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12. Introducing Volumetric Analysis - titration calculations e.g. acid-alkali titrations

This page describes and explains, with fully worked out examples, how to do simple titration calculations involving acids and alkalis. These methods of calculation involve a knowledge of the mole concept e.g. the interconversion of mass-moles-formula mass (mol = mass/Mr) and know how to calculate and use molarity (molarity = mol/volume in dm3). There is also a section describing the apparatus, choice of indicator and technique of how to carry out a simple acid-alkali titration. Overall a description and explanation of simple example of volumetric analysis. (updated Feb 23rd 2013)

On-line Quantitative Chemistry Calculations

See also Advanced level GCE-AS-A2 acid-alkali titration calculation questions

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12. Molarity, moles & mass and Volumetric titration 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)
  • 25.0 cm³ of a sodium hydroxide solution was pipetted into a conical flask and titrated with 0.200 mol dm^-3 (0.2M) hydrochloric acid.
  • Using a suitable indicator it was found that 15.0 cm³ of the acid was required to neutralise the alkali.
    • Calculate the molarity of the sodium hydroxide and its concentration in g/dm³.
      • moles = molarity x volume (in dm³ = cm³/100)
      • moles HCl = 0.200 x (15.0/1000) = 0.003 mol
      • moles HCl = moles NaOH (1 : 1 in equation)
      • so there is 0.003 mol NaOH in 25.0 cm³
      • scaling up to 1000 cm³ (1 dm³), there are ...
      • 0.003 x (1000/25.0) = 0.12 mol NaOH in 1 dm³
      • molarity of NaOH is 0.120 mol dm^-3  (or 0.12M)
      • since mass = moles x formula mass, and M_r(NaOH) = 23 + 16 + 1 = 40
      • concentration in g/dm³ = molarity x formula mass
      • concentration in g/dm³ is 0.12 x 40 = 4.80 g/dm³ 

   

• Example 12.2: Given the equation 2KOH_(aq) + H₂SO_4(aq) ==> K₂SO₄ + 2H₂O_(l)
• 20.0 cm³ of a sulphuric acid solution was titrated with 0.0500 mol dm^-3 (0.05M) potassium hydroxide.
  • If the acid required 36.0 cm³ of the alkali KOH for neutralisation what was the concentration of the acid?
    • moles = molarity x volume (in dm³ = cm³/100)
    • mol KOH = 0.0500 x (36.0/1000) = 0.0018 mol
    • mol H₂SO₄ = mol KOH / 2 (because of 2 : 1 ratio in equation above)
    • mol H₂SO₄ = 0.0018/2 = 0.0009 (in 20.0 cm³)
    • scaling up to 1000 cm³ of solution = 0.0009 x (1000/20.0) = 0.0450 mol
    • mol H₂SO₄ in 1 dm³ = 0.0450
    • so molarity of H₂SO₄ = 0.0450 mol dm^-3 (0.045M)
    • since mass = moles x formula mass, and M_r(H₂SO₄) = 2 + 32 + (4x16) = 98
    • concentration in g/dm³ is 0.045 x 98 = 4.41 g/dm³ 
• Example 12.3: 
  • -

There are more questions involving molarity in section 11. introducing molarity and section 14.3 on dilution

• 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:
  • (i) An accurate volume of acid is pipetted into the conical flasks using a suction bulb and pipette for health and safety reasons. Universal indicator is then added, which turns red in the acid.
  • 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 other possibilities are:
      • (ii) An accurate volume of alkali is measured into a flask and titrated with an acid solution of known concentration.
      • (iii) A small amount of accurately weighed solid acid is dissolved in water and titrated with alkali.
      • (iv) A small amount of accurately weighed solid alkali is dissolved in water and titrated with acid.
        • This can procedure can be used to compare the effectiveness of ant-acid indigestion tablets, which are designed to neutralise excess acid in the stomach.
        • A known and equal mass of each brand of indigestion tablet is crushed and mixed with some water eg 20 cm³ (fair test points).
        • Make sure the mixture is gently swirled to completely dissolve the crushed tablet powder.
        • The burette is filled with a standard solution of hydrochloric acid and zeroed to the top calibration mark of 0.00 cm³.
        • Universal indicator is added to the flask and the indigestion powder should turn it blue - alkaline.
        • The acid is carefully and slowly added until the indicator turns green - neutral at the end-point of the titration.
        • You then read the volume of acid required to neutralise the ant-acid powder.
        • The bigger the volume of acid required for neutralisation, the more effective the indigestion powder per mass of powder.
        • Repeat the procedure with another brand of indigestion powder using the same standard acid solution (fair test).
    • After this, the method is essentially the same as described below.
  • 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.
  • 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.
  • 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

See also Advanced level GCE-AS-A2 acid-alkali titration calculation questions

OTHER CALCULATION PAGES

1. What is relative atomic mass?, relative isotopic mass and calculating relative atomic mass

2. Calculating relative formula/molecular mass of a compound or element molecule

3. Law of Conservation of Mass and simple reacting mass calculations

4. Composition by percentage mass of elements in a compound

5. Empirical formula and formula mass of a compound from reacting masses (easy start, not using moles)

6. Reacting mass ratio calculations of reactants and products from equations (NOT using moles) and brief mention of actual percent % yield and theoretical yield, atom economy and formula mass determination

   • Reacting masses, concentration of solution and volumetric titration calculations (NOT using moles)

7. Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations (relating reacting masses and formula mass)

8. Using moles to calculate empirical formula and deduce molecular formula of a compound/molecule (starting with reacting masses or % composition)

9. Moles and the molar volume of a gas, Avogadro's Law

10. Reacting gas volume ratios, Avogadro's Law and Gay-Lussac's Law (ratio of gaseous reactants-products)

11. Molarity, volumes and solution concentrations (and diagrams of apparatus)

12. How to do volumetric titration calculations e.g. acid-alkali titrations (this page)

13. Electrolysis products calculations (negative cathode and positive anode products)

14. Other calculations e.g. % purity, % percentage & theoretical yield, volumetric titration apparatus, dilution of solutions (and diagrams of apparatus), water of crystallisation, quantity of reactants required, atom economy

15. Energy transfers in physical/chemical changes, exothermic/endothermic reactions

16. Gas calculations involving PVT relationships, Boyle's and Charles Laws

17. Radioactivity & half-life calculations including dating materials

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