Pharmaceutical Calculations Flashcards

A 78 kg ICU patient is receiving norepinephrine via a 4 mg/250 mL NS bag. The intensivist increases the dose from 0.06 mcg/kg/min to 0.14 mcg/kg/min. What is the new infusion rate in mL/hr (rounded to one decimal place)?

Answer: 41.0 mL/hr

Concentration = 4 mg/250 mL = 16 mcg/mL. New dose = 0.14 mcg/kg/min × 78 kg = 10.92 mcg/min. Rate = 10.92 mcg/min ÷ 16 mcg/mL = 0.6825 mL/min × 60 min/hr = 40.95 ≈ 41.0 mL/hr. Option A (17.6 mL/hr) is the old rate using 0.06 mcg/kg/min. Option C (81.9 mL/hr) results from using a doubled volume (4 mg/500 mL = 8 mcg/mL) — a concentration error.

A pharmacist combines 175 mL of 65% isopropyl alcohol, 200 mL of 40% isopropyl alcohol, and 125 mL of purified water to prepare a compounded antiseptic base. What is the final isopropyl alcohol concentration?

Answer: 38.75%

Using alligation medial: total alcohol = (175 × 0.65) + (200 × 0.40) + (125 × 0) = 113.75 + 80 + 0 = 193.75 mL. Total volume = 175 + 200 + 125 = 500 mL. Concentration = 193.75 ÷ 500 = 38.75%. Option A (52.5%) is the simple arithmetic average of 65% and 40%, ignoring volumes and water. Option C (51.7%) results from using only 375 mL as the denominator (omitting the water volume).

A 65-year-old female patient weighs 63 kg and stands 165 cm tall. Her serum creatinine is 1.4 mg/dL. Using the Cockcroft-Gault equation with the most appropriate body weight, what is her estimated creatinine clearance?

Answer: 36.1 mL/min

IBW (female) = 45.5 + 2.3 × (height in inches − 60). 165 cm ÷ 2.54 = 65 inches. IBW = 45.5 + 2.3 × 5 = 57 kg. Since actual weight (63 kg) exceeds IBW (57 kg), IBW is used. CrCl = [(140 − 65) × 57] ÷ (72 × 1.4) × 0.85 = (75 × 57 ÷ 100.8) × 0.85 = 42.41 × 0.85 = 36.1 mL/min. Option B uses actual body weight (63 kg). Option C uses IBW but omits the 0.85 female correction factor. Option D uses actual weight without the female correction.

A TPN bag is compounded using 400 mL of 70% dextrose, 500 mL of 10% amino acids, and 100 mL of sterile water (total bag volume: 1000 mL). A 20% lipid emulsion piggyback of 250 mL is also ordered daily. What is the total daily caloric intake from this regimen?

Answer: 1652 kcal

Dextrose: 400 mL × 0.70 = 280 g × 3.4 kcal/g = 952 kcal. Amino acids: 500 mL × 0.10 = 50 g × 4 kcal/g = 200 kcal. Lipids (20% emulsion): 250 mL × 2.0 kcal/mL = 500 kcal. Total = 952 + 200 + 500 = 1652 kcal. Option A uses 1.1 kcal/mL for the 20% lipid — that coefficient is for 10% emulsions. Option C applies 4 kcal/g to dextrose — the correct value for dextrose monohydrate in TPN is 3.4 kcal/g.

A 1 g vial of cefazolin powder for injection states: 'Add 2.5 mL of sterile water for injection to yield a final concentration of 330 mg/mL.' A nurse requires a dose of 750 mg. What volume of the reconstituted solution should be drawn up?

Answer: 2.27 mL

The label states the final concentration is 330 mg/mL — this accounts for the powder volume. Volume required = 750 mg ÷ 330 mg/mL = 2.27 mL. Option A (1.88 mL) results from incorrectly calculating concentration as 1000 mg ÷ 2.5 mL = 400 mg/mL, which ignores the powder volume displacement. Option C (2.50 mL) is the diluent volume added, not the dose volume. Option D (1.50 mL) assumes a naive 1 g/2 mL concentration.

A pharmacist prepares 60 mL of an ophthalmic solution containing 0.5% epinephrine HCl (NaCl equivalent E = 0.29) and 1.5% chlorobutanol (NaCl equivalent E = 0.24). How many milligrams of NaCl must be added to render the solution isotonic?

Answer: 237 mg

NaCl equivalents contributed: epinephrine HCl = 0.5% × 0.29 = 0.145%; chlorobutanol = 1.5% × 0.24 = 0.360%. Total = 0.505%. NaCl deficit = 0.900% − 0.505% = 0.395%. Mass of NaCl = (0.395/100) × 60 mL × 1000 mg/g = 237 mg. Option B (453 mg) results from subtracting only the epinephrine contribution (forgetting chlorobutanol). Option D (540 mg) ignores both drug contributions entirely: 0.9% × 60 mL × 1000 = 540 mg.