As a part o a clinical study, a pharmacist is asked to prepare a modi ication o a standard 22 g package o a 2% mupirocin ointment by adding the needed quantity o mupirocin powder to prepare a 3% w/w mupirocin ointment. How many milligrams o mupirocin powder are required?

240 mg

Explanation:

In a dilution, the total quantity of the solute remains equal, so the concentration multiplied by the volume, or mass, of it, must be constant. In this case, the concentration is measured by the mass (w/w), so:

C1M1 = C2M2

Where C is the concentration, M is the mass, 1 is the concentrated solution, and 2 the diluted. The powder mupirocin has 100% of concentration, and the diluted solution will be mass equal to 22 g plus the mass added, so:

100%*M1 = 3% * (22 + M1)

100M1 = 66 + 3M1

97M1 = 66

M1 = 0.6804 g

But the ointment already has 2% of mupirocin, which is in mass:

0.02 * 22 = 0.44 g

So, the mass needed to be added is 0.6804 - 0.44 = 0.24 g = 240 mg