How strong is a solution
A bottle says 5 %. Five percent of what? The letter g means grams, a unit of mass.
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Step 1 of 4
- A beaker holds 88 g of water.
- Add 12 g of sugar. It dissolves.
- The whole solution is 12 + 88 = 100 g.
- Sugar is 12 g of the 100 g. That is 12 %.
Five percent is out of the whole solution. It means 5 parts of solute in every 100 parts.
The rule
Concentration tells how much solute is in the whole solution. Mass by mass percentage is solute mass ÷ solution mass × 100.
The solution is solute plus solvent. Divide by the whole solution, not by the water alone.
The letters mL mean millilitres, a unit of liquid volume. In m/m, m/v and v/v, m means mass and v means volume.
| Way | Formula | Says |
|---|---|---|
| Mass by mass, % m/m | solute mass ÷ solution mass × 100 | grams of solute in 100 g of solution |
| Mass by volume, % m/v | solute mass (g) ÷ solution volume (mL) × 100 | grams of solute in 100 mL of solution |
| Volume by volume, % v/v | solute volume ÷ solution volume × 100 | mL of solute in 100 mL of solution |
Medicines are often given in % m/v. A liquid is easier to measure than to weigh. The % v/v form suits two liquids mixed together.
Worked examples
| Case | Working | Answer |
|---|---|---|
| 4 g of medicine in 50 mL of solution | 4 ÷ 50 × 100 | 8 % m/v |
| 5 mL of a liquid in 50 mL of spray | 5 ÷ 50 × 100 | 10 % v/v |
| A 6 % m/m powder, 250 g in all: how much solute? | 6 ÷ 100 × 250 | 15 g |
Last row: 6 % is 0.06 of the whole. So solute = 0.06 × 250 g = 15 g.