Mass per unit volume

The fractions on the last pages all compared a part with a whole. The two ways left compare a part with a volume — and unlike the fractions, they have units.

Composition as m/v

mass of solute ÷ volume of solution

commonly in g dm^-3: grams of solute per cubic decimetre of solution

This expresses the mass of solute contained in a unit volume of a mixture. It is the natural way to state a composition when the solute is weighed and the solution is measured out by volume, which is what happens in practice.

Worked example — saline

Problem

1 dm³ of a saline solution contains 5 g of sodium chloride. Find the composition of sodium chloride in it in terms of m/v.

Solution

composition (m/v) = mass of sodium chloride ÷ volume of solution

= 5 g ÷ 1 dm³

= 5 g dm^-3

Units are not optional here

A mass fraction is a bare number. This is not — 5 without g dm⁻³ after it says nothing at all, and the same solution is 5 g dm⁻³ or 0.005 g cm⁻³ depending on which volume unit you used.