Calculating concentrations - Higher

It is often more useful to know the concentration of a reactant in moles/dm3 as this relates more easily to reacting ratios.

Concentration using moles

The concentration of a solution can be calculated using:

curriculum-key-fact
concentration (mol/dm3) = \frac{number\ of\ moles\ of\ solute}{volume\ (dm^3)}

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

Question

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

concentration (mol/dm3) = \frac{number\ of\ moles\ of\ solute}{volume\ (dm^3)}

concentration = \frac{0.5\ moles}{2\ dm^3}

= 0.25 moles/dm3

Question

100 cm3 of dilute hydrochloric acid contains 0.02 moles of dissolved hydrogen chloride. Calculate the concentration of the acid in moles/dm3.

volume of acid in dm3 = 100/1,000 = 0.1 dm3

concentration of acid = mass in g/volume in dm3

= \frac{0.02}{0.1}

= \frac{0.2\ moles}{dm^3}

Converting between units

Change mass into moles to convert from g/dm3 to moles per dm3.

Use the relative formula mass Mr to do this:

number of moles = \frac{mass}{M_r}

Question

Calculate the concentration of 7.3 g/dm3 hydrochloric acid in moles/dm3. (Relative formula mass of HCl = 36.5)

number of moles = \frac{mass}{M_r}

= \frac{7.3}{36.5}

= 0.2 mol

So concentration = 0.2 moles/dm3

Converting between units

Change moles into mass to convert from moles/dm3 to g/dm3.

Rearrange the equation:

mass = Mr x number of moles

Question

Calculate the concentration of 0.1 moles/dm3 sodium hydroxide solution in g/dm3. (Relative formula mass: NaOH = 40.0)

mass = Mr x number of moles

= 40.0 × 0.1

= 4 g

So concentration = 4 g/dm3

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