Using concentrations of solutions in mol/dm3

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Notes de leçon

Concentration in mol/dm³

  • Concentration can be measured in mol/dm³ (also written as mol/dm³ or mol/dm³).
  • It is often more useful to express concentration in moles per unit volume rather than mass per unit volume.
  • The formula is: concentration (mol/dm³) = number of moles of solute (mol) ÷ volume of solution (dm³).
  • The units in the answer can be written as mol dm⁻³ or mol / dm³.
  • You may need to convert between g/dm³ and mol/dm³ depending on the question.

Concentration, moles and volume formula triangle

Concentration, moles and volume formula triangle

Converting between cm³ and dm³

  • To go from cm³ to dm³, divide by 1000.
  • To go from dm³ to cm³, multiply by 1000.
  • For example, 500 cm³ ÷ 1000 = 0.5 dm³.
  • A common mistake is forgetting to convert units, which gives an answer a thousand times out.

Calculating moles from concentration and volume

  • Rearrange the formula to find moles: moles = concentration × volume.
  • Make sure the volume is in dm³ before substituting into the equation.
  • A formula triangle can help you rearrange the relationship between concentration, moles and volume.
  • You are not given the formula triangle in exams, so you must learn it.
  • It is a good idea to write the formula down before starting a problem.

Worked example: moles from concentration

  • Calculate the moles in 2.5 dm³ of a solution of concentration 0.2 mol/dm³.
  • Moles = concentration × volume = 0.2 × 2.5.
  • The answer is 0.5 mol.

Worked example: concentration from mass

  • Calculate the concentration of sodium hydroxide, NaOH, when 80 g is dissolved in 500 cm³ of water (Na = 23, H = 1, O = 16).
  • First find the relative formula mass: Mᵣ(NaOH) = 23 + 16 + 1 = 40.
  • So 40 g NaOH = 1 mole, and 80 g NaOH = 2 moles.
  • Convert volume: 500 cm³ ÷ 1000 = 0.5 dm³.
  • Concentration = moles ÷ volume = 2 ÷ 0.5 = 4 mol/dm³.

Titration calculations

  • If the concentration of one reactant is known, the exact volumes from a titration and the balanced equation can be used to find the concentration of the other reactant.
  • Use the equation for the reaction to find the mole ratio between the acid and the base.
  • Calculate moles of the known solution using moles = (volume ÷ 1000) × concentration.
  • Use the mole ratio to deduce the moles of the unknown solution.
  • Finally, calculate concentration using concentration = moles ÷ volume (dm³).

Worked example: titration calculation

  • 25.0 cm³ of hydrochloric acid was titrated against 0.100 mol/dm³ NaOH; 12.1 cm³ of NaOH was required.
  • Equation: HCl (aq) + NaOH (aq) → NaCl (aq) + H₂O (l).
  • Moles of NaOH = 0.012 dm³ × 0.100 mol/dm³ = 1.21 × 10⁻³ mol.
  • The acid reacts in a 1:1 ratio, so moles of HCl = 1.21 × 10⁻³ mol.
  • This is present in 25.0 cm³ = 0.025 dm³.
  • Concentration of HCl = 1.21 × 10⁻³ ÷ 0.025 = 0.0484 mol/dm³.

Key terminology and practical skills

  • Titration is used to determine the concentration of a strong acid or alkali.
  • A pipette is used to measure a precise volume of one solution into a conical flask.
  • A burette is used to add the other solution until the end-point is reached.
  • A standard solution is one whose concentration is accurately known.
  • Concordant results are titres within a small range (e.g. 0.10 cm³) of each other; only these should be averaged.
  • Neutralisation occurs when an acid and alkali react completely.

Common misconceptions and errors

  • Failing to convert cm³ to dm³ gives answers a thousand times out.
  • Do not confuse g/dm³ with mol/dm³ — they are different units.
  • Do not average non-concordant titres; only use concordant results.
  • A more concentrated solution is not necessarily a stronger acid.
  • When reading a burette, read from the correct end of the scale (top to bottom).

Diapos

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  1. 1.Which equation correctly gives concentration in mol/dm³?

    Easy
    • Aconcentration = moles of solute ÷ volume of solution in dm³
    • Bconcentration = volume of solution in dm³ ÷ moles of solute
    • Cconcentration = moles of solute × volume of solution in dm³
    • Dconcentration = moles of solute ÷ volume of solution in cm³

  2. 2.A solution of sulfuric acid, H₂SO₄, contains 9.8 g of the acid in 250 cm³ of solution. What is the concentration in mol/dm³? (Ar: H = 1, S = 32, O = 16)

    Medium
    • A0.10 mol/dm³
    • B0.20 mol/dm³
    • C0.40 mol/dm³
    • D0.80 mol/dm³

  3. 3.Which of the following statements about concentration and titration are correct? (select all that apply)

    Medium
    • AConcentration can be expressed in mol/dm³ or in g/dm³.
    • BA more concentrated acid is always a stronger acid.
    • CConcordant titres are within 0.10 cm³ of each other.
    • DA burette is read from the top of the scale downwards.
    • EThe pipette is used to deliver the solution of unknown concentration into the conical flask.

  4. 4.The concentration of a solution in mol/dm³ is the number of moles of solute dissolved in 1 dm³ of solution.

    Easy

    True or false?

  5. 5.Match each piece of titration apparatus or term with its correct description.

    Medium
    • pipette
    • burette
    • conical flask
    • concordant results
    • delivers a fixed volume of solution accurately
    • delivers variable volumes and is read from the bottom of the meniscus
    • used to hold the solution during titration and swirled
    • titres that are within 0.10 cm³ of each other

  6. 6.Place the steps of a titration in the correct order.

    Medium
    • Pipette a known volume of the solution into a conical flask.
    • Add a few drops of indicator to the conical flask.
    • Fill the burette with the other solution and record the initial reading.
    • Add the solution from the burette until the indicator changes colour.
    • Record the final burette reading and repeat until concordant results are obtained.

  7. 7.How many moles of solute are present in 2 dm³ of a 0.5 mol/dm³ solution of potassium iodide?

    Medium
    • A0.5 mol
    • B1.0 mol
    • C2.0 mol
    • D10 mol

  8. 8.In a titration, 25.00 cm³ of 0.20 mol/dm³ sodium hydroxide reacted with 26.50 cm³ of hydrochloric acid. What is the concentration of the acid? (HCl + NaOH → NaCl + H₂O)

    Medium
    • A0.19 mol/dm³
    • B0.23 mol/dm³
    • C0.55 mol/dm³
    • D0.82 mol/dm³

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