10.1 Concentration, Ratio & Percentage Strength

Percentage Strength: The Three Expressions

Percentage strength states parts of active ingredient per 100 parts of the total product. The DHA exam expects you to know which of the three expressions applies and to convert between them without hesitation.

• % w/w (weight in weight): grams of solute per 100 g of final product. Used for powders, ointments and creams. 1% w/w hydrocortisone cream = 1 g hydrocortisone in 100 g cream.
• % w/v (weight in volume): grams of solute per 100 mL of final solution. This is the default expression for solutions. 5% w/v dextrose = 5 g dextrose per 100 mL. When an exam question simply says "a 2% solution" of a solid drug in liquid, assume w/v.
• % v/v (volume in volume): mL of liquid solute per 100 mL of final solution. Used for liquids dissolved in liquids. 70% v/v isopropyl alcohol = 70 mL alcohol per 100 mL solution.

The most useful conversion on the exam: 1% w/v = 1 g / 100 mL = 1000 mg / 100 mL = 10 mg/mL. So multiply any % w/v by 10 to get mg/mL (2% w/v = 20 mg/mL; 0.5% w/v = 5 mg/mL), and divide mg/mL by 10 to get % w/v.

Worked Example 1: Drug Content of a Solution

Question: How many milligrams of drug are in 15 mL of a 2% w/v solution?

1. 2% w/v = 2 g per 100 mL.
2. Convert to mg/mL: 2 g = 2000 mg, so 2000 mg / 100 mL = 20 mg/mL (shortcut: 2 x 10).
3. Multiply by the volume: 20 mg/mL x 15 mL = 300 mg.

Worked Example 2: Drug Content of a Semisolid (w/w)

Question: A 30 g tube of 5% w/w cream contains how much drug?

1. 5% w/w = 5 g drug per 100 g cream.
2. Amount = (5 / 100) x 30 g = 1.5 g = 1500 mg of drug.

Do not reach for mL here: the product is dosed and labelled by weight, so the w/w expression applies and density is irrelevant to the arithmetic.

Ratio Strength

Ratio strength expresses concentration as 1 part of ingredient in X parts of product, written 1:X. For solutions the convention is w/v unless stated otherwise, so 1:1000 means 1 g in 1000 mL = 1 mg/mL. This is why adrenaline 1:1000 injection delivers 1 mg/mL - a fact the exam tests repeatedly, because confusing 1:1000 with 1:10,000 (0.1 mg/mL, used for IV bolus in cardiac arrest) is a genuine patient-safety error.

Converting Ratio Strength to Percentage Strength

For a w/v ratio 1:X: % w/v = 100 / X.

Worked Example 3: 1:5000 to % w/v and mg/mL

Question: Express chlorhexidine 1:5000 (w/v) as a percentage strength and in mg/mL.

1. % w/v = 100 / 5000 = 0.02% w/v.
2. Check by definition: 1 g in 5000 mL = 1000 mg / 5000 mL = 0.2 mg/mL.
3. Cross-check with the mg/mL rule: 0.02% x 10 = 0.2 mg/mL. Both routes agree.

Converting Percentage to Ratio Strength

Divide 100 by the percentage: 0.1% w/v = 0.1 g / 100 mL = 1 g / 1000 mL = 1:1000. Similarly 0.5% w/v = 1:200 and 2% w/v = 1:50.

Preparing a Dilute Solution from a Concentrated Stock

A common exam task: prepare a weak solution when only a strong stock is available.

Worked Example 4: 0.1% Solution from a 5% Stock

Question: Prepare 500 mL of a 0.1% w/v solution using a 5% w/v stock.

1. Drug needed in the final product: 0.1% w/v = 0.1 g per 100 mL, so 500 mL needs (0.1 / 100) x 500 = 0.5 g.
2. Stock concentration: 5% w/v = 5 g per 100 mL = 50 mg/mL.
3. Volume of stock supplying 0.5 g (500 mg): 500 mg / 50 mg/mL = 10 mL of stock.
4. Measure 10 mL of stock and add diluent to a final volume of 500 mL.

This is really the dilution formula C1V1 = C2V2 in disguise; Section 10.3 covers it formally.

Parts per Million (ppm)

Parts per million is used for very dilute concentrations - fluoride in water, trace contaminants, some electrolyte limits.

• 1 ppm = 1 mg per litre = 1 microgram (mcg) per mL for aqueous systems.
• 2 ppm sodium fluoride = 2 mg of fluoride per litre.
• Converting from % w/v: multiply the percentage by 10,000 to get ppm. Example: 0.0005% w/v = 0.0005 x 10,000 = 5 ppm. Check: 0.0005 g / 100 mL = 0.5 mg / 100 mL = 5 mg / L = 5 ppm.

Millimoles and Electrolytes

Electrolytes are ordered in millimoles (mmol), so you must convert mass to mmol:

mmol = mass in mg / molecular weight

Worked Example 5: Potassium Chloride

Question: How many mmol of potassium are in 1.5 g of potassium chloride (MW of KCl = 74.5)?

1. 1.5 g = 1500 mg.
2. mmol = 1500 / 74.5 = 20.1, i.e. about 20 mmol of K+ (each mole of KCl gives one mole of K+).

A second classic: 0.9% w/v sodium chloride (MW 58.5) contains 9 g per litre, so 9000 / 58.5 = 153.8, approximately 154 mmol of Na+ per litre - worth memorising, as "normal saline" questions assume it.

Exam Traps in Concentration Questions

• Confusing w/v with v/v (or w/w). 2% w/v lidocaine is 20 mg/mL; if you treat a cream percentage as w/v you will be off by the density.
• Decimal slips with ratio strengths. Adrenaline 1:1000 = 1 mg/mL, but 1:10,000 = 0.1 mg/mL. Always rewrite the ratio as "1 g in X mL" and convert grams to milligrams before dividing.
• Forgetting the g-to-mg conversion. 1 g = 1000 mg; an answer 1000-fold out is the classic distractor.
• Reading "0.1%" as "1%". Write the percentage as a decimal (0.001) before multiplying when in doubt.
• Assuming ppm means mg per mL. It is mg per litre - a 1000-fold trap.

On the DHA CBT you have no formula sheet, so drill the anchors: 1% w/v = 10 mg/mL; 1:1000 = 1 mg/mL; 0.9% NaCl = 154 mmol/L; 1 ppm = 1 mg/L.