Calculating concentrations

The concentration of a solution can be shown in g/dm3 or mol/dm3. It is often more useful to know the concentration of a reactant in mol/dm3 so that the amount of reactant in a given volume can be calculated.

Concentration using moles

The concentration of a solution can be calculated using:

curriculum-key-fact
Concentration~in~mol/dm^{3} = \frac{amount~of~solute~in~mol}{volume~in~dm^{3}}

Example

0.5 mol of sodium hydroxide is dissolved in 2 dm3 of water. Calculate the concentration of the sodium hydroxide solution formed.

Concentration~in~mol/dm^{3} = \frac{amount~of~solute~in~mol}{volume~in~dm^{3}}

Concentration = \frac{\textup{0.5~mol}}{\textup{2~dm}^3}

Concentration = 0.25 mol/dm3

Volume units

Volumes used in concentration calculations must be in dm3, not in cm3. 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 0.02 mol of dissolved hydrogen chloride. Calculate the concentration of the acid in mol/dm3.

Volume of acid = 100 ÷ 1000 = 0.1 dm3

Concentration of acid = 0.02 mol ÷ 0.1 dm3

= 0.2 mol/dm3

Converting between units

The relative formula mass of the solute is used to convert between mol/dm3 and g/dm3:

  • to convert from mol/dm3 to g/dm3, multiply by the relative formula mass
  • to convert from g/dm3 to mol/dm3, divide by the relative formula mass

Remember: the molar mass is the Ar or Mr in grams per mol.

Example

Calculate the concentration of 0.1 mol/dm3 sodium hydroxide solution in g/dm3. (Mr of NaOH = 40)

Concentration = 0.1 × 40

= 4 g/dm3

Question

Calculate the concentration of 7.3 g/dm3 hydrochloric acid in mol/dm3. (Mr of HCl = 36.5)

Concentration = 7.3 ÷ 36.5

= 0.2 mol/dm3