Concentrations

Foundation of Safe Medication Compounding

In pharmacy practice, concentrations describe the amount of drug or solute present in a given amount of solution or mixture. Mastering concentration calculations is essential for accurate compounding, dosing, and medication preparation. Errors in this area can lead to underdosing, overdosing, or therapeutic failure — making this a high-yield topic on the Pharmacy Technician Certification Exam (PTCE).^[1]

Concentration problems appear throughout pharmacy calculations: from converting percentage strengths to ratio strengths, to preparing IV admixtures and topical compounds. A solid grasp of these concepts ensures safe, effective patient care and regulatory compliance.^[2]

Essential Terminology for Solution Mixing

Solute: The substance (usually the drug) dissolved in a solution.
Solvent: The liquid (e.g., water, saline, alcohol) that dissolves the solute.
Solution: A homogeneous mixture of solute and solvent.
Concentration: The ratio of the amount of solute to the total amount of solution or solvent.
Strength: Often used interchangeably with concentration; usually expressed as a percentage, ratio, or mg/mL.
Diluent: A solvent used to reduce the concentration of a solution.

Three Main Systems of Concentration Expression

Common Ways to Express Concentration

Pharmacy uses three main systems to express concentration. You must be fluent in converting between them.^[3]

Expression	Meaning	Example
Percentage (%)	Parts of solute per 100 parts of solution w/w (weight/weight), w/v (weight/volume), v/v (volume/volume)	5% w/v = 5 g solute in 100 mL solution
Ratio Strength (1:X)	1 g of solute in X mL of solution (for solids in liquids)	1:1000 = 1 g in 1000 mL
mg/mL	Milligrams of solute per milliliter of solution	10 mg/mL = 10 mg in every 1 mL

Percentage Concentration Types

Weight/Weight (w/w): Grams of solute per 100 g of product. Used for semisolid preparations (e.g., ointments, creams).
Weight/Volume (w/v): Grams of solute per 100 mL of solution. Most common for aqueous solutions and injections.
Volume/Volume (v/v): Milliliters of solute per 100 mL of solution. Used for liquid-in-liquid preparations (e.g., alcohol solutions).

Converting Between Expressions

Percentage to Ratio: A 5% w/v solution = 5 g / 100 mL → 1 g / 20 mL → ratio 1:20.
Ratio to Percentage: A 1:2000 ratio = 1 g / 2000 mL → 0.0005 g/mL → 0.05% w/v.
Percentage to mg/mL: 1% w/v = 10 mg/mL (since 1 g/100 mL = 1000 mg/100 mL = 10 mg/mL).
mg/mL to Percentage: 20 mg/mL = 2% w/v (since 20 mg/mL × 100 = 2000 mg/100 mL = 2 g/100 mL).

Practical Formulas for Compounding and IV Admixtures

Compounding

When preparing a compound, the technician must calculate the exact amount of drug (solute) needed to achieve the prescribed concentration. The formula is:

Amount of solute (g) = Desired concentration (% w/v) × Final volume (mL) ÷ 100^[3]

Example: Prepare 500 mL of a 3% w/v hydrocortisone cream.
3 × 500 ÷ 100 = 15 g of hydrocortisone powder.

IV Admixture Preparation

Concentration errors in IV bags can cause serious patient harm. Technicians must verify that the final concentration (in mg/mL) matches the order. Always double-check your math — a misplaced decimal can be fatal.^[4]

Dilution Calculations

When a stock solution is too strong, you must dilute it to the desired concentration using the formula C₁ × V₁ = C₂ × V₂.^[5]

Example: You have a 10% w/v stock solution and need 200 mL of a 2% w/v solution.
(10%) × V₁ = (2%) × 200 mL → V₁ = 40 mL of stock + 160 mL diluent.

Risk Mitigation in Concentration Calculations

Misidentifying concentration type: Confusing w/w with w/v is a common exam trap. Always check the units and context.
Decimal errors: Moving the decimal incorrectly during conversions can lead to 10× or 100× dosing mistakes. Use dimensional analysis as a safety check.^[6]
Ratio confusion: A 1:1000 ratio is NOT the same as 1:100. Always verify the colon number carefully.
Overlooking the final volume: When compounding, remember that the total solution volume includes both solute and solvent. Adding 10 g of powder to 100 mL of water yields more than 100 mL — adjust accordingly.
Always label clearly: Each compounded preparation must show the concentration, ingredients, date, and beyond-use date.^[2]

Rapid Mental Math and Conversion Shortcuts

Memorize the 1% = 10 mg/mL conversion — it's one of the most tested facts on the PTCE.
When converting ratio to percentage: divide 1 by the second number (e.g., 1:2000 → 1 ÷ 2000 = 0.0005 → 0.05%).
Use the "is over of" method for percentage problems: (part ÷ whole) × 100 = % concentration.
For dilution problems, always write down C₁, V₁, C₂, V₂ and solve systematically.
Common ratio-to-percentage pairings to know:
- 1:100 = 1%
- 1:1000 = 0.1%
- 1:10,000 = 0.01%
- 1:100,000 = 0.001%
Memory Aid: "Percent to mg/mL, move the decimal one place to the right" — 5% → 50 mg/mL? No! Correct: 5% = 50 mg/mL only if you multiply 5 × 10 = 50 mg/mL. 1% = 10 mg/mL, so 5% = 5 × 10 = 50 mg/mL.
Practice with real-world scenarios: reading prescription labels, interpreting IV bag concentrations, and calculating drip rates based on concentration.