Expressing Concentration of Solutions

The concentration of a solution tells us how much solute is dissolved in a given amount of solvent or solution. We can describe this qualitatively — calling a solution dilute when it holds relatively little solute, or concentrated when it holds a lot — but such words are vague and lead to confusion. In real chemistry we need a precise, quantitative measure, and there are several standard ways to express it. Each has its own definition, units and uses, so it helps to learn them side by side.

(i) Mass Percentage (w/w)

The mass percentage of a component is the mass of that component present in every 100 units of mass of the whole solution.

• $w_{\text{component}}$ = mass of the component
• $w_{\text{solution}}$ = total mass of the solution

For instance, a solution labelled "10% glucose in water by mass" contains 10 g of glucose dissolved in 90 g of water, giving 100 g of solution overall. This unit is widely used in industry — for example, commercial bleaching liquid is quoted as containing 3.62 mass percent of sodium hypochlorite in water.

(ii) Volume Percentage (V/V)

When both components are liquids, it is often convenient to work with volumes. The volume percentage is the volume of a component per 100 units of volume of the solution.

• $V_{\text{component}}$ = volume of the component
• $V_{\text{solution}}$ = total volume of the solution

A "10% ethanol solution in water" therefore means 10 mL of ethanol made up to a total volume of 100 mL. A common real example is a 35% (v/v) solution of ethylene glycol used as an antifreeze in car radiators; at this concentration it lowers the freezing point of water to about 255.4 K (−17.6 °C).

(iii) Mass by Volume Percentage (w/V)

This unit, favoured in medicine and pharmacy, mixes the two ideas above: it is the mass of solute dissolved in 100 mL of solution.

(iv) Parts Per Million (ppm)

When a solute is present only in trace amounts, percentages become inconveniently small. In such cases concentration is expressed in parts per million, defined as the number of parts of the component in every million (10⁶) parts of the solution.

Just like percentages, ppm can be measured on a mass-to-mass, volume-to-volume, or mass-to-volume basis. As an illustration, one litre of sea water (which weighs about 1030 g) contains roughly 6 × 10⁻³ g of dissolved oxygen; this tiny amount is equivalently written as 5.8 g per 10⁶ g, i.e. 5.8 ppm. Concentrations of pollutants in water or air are commonly reported in µg mL⁻¹ or in ppm.

(v) Mole Fraction (x)

Mole fraction relates the amount of one component to the total amount of all components, counted in moles. It is written with the symbol $x$, and a subscript on the right identifies which component is meant.

For a binary mixture of A and B with $n_A$ and $n_B$ moles respectively, the mole fraction of A is

More generally, for a solution containing $i$ components,

• $n_i$ = number of moles of component $i$
• $\sum n_i$ = total moles of all components

A useful property follows directly from the definition: the mole fractions of all the components of a solution always add up to one.

Mole fraction is especially valuable when relating a physical property such as vapour pressure to composition, and when handling calculations that involve gas mixtures.

(vi) Molarity (M)

Molarity is the number of moles of solute dissolved in one litre (equivalently, one cubic decimetre) of solution.

• $n_B$ = moles of solute
• $V$ = volume of the solution in litres (L or dm³)

Its unit is mol L⁻¹ (also written M or mol dm⁻³). For example, a 0.25 mol L⁻¹ (0.25 M) solution of NaOH means that 0.25 mol of NaOH is dissolved to make one litre of solution. …