6 min readConcept sheetPart II (2 marks: a one-step percentage sum) and Part III (4 marks: definitions with sums)

Mass percentage and volume percentage

Mass percentage is (mass of solute ÷ mass of solution) × 100. Volume percentage is (volume of solute ÷ volume of solution) × 100. Always divide by the whole solution.

Mass percentage (% w/w)(mass of solute ÷ mass of solution) × 100

Mass of solutionMass of solute + mass of solvent

Volume percentage (% v/v)(volume of solute ÷ volume of solution) × 100

UnitsNo unit; the answer is written as a percentage

Saying how strong a solution is

The concentration of a solution tells how much solute is present in a given amount of solution. A dilute solution has little solute; a concentrated one has a lot. To give an exact value we use percentages. Mass percentage suits a solid dissolved in a liquid. Volume percentage suits a liquid dissolved in a liquid, because liquids are easier to measure by volume.

Worked example: mass percentage

Problem

5 g of sugar is dissolved in 45 g of water. Find the mass percentage of sugar and of water.

Working

Mass of solution = 5 g + 45 g = 50 g
Formula: mass percentage = (mass of solute ÷ mass of solution) × 100
Sugar: (5 ÷ 50) × 100 = 10%
Water: (45 ÷ 50) × 100 = 90%
Check: 10% + 90% = 100%

Answer

The solution is 10% sugar and 90% water by mass (10% w/w sugar).

Worked example: volume percentage

Problem

25 mL of ethanol is mixed with water to make 200 mL of solution. Find the volume percentage of ethanol.

Working

Formula: volume percentage = (volume of solute ÷ volume of solution) × 100
= (25 mL ÷ 200 mL) × 100
= 0.125 × 100 = 12.5%

Answer

The solution is 12.5% v/v ethanol.

Worked example: making a solution of a given strength

Problem

How much glucose and how much water are needed to make 400 g of a 5% (by mass) glucose solution?

Working

5% by mass means 5 g of glucose in every 100 g of solution
Glucose = (5 ÷ 100) × 400 g = 20 g
Water = 400 g − 20 g = 380 g

Answer

Dissolve 20 g of glucose in 380 g of water.

Mass percentage vs solubility

Mass percentageDivides by the mass of the whole solution (solute + solvent). Can be worked out for any solution.

SolubilityDivides by the mass of the solvent only, and is always for a saturated solution at a stated temperature.

The most common mistake is dividing by the solvent when the question asks for mass percentage.

In real life

Labels use these numbers. A hand sanitiser may say 70% v/v alcohol. When families make ORS at home, they follow a fixed recipe so that the salt and sugar are at the right percentage.

Exam angle

2 marks: “Calculate the mass percentage of a solution made by dissolving 10 g of salt in 90 g of water.” Mass of solution = 10 + 90 = 100 g. Mass percentage = (10 ÷ 100) × 100 = 10%.

4 marks: “Define mass percentage and volume percentage. A solution contains 30 mL of alcohol in 150 mL of solution. Find its volume percentage.” Both formulas and when each is used. (30 ÷ 150) × 100 = 20% v/v.

Remember it

Part over whole, times one hundred. The whole is always the solution, never just the solvent.