🧮 Pharmaceutical Calculations, Compounding and Pharmacokinetics

1. How many milligrams of sodium chloride are in each millilitre of a 0.9% w/v solution?

1. 0.09 mg/mL.
2. 0.9 mg/mL.
3. 90 mg/mL.
4. 9 mg/mL.

Per cent weight in volume means grams of solute in 100 mL, so 0.9 g in 100 mL is 900 mg in 100 mL, that is 9 mg in each millilitre. Multiplying the percentage by 10 converts directly to milligrams per millilitre. Source: USP conventions for expressions of concentration.

2. How much sodium chloride does a 500 mL bag of 0.9% sodium chloride contain?

1. 0.45 g.
2. 4.5 g.
3. 45 g.
4. 9 g.

0.9 g per 100 mL gives 9 mg per millilitre, and 9 mg × 500 mL = 4500 mg, which is 4.5 g. Checking the magnitude against the familiar 9 g per litre confirms the answer is plausible. Source: USP conventions for expressions of concentration.

3. How much dextrose is contained in one litre of 5% dextrose in water?

1. 50 g.
2. 5 g.
3. 500 g.
4. 0.5 g.

5 g per 100 mL multiplied by ten gives 50 g per litre, or 50 mg per millilitre, which is why one litre supplies about 170 kilocalories. Source: USP conventions for expressions of concentration.

4. How many milligrams of lidocaine are in 5 mL of a 2% solution?

1. 1000 mg.
2. 10 mg.
3. 100 mg.
4. 20 mg.

A 2% solution contains 20 mg per millilitre, so 5 mL contains 100 mg. Converting the percentage to milligrams per millilitre first is the step that prevents an order-of-magnitude error. Source: USP conventions for expressions of concentration.

5. What is the concentration of a 1:1000 epinephrine solution?

1. 0.1 mg/mL.
2. 1 mcg/mL.
3. 10 mg/mL.
4. 1 mg/mL.

A ratio strength of 1 in 1000 means one gram in one thousand millilitres, which is 1000 mg in 1000 mL, that is 1 mg per millilitre. The 1:10 000 presentation used in cardiac arrest is one tenth of this. Source: USP conventions for ratio strength.

6. What is the concentration of a 1:10 000 epinephrine solution?

1. 10 mcg/mL.
2. 1 mg/mL.
3. 0.01 mg/mL.
4. 0.1 mg/mL.

One gram in ten thousand millilitres is 1000 mg in 10 000 mL, that is 0.1 mg in each millilitre, so a 10 mL prefilled syringe contains 1 mg. Confusing this with the 1:1000 ampoule is a classic and dangerous error. Source: USP conventions for ratio strength.

7. How much bupivacaine is contained in 20 mL of a 0.5% solution?

1. 100 mg.
2. 10 mg.
3. 1000 mg.
4. 50 mg.

0.5% is 5 mg per millilitre, so 20 mL delivers 100 mg, a figure that matters because local anaesthetic systemic toxicity is dose-related and maximum doses are expressed in milligrams per kilogram. Source: USP conventions for expressions of concentration.

8. A local anaesthetic contains epinephrine 1:200 000. How many micrograms of epinephrine are in each millilitre?

1. 0.5 mcg/mL.
2. 50 mcg/mL.
3. 5 mcg/mL.
4. 20 mcg/mL.

One gram in 200 000 mL is 1 000 000 mcg in 200 000 mL, which is 5 mcg per millilitre. The same reasoning converts any ratio strength: write the gram amount in the units of the answer, then divide by the volume. Source: USP conventions for ratio strength.

9. How much calcium gluconate is in a 10 mL ampoule of a 10% solution?

1. 10 g.
2. 100 mg.
3. 1 g.
4. 10 000 mg.

A 10% solution is 100 mg per millilitre, so a 10 mL ampoule contains 1000 mg, that is 1 g of the salt. Note that the elemental calcium content is far lower than the salt weight, which is why calcium chloride and calcium gluconate are not interchangeable by volume. Source: USP conventions for expressions of concentration.

10. A municipal water supply contains fluoride at 5 ppm. How much fluoride is in one litre?

1. 5 mg.
2. 5 g.
3. 0.5 mg.
4. 50 mg.

Parts per million for a dilute aqueous solution is milligrams per litre, so 5 ppm is 5 mg per litre; it is also 1 part in 200 000 by ratio strength. Source: USP conventions for expressions of concentration.

11. What does 23.4% sodium chloride contain per millilitre?

1. 2.34 mg/mL.
2. 23.4 mg/mL.
3. 234 mg/mL.
4. 2340 mg/mL.

Multiplying the percentage by ten gives milligrams per millilitre, so this hypertonic concentrate holds 234 mg in each millilitre and must always be diluted before administration. Source: USP conventions for expressions of concentration.

12. What does a weight-in-weight percentage describe?

1. Grams of ingredient in one hundred millilitres of solvent.
2. Grams of ingredient in 100 g of finished preparation.
3. Millilitres of ingredient in one hundred grams of base.
4. Grams of ingredient in one thousand grams of base.

Weight in weight is used for ointments, creams and powders and refers to the total finished weight, not to the weight of base alone, which is why 5 g of drug is added to 95 g of base to make 100 g of a 5% w/w preparation. Source: USP conventions for expressions of concentration.

13. How much salicylic acid is needed to make 100 g of a 5% w/w ointment, and how much base?

1. 0.5 g of acid and 99.5 g of base.
2. 5 g of acid and 100 g of base.
3. 5 mL of acid and 95 g of base.
4. 5 g of acid and 95 g of base.

The percentage refers to the finished 100 g, so the base is reduced by the weight of drug added. Adding 5 g to a full 100 g of base would give a 4.76% preparation and a total weight of 105 g. Source: USP conventions for expressions of concentration.

14. You have 100 mL of a 10% solution and need a 4% solution. What final volume is required?

1. 250 mL.
2. 400 mL.
3. 40 mL.
4. 140 mL.

Because the quantity of solute does not change, C₁V₁ = C₂V₂: 10 × 100 = 4 × V₂, so V₂ = 250 mL, meaning 150 mL of diluent is added. The final volume is always larger than the starting volume when the strength falls. Source: standard dilution relationship, USP.

15. How much diluent must be added to 50 mL of a 5% solution to obtain a 2% solution?

1. 125 mL.
2. 75 mL.
3. 25 mL.
4. 100 mL.

C₁V₁ = C₂V₂ gives a final volume of 5 × 50 ÷ 2 = 125 mL, and the diluent added is the difference, 125 − 50 = 75 mL. Reading the question carefully matters: the final volume and the volume added are different numbers. Source: standard dilution relationship, USP.

16. How much water is added to 500 mL of a 1:200 solution to make it 1:1000?

1. 1500 mL.
2. 2500 mL.
3. 2000 mL.
4. 500 mL.

Converting the ratios first, 1:200 is 0.5% and 1:1000 is 0.1%; the final volume is 0.5 × 500 ÷ 0.1 = 2500 mL, so 2000 mL of water is added. Converting both strengths into the same form before calculating avoids the commonest error here. Source: standard dilution relationship, USP.

17. How much water is added to 240 mL of 70% isopropyl alcohol to make a 50% preparation?

1. 120 mL.
2. 336 mL.
3. 96 mL.
4. 170 mL.

The final volume is 70 × 240 ÷ 50 = 336 mL, so 96 mL of water is added. The alcohol content in millilitres, 168 mL, is unchanged by the dilution. Source: standard dilution relationship, USP.

18. A 30 g tube of 0.1% ointment must be diluted to 0.025%. What total weight results, and how much base is added?

1. 90 g in total, so 60 g of base is added.
2. 60 g in total, so 30 g of base is added.
3. 150 g in total, so 120 g of base is added.
4. 120 g in total, so 90 g of base is added.

The same relationship applies to weights: 0.1 × 30 ÷ 0.025 = 120 g, so 90 g of base is incorporated. Diluting a corticosteroid ointment changes its potency class and is only done on a prescriber's instruction. Source: standard dilution relationship, USP.

19. Using 10% and 1% hydrocortisone ointments, how much of each is needed to make 100 g of a 3% preparation?

1. About 70 g of the 10% and 30 g of the 1%.
2. About 30 g of the 10% and 70 g of the 1%.
3. About 22.2 g of the 10% and 77.8 g of the 1%.
4. About 50 g of each of the two ointments.

Alligation alternate gives parts of 3 − 1 = 2 for the stronger and 10 − 3 = 7 for the weaker, a total of 9 parts, so the stronger contributes 2 ÷ 9 × 100 = 22.2 g and the weaker 77.8 g. Checking the total drug, 2.22 g plus 0.78 g, returns 3 g as required. Source: alligation method, USP.

20. How much 20% ointment and how much white petrolatum are needed for 60 g of a 5% preparation?

1. 20 g of the 20% ointment and 40 g of petrolatum.
2. 15 g of the 20% ointment and 45 g of petrolatum.
3. 12 g of the 20% ointment and 48 g of petrolatum.
4. 30 g of the 20% ointment and 30 g of petrolatum.

Petrolatum counts as 0%, so the parts are 5 and 15, a total of 20, and the stronger ointment contributes 5 ÷ 20 × 60 = 15 g. The drug check is 15 × 0.20 = 3 g, which is 5% of 60 g. Source: alligation method, USP.

21. How much 5% and how much 1% cream are needed to prepare 30 g of a 2.5% cream?

1. 18.75 g of the 5% and 11.25 g of the 1%.
2. 15 g of each of the two creams.
3. 11.25 g of the 5% and 18.75 g of the 1%.
4. 7.5 g of the 5% and 22.5 g of the 1%.

The parts are 2.5 − 1 = 1.5 for the stronger and 5 − 2.5 = 2.5 for the weaker, four parts in total, so the stronger supplies 1.5 ÷ 4 × 30 = 11.25 g. Because the target sits nearer the weaker product, more of the weaker product is required. Source: alligation method, USP.

22. What strength results from mixing 200 mL of 70% alcohol with 300 mL of 30% alcohol?

1. 46%.
2. 50%.
3. 40%.
4. 56%.

Alligation medial is a weighted average: (200 × 70 + 300 × 30) ÷ 500 = 23 000 ÷ 500 = 46%. The result must lie between the two starting strengths and nearer the one present in the larger volume. Source: alligation medial, USP.

23. What is the difference between alligation medial and alligation alternate?

1. Medial is used for two components and alternate for three or more.
2. Medial is used for liquids and alternate only for solids.
3. Medial applies to ratio strengths and alternate to percentages.
4. Medial finds the strength; alternate finds the parts.

They are the same conservation of mass approached from opposite directions, so a result from one can always be checked with the other. Neither is restricted by dosage form or by the way strength is expressed. Source: alligation method, USP.

24. Express a 1:2500 solution as a percentage.

1. 0.04%.
2. 0.4%.
3. 0.25%.
4. 4%.

One gram in 2500 mL is 0.04 g in 100 mL, that is 0.04% w/v, obtained by dividing 100 by the ratio denominator. The same conversion in reverse turns a percentage into a ratio strength. Source: USP conventions for ratio strength.

25. Express 0.02% w/v as a ratio strength.

1. 1:200.
2. 1:500.
3. 1:50 000.
4. 1:5000.

0.02 g in 100 mL is 1 g in 5000 mL, so the ratio strength is 1 in 5000; dividing 100 by the percentage gives the denominator directly. Source: USP conventions for ratio strength.

26. Glycerin has a specific gravity of 1.25. What volume of glycerin weighs 100 g?

1. 80 mL.
2. 125 mL.
3. 100 mL.
4. 40 mL.

Specific gravity is the ratio of the weight of a volume of the substance to the weight of the same volume of water, so volume = weight ÷ specific gravity = 100 ÷ 1.25 = 80 mL. A liquid denser than water always occupies less volume than its weight in millilitres. Source: USP conventions for density and specific gravity.

27. What does 1 mL of a liquid with a specific gravity of 1.25 weigh?

1. 1.25 g.
2. 0.8 g.
3. 1 g.
4. 12.5 g.

Multiplying the volume by the specific gravity gives the weight, so 1 mL weighs 1.25 g. Formulae written by weight must be converted before a dense liquid such as glycerin is measured by volume. Source: USP conventions for density and specific gravity.

28. A balance has a sensitivity requirement of 6 mg and the acceptable error is 5%. What is the minimum weighable quantity?

1. 600 mg.
2. 30 mg.
3. 120 mg.
4. 12 mg.

The minimum weighable quantity is the sensitivity requirement divided by the acceptable error expressed as a decimal, so 6 ÷ 0.05 = 120 mg; anything lighter must be handled by an aliquot. Source: USP chapter on weighing and measuring in compounding.

29. Why is an aliquot method used when a formula calls for 5 mg of a potent drug?

1. Because potent drugs may never be weighed at all.
2. Because 5 mg is below the minimum weighable quantity.
3. Because the drug would decompose if weighed directly.
4. Because the balance cannot be calibrated below one gram.

Weighing below the minimum weighable quantity exceeds the acceptable error, so a weighable quantity is triturated with a known weight of inert diluent and the required fraction of the mixture is taken. Source: USP chapter on weighing and measuring in compounding.

30. You weigh 120 mg of drug and dilute it with 480 mg of lactose. How much of the mixture supplies 5 mg of drug?

1. 5 mg of the mixture.
2. 25 mg of the mixture.
3. 50 mg of the mixture.
4. 120 mg of the mixture.

The mixture weighs 600 mg and contains 120 mg of drug, so it is 1 part drug in 5 parts mixture; 5 mg of drug is therefore contained in 5 × 5 = 25 mg of mixture. Checking by proportion, 25 ÷ 600 × 120 returns 5 mg. Source: USP chapter on weighing and measuring in compounding.

31. Twelve 2 g suppositories each contain 200 mg of a drug whose displacement value is 1.5. How much base is required?

1. 22.4 g.
2. 24 g.
3. 21.6 g.
4. 20 g.

The total drug is 2.4 g, and a displacement value of 1.5 means 1.5 g of drug displaces 1 g of base, so the base displaced is 2.4 ÷ 1.5 = 1.6 g; the base required is 24 − 1.6 = 22.4 g. Ignoring displacement overfills the mould and under-doses each suppository. Source: standard suppository displacement calculation.

32. What does the displacement value of a drug in a suppository base express?

1. The proportion of the drug that is absorbed rectally.
2. The volume of the mould in millilitres.
3. The melting point of the finished suppository.
4. The weight of base displaced by a given weight of the drug.

Because drug and base differ in density, a fixed-volume mould holds less base once drug is added, and the displacement value quantifies that so each suppository contains the intended dose. It says nothing about absorption or melting behaviour. Source: standard suppository displacement calculation.

33. What is geometric dilution and why is it used?

1. Adding the whole diluent to the drug in a single step and mixing hard.
2. Dissolving the drug in the smallest possible volume of water first.
3. Doubling the quantity of diluent at each successive addition.
4. Halving the dose at each step until the target strength is reached.

Doubling the quantity at each addition keeps the proportions manageable and gives a uniform powder or ointment; adding all the diluent at once leaves pockets of concentrated drug, which is a content uniformity failure. Source: USP chapter on non-sterile compounding.

34. What is levigation in the preparation of an ointment?

1. Adding a preservative to prevent microbial growth.
2. Heating the base until it melts completely.
3. Passing the finished ointment through a fine sieve.
4. Wetting the powder with a compatible liquid first.

A levigating agent such as mineral oil for an oleaginous base, or glycerin for a water-miscible base, produces a smooth paste and prevents grittiness in the finished product. Source: USP chapter on non-sterile compounding.

35. Which ointment base is best suited to a preparation that must be washable from the skin and can carry water?

1. An oleaginous base such as white petrolatum.
2. A water-removable base such as a cream.
3. An absorption base such as hydrophilic petrolatum.
4. A water-soluble base such as polyethylene glycol ointment.

Water-removable oil-in-water bases wash off with water and accept aqueous solutions, whereas oleaginous bases are occlusive and take up almost no water, absorption bases take up water to form emulsions, and water-soluble bases contain no oil at all. Source: USP chapter on non-sterile compounding.