Calculating Concentration (Cambridge International IGCSE Chemistry)

Units of concentration

Spec point — State that concentration can be measured in g /dm3 or mol/dm3

• A solute is a solid substance that dissolves into a liquid

  • The amount of solute can be expressed in grams (g) or moles (mol)

• A solvent is the liquid that a solute dissolves in

  • The amount / volume of a solvent is measured in cm³ or dm³

• Most chemical reactions occur between solutes which are dissolved in solvents, such as water or an organic solvent

• A solution is the mixture formed when a solute dissolves in a solvent

  • The amount / volume of a solution measured in cm³ or dm³

• Concentration refers to the amount of solute there is in a specific volume of the solvent

  • The greater the amount of solute in a given volume, the greater the concentration

  • Concentration is sometimes commonly referred to as strength

    • For example, dissolving more coffee in hot water results in a stronger coffee

• Typically, concentration is expressed in terms of the amount of substance per dm³

  • Therefore, the units of concentration are:

    • g / dm³
    • mol / dm³

Calculating concentration

Spec point — Calculate stoichiometric reacting masses, limiting reactants, volumes of gases at r.t.p., volumes of solutions and concentrations of solutions expressed in g /dm3 and mol/dm3 , including conversion between cm3 and dm3

Extended tier only

Calculating concentration using mass

• The general formula to calculate the concentration in g / dm³ is:

concentration (g / dm³) = $\frac{\mathrm{mass} \mathrm{of} \mathrm{solute}(g)}{\mathrm{volume} \mathrm{of} \mathrm{solution}(\mathrm{dm}^{3})}$

• Concentration can also be measured in grams per cubic decimetre

  • 1 decimetre cubed (dm³) = 1000 cm³
  • 1 decimetre cubed (dm³) is the same as 1 litre

• You may be given data in a question which needs to be converted from cm³ to dm³ or the other way around

Converting cm³ and dm³

To go from cm³to dm³ divide by 1000. To go from dm³ to cm³multiply by 1000

Worked Example A student dissolved 10 g of sodium hydroxide, NaOH, in 2 dm³ of distilled water. Calculate the concentration of the solution in g / dm³.

Answer:

• Write down the information you are given in the question:

  • Mass of solute: 10 g
  • Volume of solution: 2 dm³

• Calculate the concentration:

  • Concentration = $\frac{ \text{mass} of \text{solute} ( \mathrm{g} ) }{ \text{volume} ( dm ^{3} ) }$
  • Concentration = $\frac{10g}{2\mathrm{dm}^{3}}$ = 5 g / dm³

Calculating concentration using moles

• It is more useful to a chemist to express concentration in terms of moles per unit volume rather than mass per unit volume
• Concentration can therefore be expressed in moles per decimetre cubed and calculated using the following equation:

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

• We can modify the concentration formula to include moles

  • The units in the answer can be written as mol / dm³ (this can also be written as mol dm^-3)

• You may have to convert from g / dm³ into mol / dm³ and vice versa depending on the question

• To go from g / dm³ to mol / dm³

  • Divide by the molar mass in grams

• To go from mol / dm³ to g / dm³

  • Multiply by the molar mass in grams

• Some students find formula triangles help them to understand the relationship:

The concentration-moles formula triangle can help you solve these problems

Worked Example Calculate the amount of solute, in moles, present in 2.5 dm³ of a solution whose concentration is 0.2 mol / dm³.

Answer:

• Write down the information you are given in the question:

  • Concentration of solution: 0.2 mol / dm³
  • Volume of solution: 2.5 dm³

• Calculate the number of moles:

  • Moles = concentration x volume
  • Moles = 0.2 x 2.5 = 0.5 mol

Worked Example Calculate the concentration of a solution of sodium hydroxide, NaOH, in mol / dm³, when 80 g is dissolved in 500 cm³ of water.

Relative atomic masses, A_r: Na = 23; H = 1; O = 16

Answer:

• Calculate the M_r of NaOH:

  • 23 + 16 + 1 = 40

• Determine the number of moles of NaOH:

  • 40 g = 1 mole
  • So, 80 g = 2 moles

• Convert cm³ to dm³:

  • $\frac{500}{1000}$ = 0.5 dm³

• Calculate the concentration:

  • Concentration = $\frac{\mathrm{moles}}{\mathrm{volume}}$
  • Concentration = $\frac{2}{0.5}$ = 4 mol / dm³

Worked Example 25.0 cm³ of 0.050 mol / dm³ sodium carbonate was completely neutralised by 20.00 cm³ of dilute hydrochloric acid. Calculate the concentration in mol / dm³ of the hydrochloric acid.

Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂

Answer:

• Calculate the moles of sodium carbonate:

  • Moles of Na₂CO₃ = concentration x volume

    • Remember: The volume needs to be in dm³

  • Moles of Na₂CO₃ = 0.05 x $\frac{25.0}{1000}$ = 0.00125

• Calculate the moles of hydrochloric acid:

  • The balanced symbol equation shows that 1 mole of Na₂CO₃ reacts with 2 moles of HCl
  • So, 0.00125 moles of Na₂CO₃ reacts with 0.00250 moles of HCl

• Calculate the concentration of hydrochloric acid:

  • Concentration = $\frac{\mathrm{moles}}{\mathrm{volume}}$

    • Remember: The volume needs to be in dm³
    • 20 cm³ ÷ 1000 = 0.02 dm³

  • Concentration = $\frac{0.00250}{0.02}$ = 0.125 mol / dm³

Exam Hint Remember: Always convert the units from cm³ to dm³ by dividing by 1000.