GPhC Pharmaceutical Calculations 2

Question 1

A pharmacist needs to prepare 200mL of a 5% w/v solution from a 20% w/v stock solution and water. What volumes of stock solution and water are needed?

Accepted Answer

50mL stock + 150mL water

Answer

Using C₁V₁ = C₂V₂: 20% × V₁ = 5% × 200mL. V₁ = (5 × 200) ÷ 20 = 50mL of stock solution. Water needed = 200mL - 50mL = 150mL.

Question 2

An insulin pen delivers 100 units/mL. A patient is prescribed 36 units twice daily. How many days will a 3mL cartridge last?

Accepted Answer

4 days

Answer

Total units in cartridge = 100 units/mL × 3mL = 300 units. Daily dose = 36 units × 2 = 72 units/day. Days supply = 300 ÷ 72 = 4.17 days, so the cartridge will last 4 complete days.

Question 3

A prescription asks for coal tar solution 5% in aqueous cream to make 100g. The coal tar solution BP contains coal tar 20% w/w. How much coal tar solution BP is required?

Accepted Answer

25g

Answer

The final product needs 5% coal tar solution, i.e., 5g of coal tar solution in 100g. But the coal tar solution BP is 20% w/w coal tar. The prescription asks for 'coal tar solution 5%' — meaning 5g of coal tar solution BP per 100g total. Therefore 25g of coal tar solution BP is needed to provide 5g of actual coal tar (25g × 20% = 5g coal tar).

Question 4

A patient weighing 70kg requires gentamicin at 5mg/kg/day administered in two divided doses. Gentamicin injection is available as 80mg/2mL. What volume is needed per dose?

Accepted Answer

4.38mL

Answer

Daily dose = 5mg/kg × 70kg = 350mg. Per dose = 350 ÷ 2 = 175mg. Concentration = 80mg/2mL = 40mg/mL. Volume = 175mg ÷ 40mg/mL = 4.375mL, approximately 4.38mL.

Question 5

A pharmacist prepares 500mL of an oral solution. The displacement value of the suspended powder is 0.8mL/g, and 25g of powder is used. What volume of vehicle is needed?

Accepted Answer

480mL

Answer

Displacement volume of powder = 25g × 0.8mL/g = 20mL. The powder displaces 20mL when suspended. Therefore, vehicle needed = 500mL - 20mL = 480mL to give a final volume of 500mL.

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GPhC Pharmaceutical Calculations 2