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12. Volumetric calculations e.g. acid-alkali titrations

• Titrations can be used to find the concentration of an acid or alkali from the relative volumes used and the concentration of one of the two reactants. The method and apparatus used are briefly described at the end of this page.
• You should be able to carry out calculations involving neutralisation reactions in aqueous solution given the balanced equation or from your own practical results.
• The examples in section 7. moles and mass. and section 11. concentration will help you follow the calculations below.
  • Note again: 1dm³ = 1 litre = 1000ml = 1000 cm³, so dividing cm³/1000 gives dm³.
  • and other useful formulae or relationships are:
    • moles = molarity (mol/dm³) x volume (dm³=cm³/1000),
    • molarity (mol/dm³) = mol / volume (dm³=cm³/1000),
    • 1 mole = formula mass in grams.
  • In most volumetric calculations of this type, you first calculate the known moles of one reactant from a volume and molarity. Then, from the equation, you relate this to the number of moles of the other reactant, and then with the volume of the unknown concentration, you work out its molarity.
• Example 12.1: Given the equation NaOH_(aq) + HCl_(aq) ==> NaCl_(aq) + H₂O_(l)
• 25 cm³ of a sodium hydroxide solution was pipetted into a conical flask and titrated with 0.2M hydrochloric acid. Using a suitable indicator it was found that 15 cm³ of acid was required to neutralise the alkali. Calculate the molarity of the sodium hydroxide and concentration in g/dm³.
  • moles HCl = (15/1000) x 0.2 = 0.003 mol
  • moles HCl = moles NaOH (1 : 1 in equation)
  • so there is 0.003 mol NaOH in 25 cm³
  • scaling up to 1000 cm³ (1 dm³), there are ...
  • 0.003 x (1000/25) = 0.12 mol NaOH in 1 dm³
  • molarity of NaOH is 0.12M or mol dm^-3 
  • since mass = moles x formula mass, and M_r(NaOH) = 23 + 16 + 1 = 40
  • concentration in g/dm³ is 0.12 x 40 = 4.41g/dm³ 

   

• Example 12.2: Given the equation 2KOH_(aq) + H₂SO_4(aq) ==> K₂SO₄ + 2H₂O_(l)
• 20 cm³ of a sulphuric acid solution was titrated with 0.05M potassium hydroxide. If the acid required 36 cm³ of the alkali KOH for neutralisation what was the concentration of the acid?
  • mol KOH = 0.05 x (36/1000) = 0.0018 mol
  • mol H₂SO₄ = mol KOH / 2 (because of 1 : 2 ratio in equation above)
  • mol H₂SO₄ = 0.0018/2 = 0.0009 (in 20 cm³)
  • scaling up to 1000 cm³ of solution = 0.0009 x (1000/20) = 0.045 mol
  • mol H₂SO₄ in 1 dm³ = 0.045, so molarity of H₂SO₄ = 0.045M or mol dm^-3 
  • since mass = moles x formula mass, and M_r(H₂SO₄) = 2 + 32 + (4x16) = 98
  • concentration in g/dm³ is 0.045 x 98 = 4.41g/dm³ 
• Example 12.3: 
  • -
• How to carry out a titration?

• The right diagrams show the typical apparatus (1)-(6) used in manipulating liquids and on the left a brief three stage description of titrating an acid with an alkali:
  1. An accurate volume of acid is pipetted into the conical flasks using a suction bulb for health and safety reasons. Universal indicator is then added, which turns red in the acid.
  2. The alkali, of known accurate concentration, is put in the burette and you can conveniently level off the reading to zero (the meniscus on the liquid surface should rest on the zero -- graduation mark).
     • Note in stage 2. other possibilities are:
       • A small amount of accurately weighed solid acid is dissolved in water and titrated with alkali.
       • A small amount of accurately weighed solid alkali is dissolved in water and titrated with acid.
     • After this, the method is essentially the same as described below.
  3. The alkali is then carefully added by running it out of the burette in small quantities, controlling the flow with the tap, until the indicator seems to be going yellow-pale green. The conical flask should be carefully swirled after each addition of alkali to ensure all the alkali reacts.
  4. Near the end of the titration, the alkali should added drop-wise until the universal indicator goes green. This is called the end-point of the titration and the green means that all the acid has been neutralised. The volume of alkali needed to titrate-neutralise the acid is read off from burette scale, again reading the volume value on the underside of the meniscus. The calculation can then be done to work out the concentration of the alkali.
  5. Universal indicator, and most other acid-base indicators, work for strong acid and alkali titrations, but universal indicator is a somewhat crude indicator for other acid-alkali titrations because it gives such a range of colours for different pH's. Examples of more accurate and 'specialised' indicators are:
     • titrating a strong alkali with a strong acid (or vice versa):
       • e.g. for sodium hydroxide (NaOH) - hydrochloric/sulphuric acid (HCl/H₂SO₄) titrations, use ...
       • phenolphthalein indicator (pink in alkali, colourless in acid-neutral solutions), the end-point is the pink <==> colourless change.
       • Litmus works too, the end point is the red <==> purple/blue colour change.
     • titrating a weak alkali with a strong acid:
       • e.g. for titrating ammonia (NH₃) with hydrochloric/sulfuric acid (HCl/H₂SO₄), use ...
       • methyl orange indicator (red in acid, yellowish-orange in neutral-acid), the end-point is an 'orange' colour, not easy to see accurately.
       • screened methyl orange indicator is a slightly different dye-indicator mixture that is reckoned to be easier to see than methyl orange, the end-point is a sort of 'greyish orange', but still not easy to do accurately.
     • titrating a weak acid with a strong alkali:
       • e.g. for titrating ethanoic acid (CH₃COOH) with sodium hydroxide (NaOH), use ...
       • phenolphthalein indicator (pink in alkali, colourless in acid-neutral solutions, pink in alkali), the end-point is the first permanent pink.
       • methyl red indicator (red in acid, yellow in neutral-alkaline), the end-point is 'orange'.
     • titrating a weak acid with a weak alkali (or vice versa):
       • These are NOT practical titrations because the pH changes at the end-point are not great enough to give a sharp colour change with any indicator.
     • The Acids, Bases, pH page section (2) lists common indicators.
     • The theory, and examples of strong/weak acids/alkalis (soluble bases) are described on the Extra Aqueous Chemistry page section 3,
     • and the Acids, Bases, pH page section (7) explains the changes in pH in the titration.
     • Advanced level theory of indicators and titrations and advanced acid-alkali titration questions (GCE-AS-A2-IB students only!)

Self-assessment Quiz on titrations [vct]

type in answer Honly

or multiple choice Honly