1a. How many grams of a 2.5% hydrocortisone cream should be mixed with 360 grams

Question

1a. How many grams of a 2.5% hydrocortisone cream should be mixed with 360 grams of a 0.25% hydrocortisone cream
to make a 1% cream?

1b. The package insert of a 20 mL vial of an injectable powder for reconstitution notes that 12 mL of sterile water should
be added to result in a product with a final concentration of 2 mg/mL. A person accidentally added 15 mL of sterile water instead of the 12 mL as instructed. What is the new concentration (in mg/mL) of the reconstituted medication? Round your answer to the nearest 1/10th of a mL.

Explanation / Answer

Ans. #1a. Initial hydrocortisone (HC) content in cream = 0.25 % of 360.0 g = 0.900 g

# Let the required mass of additional HC cream = X g

Amount of HC in X g HC cream = 2.5 % of X = 0.025X g

Total mass of cream after adding additional HC cream = 360.0 g + X g

Total mass of HC in the final cream = 0.900 g + 0.025X g

Now,

            1.00 % of total cream mass = Mass of HC

Or, 1.0 % of (360.0 + X) g = (0.900 + 0.025X) g

Or, 0.010 x (360.0 + X) = (0.900 + 0.025X)

            Or, 3.60 + 0.010X = 0.900 + 0.025X

            Or, 0.025X – 0.010X = 3.60 – 0.90 = 2.70

            Or, X = 2.70 / 0.015

            Hence, X = 180.0

Therefore, required mass of 2.5% HC cream = 180.0 g

#1b. Step 1: Total volume of CORRECTLY reconstituted solution

= 20.0 mL + 12.0 mL = 32.0 mL

Given, the concertation of CORRECTLY reconstituted solution = 2 mg/ mL

Therefore, total mass of active molecule in original vial =

                                    Concertation x Total volume of CORRECTLY reconstituted solution

                                    = (2 mg/ mL) x 32.0 mL

                                    = 64.0 mg

Therefore, 20.0 mL of original vial consists of 64.0 mg of the active molecule.

# Step 2: Total volume of INCORRECTLY reconstituted solution

= 20.0 mL + 15.0 mL = 35.0 mL

# Reconstitution does not affect the total mass of the active drug, it remains constant.

Now,

            Concertation = Total mass of active molecule / Total volume made upto

                                    = 64.0 mg / 35.0 mL

                                    = 1.829 mg/ mL

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