Calculating concentrations - Higher

Concentration using mass

The concentration of a solution can be calculated using:

concentration\ in\ g/dm^{3}\ = \tfrac{mass\ of\ solute\ in\ g}{volume\ in\ dm^{3}}

The solute is the substance that is dissolved. The volume is the volume of the solution or the solvent.

Example

5.0 g of sodium hydroxide is dissolved in 250 cm3 of water. Calculate the concentration of the sodium hydroxide solution formed in g/dm3.

250 cm3 = 250 ÷ 1,000 = 0.250 dm3

concentration\ = \tfrac{mass}{volume}

concentration\ = \tfrac{5.0 g}{0.250 dm^{3}}

= 20 g/dm3

Concentration using volume

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.

The concentration of a solution can be calculated using:

concentration\ in\ mol\ dm^{3}\ = \tfrac{amount\ of\ solute\ in\ mol}{volume\ in\ dm^{3}}

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The units for concentration are sometimes shown as mol dm-3 or M (for ‘molar’), but this means the same as mol/dm3.

Example

0.50 mol of sodium hydroxide is dissolved in 2.0 dm3 of water. Calculate the concentration of the sodium hydroxide solution formed in mol/dm-3.

concentration\ = \tfrac{amount}{volume}

concentration\ = \tfrac{0.5\ mol}{2.0\ dm^{3}}

concentration = 0.25 mol/dm3

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 ÷ 1,000 = 0.1 dm3

concentration of acid = 0.02 ÷ 0.1

= 0.2 mol/dm3

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