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study examples carefully12. Introducing Volumetric Analysis - titration calculations e.g. acid-alkali titrations

How to you do acid-alkali titration calculations? What is the procedure for doing acid-alkali titrations? How do you do a titration? What apparatus do you need to do a titration? Help for problem solving in doing volumetric titration calculations. Practice revision questions on titrations, using experiment data. 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.

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

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study examples carefully12. 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.
  • I haven't quoted separately the atomic masses used in the titration calculations, but they quoted as part of the calculation and its pretty obvious what is what!

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  • Titration calculation 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 a standard solution of 0.200 mol dm-3 (0.2M) hydrochloric acid.
    • Using phenolphthalein indicator for the titration it was found that 15.0 cm3 of the acid was required to neutralise the alkali. In the appendix this is titration procedure 3.
      • 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 Mr(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 

     

  • Titration calculation Example 12.2
    • Given the equation: 2KOH(aq) + H2SO4(aq) ==> K2SO4 + 2H2O(l)
    • 20.0 cm3 of a sulphuric acid solution was titrated with a standardised solution of 0.0500 mol dm-3 (0.05M) potassium hydroxide.
    • Using phenolphthalein indicator for the titration, the acid required 36.0 cm3 of the alkali KOH for neutralisation what was the concentration of the acid?  In the appendix this is titration procedure 2.
      • 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 Mr(H2SO4) = 2 + 32 + (4x16) = 98
      • concentration in g/dm3 is 0.045 x 98 = 4.41 g/dm3 
    • -
  • Titration Calculation Example 12.3
    • Given the equation: NaOH(aq) + HCl(aq) ==> NCl(aq) + H2O(l)
    • 25.00 cm3 portions of a dilute hydrochloric acid solution were titrated with a standard solution of sodium hydroxide solution of concentration 0.250 mol/dm3. In the appendix this is titration procedure 2.
    • Using phenolphthalein indicator for the titration, it was found that the average titration was 18.50 cm3 of sodium hydroxide, calculate (i) the molarity of the sodium hydroxide and (ii) its concentration in g/dm3.
      • moles NaOH = molarity NaOH x volume of NaOH (in dm3 = cm3/100)
      • moles NaOH = 0.250 x (18.5 / 1000) = 0.004625
      • In the equation 1 mole of HCl reacts with 1 mole of HCl
      • therefore in the titration reaction moles HCl = moles NaOH
      • therefore there were 0.004625 moles HCl in 25.00 cm3.
      • molarity = moles / volume in dm3     (1 dm3 = 1000 cm3)
      • (i) molarity HCl = 0.004625 / (25.00/1000) = 0.004625/0.025 = 0.185 mol/dm3
      • (ii) concentration = molarity x formula mass
        • formula mass HCl = 1 + 35.5 = 36.5
        • = 0.185 x 36.5 = 6.75 g/dm3
    • -
  • Titration Calculation Example 12.4
    • Given the equation: 2NaOH(aq) + H2SO4(aq) ==> Na2SO4 + 2H2O(l)
    • 25.00 cm3 portions of a sodium hydroxide were titrated with a standardised solution of 0.75 mol/dm3 sulphuric acid solution using phenolphthalein indicator. In the appendix this is titration procedure 1.
    • If the average titration was 17.70 cm3 of sulfuric acid, what is the molar concentration of the sodium hydroxide?
      • moles H2SO4 in titration = molarity H2SO4 x volume in dm3
      • moles H2SO4  = 0.75 x (17.70/1000) = 0.013275 mol
      • From the balanced equation, for every mole of H2SO4, two moles of NaOH react
      • Therefore moles NaOH = 2 x moles H2SO4
      • moles NaOH = 0.013275 x 2 = 0.02655 mol
      • molarity of NaOH = moles NaOH / volume in dm3
      • molarity NaOH = 0.02655 / (25.00/1000) = 1.062 mol/dm3
    • -
  • Titration Calculation Example 12.5
    • Given the equation: NH3(aq) + HCl(aq) ==> NH4Cl(aq)
    • 5.00 cm3 portions of household ammonia were titrated with a standard hydrochloric acid solution of 1.00 mol/dm3. In the appendix this is titration procedure 2.
    • If the average titration, using methyl orange indicator, was 22.5 cm3 of hydrochloric acid, calculate (i) the molarity of the ammonia solution, and its concentration in (ii) g/dm3 and (iii) g/cm3.
      • (i) mol HCl in titration = molarity HCl x volume of HCl in dm3
      • mol HCl = 1.00 x (22.50/1000) = 0.0225 mol HCl
      • From the equation, 1 mole of NH3 reacts with 1 mole of HCl
      • Therefore mol HCl  = mol NH3 = 0.0225
      • molarity of NH3 = mol NH3 / volume NH3in dm3
      • molarity of NH3 = 0.0225 / (5.00/1000) = 4.50 mol/dm3
      • (ii) concentration = formula mass x molarity
      • formula mass NH3 = 14 + (3x1) = 17
      • concentration of NH3 = 17 x 4.50 = 76.5 g/dm3
      • (iii) since there are 1000 cm3 in 1 dm3
      • concentration of NH3 = 76.5/1000 = 0.0765 g/cm3
    • -
  • Titration Calculation Example 12.6
    • Given the equation: CH3COOH(aq) + NaOH(aq) ==> CH3COONa(aq) + H2O(l)
    • 25.00 cm3 portions of vinegar (ethanoic acid, CH3COOH, 'acetic acid') from a local supermarket were pipetted into a conical flask and titrated with a standardised solution of sodium hydroxide, of concentration 0.2000 mol/dm3 using phenolphthalein indicator. In the appendix this is titration procedure 2.
    • (i) If the average titration value was 14.70 cm3 of the sodium hydroxide solution, what is the molarity of the ethanoic acid in the vinegar?
      • moles NaOH in titration = molarity x volume in dm3
      • mole NaOH = 0.200 x (14.70/1000) = 0.00294 moles
      • from the equation moles NaOH = moles CH3COOH = 0.00294
      • molarity CH3COOH = mol CH3COOH/volume CH3COOH in dm3
      • molarity CH3COOH = 0.00294 / (25.00/1000) =  0.1176 mol/dm3
    • (ii) If a bottle of vinegar from the super-market contained 250 cm3 of liquid, how many grams of ethanoic acid are in the solution?
      • concentration CH3COOH = formula mass CH3COOH x molarity of CH3COOH
      • formula mass CH3COOH = 12 + (3x1) + 12 +(2x32) + 1 = 60
      • concentration CH3COOH = 60 x 0.1176 = 7.056 g/dm3
      • Since 1 dm3 = 1000 cm3, there must be proportionately
      • 7.056 x (250/1000) = 1.764 g of CH3COOH in the bottle of vinegar
    • -
  • To all GCSE/IGCSE/O Level/A Level students - Recently added the last four questions (12.3 to 12.6), if you spot any 'typos' let me know, and if you find the descriptions of the titrations helpful or you think something is missing in the titration method descriptions, let me know that too! Sorry I didn't have these ready for the summer exams of 2014.
  • See also acid-alkali titration questions for Advanced Level students

top sub-indexThere are more questions involving molarity in section 11. introducing molarity and section 14.3 on dilution

volumetric apparatus for a titration volumetric apparatus

A variety of apparatus you might come across, particularly the pipette (1) for measuring accurately volumes of solutions to be analysed by titration with a standard solution in a burette (3)

  • 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.
    • top sub-indexThe 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!)

type in answer click me for QUIZ!Honly  or multiple choice click me for QUIZ!Honly

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


 

APPENDIX - More examples of HOW TO DO TITRATIONS - apparatus and procedures

 

1. The titration of a weak base-alkali with a strong acid

e.g titrating ammonia (pipetted) with standardised hydrochloric acid (in burette)

The apparatus, chemicals and indicator colours are illustrated in the diagram on the left.

Initially the burette is clamped carefully in position and filled with standard hydrochloric acid (e.g. 0.10 to 1.0 mol/dm3, but accurately known, preferably to 4 sig. figs.). The acid is run through until the reading below the meniscus is 0.00 cm3 (the reading in the diagram is 7.00 cm3). The burette is usually calibrated to 50.00 cm3 (only 10.00 cm3 in diagram - couldn't fit rest of scale on!)

The ammonia solution is accurately measured out into the conical flask with e.g. a 25 cm3 pipette and suction bulb (see diagram further down). Add a few drops of methyl orange indicator to the ammonia solution and it should turn yellow for an alkali. Carefully place the conical flask under the tip of the burette so drops don't go astray!

The titration: You carefully add small portions of the acid, swirling after each addition and checking the colour of the indicator (not shown in the diagram, but its good to stand the flask on white tile). At the start of the titration the methyl orange indicator is yellow. As you add the acid you get 'splurges' of reddish-orange colour until the mixture is swirled in the conical flask. The swirling of the flask contents is important, it ensures all the added hydrochloric acid reacts with the ammonia solution.

Try to add dropwise when you seem to be near the orange colour at the endpoint. The end-point is an orange colour indicating when all the ammonia is neutralised by which ever acid you are using.

If you 'overshoot' the titration with excess acid, the methyl orange indicator turns red. The titration should be repeated several times with other 25 cm3 portions and the average (mean) titration value calculated to use in any subsequent calculations.

 

 

2. The titration of a weak/strong a strong acid with sodium hydroxide solution

e.g titrating ethanoic acid or hydrochloric acid (pipetted) with standardised sodium hydroxide solution (in burette)

The apparatus, chemicals and indicator colours are illustrated in the diagram on the left.

Initially the burette is clamped carefully in position and filled with standard sodium hydroxide solution (e.g. 0.10 to 1.0 mol/dm3, but accurately known, preferably to 4 sig. figs.). The sodium hydroxide solution is run through until the reading below the meniscus is 0.00 cm3 (the reading in the diagram is 7.00 cm3). The burette is usually calibrated to 50.00 cm3 (only 10.00 cm3 in diagram - couldn't fit rest of scale on!)

The acid solution is accurately measured out into the conical flask with e.g. a 25 cm3 pipette and suction bulb (see diagram further down). Add a few drops of phenolphthalein indicator to the acid solution and it should turn colourless for an acid. Carefully place the conical flask under the tip of the burette so drops don't go astray!

The titration: You carefully add small portions of the sodium hydroxide, swirling after each addition and checking the colour of the indicator (not shown in the diagram, but its good to stand the flask on white tile). At the start of the titration the phenolphthalein indicator is colourless. As you add the alkali you get 'splurges' of pink colour until the mixture is swirled in the conical flask. The swirling of the flask contents is important, it ensures all the added sodium hydroxide reacts with the acid in the flask.

Try to add dropwise when you seem to be near the faint pink colour of the endpoint. The end-point is the first faint, but permanent pink colour, that is when all the acid is neutralised by the sodium hydroxide.

If you 'overshoot' the titration with excess alkali, the phenolphthalein indicator becomes an even deeper pinkish-red. The titration should be repeated several times with other 25 cm3 portions and the average (mean) titration value calculated to use in any subsequent calculations.

 

 

3. The titration of a strong base-alkali with hydrochloric solution

e.g titrating sodium hydroxide solution (pipetted) with standardised hydrochloric solution (in burette)

The apparatus, chemicals and indicator colours are illustrated in the diagram on the left.

Initially the burette is clamped carefully in position and filled with standard hydrochloric acid (e.g. 0.10 to 1.0 mol/dm3, but accurately known, preferably to 4 sig. figs.). The hydrochloric acid is run through until the reading below the meniscus is 0.00 cm3 (the reading in the diagram is 7.00 cm3). The burette is usually calibrated to 50.00 cm3 (only 10.00 cm3 in diagram - couldn't fit rest of scale on!)

The alkali solution is accurately measured out into the conical flask with e.g. a 25 cm3 pipette and suction bulb (see diagram further down). Add a few drops of phenolphthalein indicator to the alkali solution and it should turn deep pink for an alkali. Carefully place the conical flask under the tip of the burette so drops don't go astray!

The titration: You carefully add small portions of the acid, swirling after each addition and checking the colour of the indicator (not shown in the diagram, but its good to stand the flask on white tile). At the start of the titration the phenolphthalein indicator is a deep reddish-pink in alkaline solution. As you add the acid you get 'splurges' of colourless solution until the mixture is swirled in the conical flask. The swirling of the flask contents is important, it ensures all the added hydrochloric acid reacts with the sodium hydroxide.

Try to add dropwise when you seem to be near the faintest pinkness left in the solution near the endpoint.

The end-point is when the last trace of pink colour first disappears from the solution. If you 'overshoot' the titration with excess acid, it still stays colourless! The titration should be repeated several times with other 25 cm3 portions and the average (mean) titration value calculated to use in any subsequent calculations.

 

 


top sub-indexSelf-assessment Quiz on titrations [vct]

type in answer click me for QUIZ!Honly  or multiple choice click me for QUIZ!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

  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 acid-alkali titration calculations, diagrams of apparatus, details of procedures (this page)

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

  14. Other calculations e.g. % purity, % percentage & theoretical yield, 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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