GPhC Pharmaceutical Calculations — Questions and Answers
Question 1: A prescription requires 150mL of a 1 in 10,000 solution of potassium permanganate. How many milligrams of potassium permanganate are needed?
- 0.015mg
- 1.5mg
- 15mg (Correct answer)
- 150mg
Correct answer: 15mg
A '1 in 10,000' solution means 1g in 10,000mL. For 150mL: (1g ÷ 10,000mL) × 150mL = 0.015g = 15mg. Remember that 'x in y' concentrations express grams per millilitres.
Question 2: A child weighing 22kg requires amoxicillin at a dose of 25mg/kg/day in three divided doses. The suspension available is 250mg/5mL. What volume should be given per dose?
- 3.7mL
- 7.3mL (Correct answer)
- 11mL
- 22mL
Correct answer: 7.3mL
Total daily dose = 25mg/kg × 22kg = 550mg/day. Per dose = 550mg ÷ 3 = 183.3mg. Volume = (183.3mg ÷ 250mg) × 5mL = 3.67mL, rounded to 3.7mL per dose.
Question 3: How many millimoles of sodium are in 500mL of sodium chloride 0.9% infusion? (Molecular weight of NaCl = 58.5, Na = 23, Cl = 35.5)
- 38.5 mmol
- 77 mmol (Correct answer)
- 154 mmol
- 308 mmol
Correct answer: 77 mmol
NaCl 0.9% = 0.9g per 100mL = 4.5g per 500mL. Moles of NaCl = 4.5g ÷ 58.5g/mol = 0.0769 mol = 76.9 mmol. Since each NaCl molecule gives one Na⁺ ion, sodium content = 77 mmol. (Note: 154 mmol would be per litre.)
Question 4: A pharmacist needs to dilute a 95% v/v ethanol solution to produce 500mL of 70% v/v ethanol. What volume of the 95% solution is required?
- 263mL
- 368mL (Correct answer)
- 432mL
- 475mL
Correct answer: 368mL
Using C₁V₁ = C₂V₂: 95% × V₁ = 70% × 500mL. V₁ = (70 × 500) ÷ 95 = 35,000 ÷ 95 = 368.4mL. Therefore approximately 368mL of the 95% solution is needed, made up to 500mL with purified water.
Question 5: A patient is prescribed an IV infusion of 1 litre of 5% glucose to run over 8 hours using a giving set that delivers 20 drops/mL. What is the required drip rate in drops per minute?
- 21 drops/min
- 42 drops/min (Correct answer)
- 63 drops/min
- 84 drops/min
Correct answer: 42 drops/min
Total volume = 1000mL. Total drops = 1000mL × 20 drops/mL = 20,000 drops. Time = 8 hours × 60 min = 480 minutes. Drip rate = 20,000 ÷ 480 = 41.7, rounded to 42 drops per minute.
Question 6: A cream contains 0.025% w/w of betamethasone valerate. How many micrograms of betamethasone valerate are in 30g of the cream?
- 750 micrograms
- 7,500 micrograms (Correct answer)
- 75,000 micrograms
- 750,000 micrograms
Correct answer: 7,500 micrograms
0.025% w/w = 0.025g per 100g. In 30g: (0.025g ÷ 100g) × 30g = 0.0075g = 7.5mg = 7,500 micrograms.
GPhC Pharmaceutical Calculations
A prescription requires 150mL of a 1 in 10,000 solution of potassium permanganate.
How many milligrams of potassium permanganate are needed?