Most tested C4.9

Solution Concentration and Solubility

This topic covers the essential calculations for solutions, focusing on how to determine concentration in different units (mol dm⁻³ and g dm⁻³). It also defines the limits of dissolving a substance through the concepts of saturation and solubility.

Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.

Key points

  • Concentration measures the amount of solute dissolved in a specific volume of the final solution, not the solvent.
  • The two key units for concentration are grams per cubic decimetre (g dm⁻³) and moles per cubic decimetre (mol dm⁻³).
  • To convert between mass concentration (g dm⁻³) and molar concentration (mol dm⁻³), use the molar mass (Mr) of the solute.
  • Solubility is the specific concentration of a saturated solution at a given temperature, often expressed as grams of solute per 100g of solvent.
  • You must be able to convert between volume units, most commonly from cm³ to dm³ by dividing by 1000.

Formulae

Concentration (g dm-3) = Mass (g) / Volume (dm3)

To find concentration when given the mass of solute and the total volume of the solution.

Concentration (mol dm-3) = Moles (mol) / Volume (dm3)

To find concentration when given the number of moles of solute and the total volume of the solution.

Moles (mol) = Mass (g) / Molar Mass (Mr)

To convert the mass of a substance into moles, a necessary step when converting between mass and molar concentrations.

Definitions

Concentration
The amount of a solute (in mass or moles) dissolved per unit volume of the solution.
Saturated Solution
A solution that contains the maximum possible amount of dissolved solute at a specific temperature. No more solute can be dissolved.
Solubility
A measure of the maximum mass of a substance that will dissolve in a given amount of solvent (e.g., 100g) at a specific temperature.

Worked example

4.0 g of sodium hydroxide (NaOH) is dissolved in water to create a 200 cm³ solution. What is the concentration of this solution in mol dm⁻³? (Relative atomic masses: Na=23, O=16, H=1)

  1. 1

    First, calculate the molar mass (Mr) of NaOH:

    23 + 16 + 1 = 40 g/mol
  2. 2

    Next, calculate the number of moles of NaOH:

    Moles = Mass / Mr = 4.0 g / 40 g/mol = 0.1 mol
  3. 3

    Then, convert the volume from cm³ to dm³.

    Since 1000 cm³ = 1 dm³, 200 cm³ = 200 / 1000 = 0.2 dm³.

  4. 4

    Finally, calculate the concentration:

    Concentration = Moles / Volume (dm³) = 0.1 mol / 0.2 dm³.

  5. 5

    To calculate 0.1 / 0.2, this is the same as 1 / 2, which is 0.5.

    The concentration is 0.5 mol dm⁻³.

Answer: 0.5 mol dm⁻³

Common mistakes

  • ×Forgetting to convert the volume from cm³ to dm³. This is the most common error and will make your answer incorrect by a factor of 1000.
  • ×Making arithmetic mistakes with decimals, such as misplacing the decimal point during multiplication or division.
  • ×Using the mass in grams directly in the molar concentration formula without first converting it to moles.

No-calculator tips

  • ✓To divide by a simple decimal, turn it into a fraction. For example, dividing by 0.2 is the same as dividing by 1/5, which is the same as multiplying by 5.
  • ✓When calculating moles, look for easy relationships between the mass and the molar mass. In the example, 4.0 is one-tenth of the Mr (40), so you instantly know it's 0.1 moles.
  • ✓Memorise common volume conversions to save time: 200 cm³ = 0.2 dm³, 250 cm³ = 0.25 dm³, 500 cm³ = 0.5 dm³.

Read this topic in the official UAT-UK ESAT guide →

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