Concentration of solutions

A solution forms when a solute dissolves in a solvent. The concentration of a solution is a measure of how 'crowded' the solute particles are. The more concentrated the solution, the more particles it contains in a given volume.

Calculating concentration

The concentration of a solution can be calculated using:

  • the mass of dissolved solute in grams, g
  • the volume of solution (or solvent) in cubic decimetres, dm3
curriculum-key-fact
concentration~in~g/dm^3 = \frac{mass~of~solute~in~g}{volume~in~dm^3}

The units for concentration can also be shown as g dm-3, but this means the same as g/dm3.

Worked example

8 g of sodium hydroxide is dissolved in 2 dm3 of water. Calculate the concentration of the sodium hydroxide solution formed.

concentration = \frac{\textup{mass~of~solute~in~g}}{\textup{volume~in~dm}^3}

concentration = \frac{\textup{8~g}}{\textup{2~dm}^3}

concentration = 4 g/dm3

Volume units

Apparatus used to measure volumes is usually marked in cm3 or ml. Although these are different units, they describe the same volume. For example, 250 ml = 250 cm3.

Volumes used in concentration calculations must be in dm3, not in cm3 or ml. It is useful to know that 1 dm3 = 1000 cm3. This means:

  • divide by 1000 to convert from cm3 to dm3
  • multiply by 1000 to convert from dm3 to cm3

For example, 250 cm3 is 0.25 dm3 (250 ÷ 1000). It is often easiest to convert from cm3 to dm3 before continuing with a concentration calculation.

Question

100 cm3 of dilute hydrochloric acid contains 0.5 g of dissolved hydrogen chloride. Calculate the concentration of the acid in g/dm3.

volume of acid = 100 ÷ 1000 = 0.1 dm3

concentration of acid = \frac{\textup{0.5}}{\textup{0.1}}

= 5 g/dm3

Calculating the mass of solute

Rearranging the equation for concentration allows the mass of solute to be calculated:

mass of solute in g = concentration in g/dm3 × volume in dm3

Worked example

A solution of sodium chloride has a concentration of 10 g/dm3. What mass of sodium chloride is dissolved in 2 dm3 of the solution?

mass of solute in g = concentration in g/dm3 × volume in dm3

= 10 g/dm3 × 2 dm3

= 20 g

Higher tier

The concentration of a solution can be changed:

  • concentration can be increased by dissolving more solute in a given volume of solution - this increases the mass of the solute
  • concentration can be increased by allowing some of the solvent to evaporate - this decreases the volume of the solution