Concentrations, ratios and dilutions

What you will learn

• Interpret percent and ratio strengths using the stated mass/volume basis.
• Calculate ingredient amount in a final quantity.
• Use conservation of ingredient amount to solve a simple dilution.

Before you start

Review unit conversion and dose calculations. These are invented mathematical mixtures, not instructions for compounding a medicine. Actual preparation requires approved ingredients, compatibility, stability and a validated procedure.

Read what the percentage compares

Percent means per hundred, but you must know which quantities are compared. A 2% weight/volume (w/v) solution contains 2 g in 100 mL of final solution. A 2% weight/weight (w/w) mixture contains 2 g in 100 g of final mixture. A 2% volume/volume (v/v) mixture contains 2 mL in 100 mL of final mixture.

Do not swap grams and milliliters merely because the percentage is the same. For an invented 3% w/v solution:
3 g/100 mL = 3,000 mg/100 mL = 30 mg/mL.

In 20 mL, the ingredient amount is 20 mL × 30 mg/mL = 600 mg. Reverse-check: 600 mg is 0.6 g; scaling 20 mL up fivefold gives 3 g in 100 mL.

Ratio strength needs the same care

A ratio written 1:1,000 w/v means 1 g in 1,000 mL of final solution, or 1 mg/mL. It is not 1 g added to 1,000 mL of liquid without regard to final volume.

Now change only the denominator to 100: 1:100 w/v is 1 g in 100 mL, or 10 mg/mL. A smaller denominator makes the mixture more concentrated. The ratio's numbers must be read together with its basis.

Pause and predict

Which supplied mathematical solution is more concentrated: 1:100 w/v or 1:1,000 w/v?

Dilution preserves ingredient amount

For a simple dilution with no ingredient loss and compatible concentration units, concentration × volume before equals concentration × volume after:
C1 × V1 = C2 × V2.

To make an invented final 200 mL at 5 mg/mL from 20 mg/mL stock:
20 mg/mL × V1 = 5 mg/mL × 200 mL.
V1 = 1,000 mg ÷ 20 mg/mL = 50 mL of stock.

The final mixture must be brought to 200 mL, not have 200 mL added to the stock. Under a stated additive-volume classroom assumption, this corresponds to 150 mL diluent. Real preparation follows its validated final-volume method.

Check: 50 mL × 20 mg/mL = 1,000 mg; 200 mL × 5 mg/mL = 1,000 mg. Ingredient amount agrees. A target concentration above the stock concentration cannot be achieved by adding only diluent.

Try it without the walkthrough

1. Convert 0.5% w/v to mg/mL.
2. How many grams are in 250 mL of an invented 4% w/v solution?
3. What volume of 10 mg/mL stock is needed for 100 mL final solution at 2 mg/mL?
4. Can adding only diluent turn 5 mg/mL stock into 10 mg/mL?

Keep this pattern

State the basis, convert units, and preserve ingredient amount. Final volume and added volume are different quantities.