation is (5 grams/100 mL) * 30 mL = 1.5 grams.

C (15) YOUR ANSWER

This choice indicates a misunderstanding of the percentage concentration. It suggests that for 30 mL of a 5% solution, there would be 15 grams of active ingredient, which is incorrect. The calculation shows that only 1.5 grams is needed.

D (150) YOUR ANSWER

This choice is significantly higher than the actual requirement. A 5% w/v solution does not contain 150 grams in 30 mL; it instead contains only 1.5 grams. This choice reflects a fundamental error in understanding the conversion from percentage concentration to grams.

Conclusion

In summary, the calculation for a 5% w/v solution shows that 1.5 grams of active ingredient are needed for a 30 mL preparation. The other options present incorrect calculations based on misunderstandings of weight/volume percentage and its application to solution preparation. Understanding the relationship between percentage concentration and the volume of solution is crucial for accurate dosing in pharmaceutical contexts.

A prescription calls for 30 mL of a 5% w/v solution. How many grams of active ingredient are required?

1.5 grams of active ingredient are required for a 30 mL of a 5% w/v solution.

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