1.27 carry out mole calculations using volumes and molar concentrations.

Moles can be calculated from masses of solids and pure liquids and also volumes of gases. Frequently, though, we are dealing with solutions which can vary in concentration. Concentration is measured in moles per litre, written as mol/dm3.

MOLES = VOLUME x CONCENTRATION CONCENTRATION = MOLES ÷ VOLUME VOLUME = MOLES ÷ CONCENTRATION

In these equations it is important to have the volumes in dm3 (litres)

1 dm3 = 1000 cm3 (or 1 litre = 1000 ml)

e.g.       What volume of 2.0 mol/dm3 sulphuric acid is required to react completely with 3.8 g of calcium?

Ca + H2SO4 → CaSO4 + H2

Moles of Ca                               = 3.8 g ÷ 40      = 0.095 mol

Ratio of Ca : H2SO4                         = 1 : 1

Moles of H2SO4 needed             = 0.095 mol

volume of H2SO4                              = moles ÷ concentration

= 0.095 mol ÷ 2.0 mol/dm3                = 0.0475 dm3

e.g.       In a titration, 13.7cm3 of NaOH reacted with 25.0cm3 of H2SO4 of concentration 0.150 mol/dm3. What is the concentration of the NaOH?

2NaOH + H2SO4 → Na2SO4 + 2H2O

Moles of H2SO4                                = volume (in dm³) x concentration

= (25.0 cm3 ÷ 1000) x 0.150

= 0.00375 mol

Moles of NaOH                         = 2 × moles H2SO4                                                (ratio from equation)

= 2 × 0.00375 mol

= 0.00750 mol of NaOH

Concentration of NaOH             = moles ÷ volume (in dm³)

= 0.00750 mol ÷ (13.7 cm3 ÷1000)

= 0.547 mol/dm3

(note how volumes in cm3 were converted to dm3 by dividing by 1000)

For practical details of titrations, and how to work out the average titre, see Section 4.9.