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Lesson: Chapter 3 — Mixtures

3.2. The composition of a mixture 2 of 5

Mass fraction

The first way of stating a composition, and the simplest: weigh the component, weigh the whole thing, divide.

Mass fraction of A

mass of A ÷ (mass of A + mass of B)

that is, mass of A ÷ total mass of the mixture

The mass fraction of a component of a mixture is the ratio its mass bears to the total mass of the mixture. It is a ratio of two masses, so it has no units.

Example 1 — a solute in 100 g of solution

Problem

A solution of 100 g contains 5 g of solute. Express the composition of the solute in it as a mass fraction.

Solution

mass fraction of solute = mass of solute ÷ mass of solution

= 5 g ÷ 100 g

= 1 ÷ 20

= 0.05

Example 2 — evaporating a salt solution

Problem

250 g of a salt (NaCl) solution is measured out accurately, and when all the water in it is evaporated off, 10 g of salt is obtained. Give the composition of the salt in this solution as a mass fraction.

Solution

mass fraction of salt = 10 g ÷ 250 g

= 1 ÷ 25

= 0.04

Evaporating the water is what makes the mass of solute measurable. The 250 g was the whole solution, water included.

A check worth doing

A mass fraction can never come out greater than 1, because the part can never be heavier than the whole. An answer above 1 means the division went the wrong way round.