Acid-base titrations

1. Overview

An acid-base titration is a fundamental laboratory technique used to determine the exact volume of one solution needed to react completely with a known volume of another solution. This process is essential for calculating the unknown concentration of an acid or an alkali through a neutralisation reaction.

Key Definitions

• Titration: A method of quantitative chemical analysis used to determine the concentration of an unknown solution.
• End-point: The point during a titration when the indicator changes colour, signaling that the reaction is complete.
• Indicator: A chemical that changes colour depending on the pH, used to identify the end-point.
• Burette: A long, graduated glass tube with a tap at the bottom used to deliver known, variable volumes of a liquid.
• Pipette: A piece of glassware used to measure and transfer a highly accurate, fixed volume of a liquid.
• Titre: The volume of solution added from the burette during a titration.
• Concordant results: Titres that are within 0.10 cm³ of each other.

Core Content

The Apparatus

To perform a titration, specific glassware is required to ensure high precision:

• Volumetric Pipette: Used to measure a fixed volume (usually 25.0 cm³) of the base/acid into the conical flask.
• Burette: Filled with the other reactant; it allows for the controlled addition of liquid drop-by-drop.
• Conical Flask: Used to hold the reaction mixture because its shape allows for easy swirling without splashing.
• White Tile: Placed under the flask to make the indicator colour change easier to see.

The Procedure

1. Use a pipette and pipette filler to measure exactly 25.0 cm³ of alkali into a clean conical flask.
2. Add a few drops of a suitable indicator (e.g., phenolphthalein) to the flask.
3. Fill a burette with acid and record the initial volume reading.
4. Slowly add the acid from the burette to the flask, swirling the flask constantly.
5. As the end-point approaches, add the acid drop-by-drop until the indicator undergoes a permanent colour change.
6. Record the final volume on the burette and calculate the titre (Final volume - Initial volume).
7. Repeat the experiment until you achieve concordant results (two or more results within 0.10 cm³ of each other).

Identifying the End-point

Indicators are used to show when the acid has exactly neutralised the base. Common indicators used in IGCSE include:

Indicator	Colour in Acid	Colour in Alkali	End-point Colour
Methyl orange	Red	Yellow	Orange
Phenolphthalein	Colourless	Pink	Pale Pink
Litmus	Red	Blue	Purple

Neutralisation Reactions

The chemical reaction occurring in the flask is a neutralisation reaction.

Word Equation: $\text{Acid} + \text{Alkali} \rightarrow \text{Salt} + \text{Water}$

Symbol Equation (Example: Hydrochloric acid and Sodium hydroxide): $HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)$

Symbol Equation (Example: Sulfuric acid and Potassium hydroxide): $H_2SO_4(aq) + 2KOH(aq) \rightarrow K_2SO_4(aq) + 2H_2O(l)$

Extended Content (Extended Only)

There is no additional supplement-specific content for the procedural description of titrations in this section. However, the calculation of concentrations using titration data is covered in Topic 3: Stoichiometry.

Key Equations

• Titre Calculation: $\text{Titre} = \text{Final Burette Reading} - \text{Initial Burette Reading}$
• Average (Mean) Titre: $\text{Mean Titre} = \frac{\text{Sum of concordant titres}}{\text{Number of concordant titres}}$

Common Mistakes to Avoid

• ❌ Wrong: Including the "rough" (first) titration when calculating the mean titre.
  • ✓ Right: Only use concordant results (those within 0.10 cm³ of each other) for the average.
• ❌ Wrong: Reading the burette from the top of the liquid curve.
  • ✓ Right: Always read the volume from the bottom of the meniscus at eye level.
• ❌ Wrong: Forgetting to remove the funnel from the top of the burette after filling.
  • ✓ Right: Always remove the funnel, as remaining drops could fall into the burette during the titration, changing the volume reading.
• ❌ Wrong: Using a beaker instead of a conical flask.
  • ✓ Right: Use a conical flask to allow for vigorous swirling without losing any of the reaction mixture.

Exam Tips

• Burette Readings: Always record burette readings to two decimal places (e.g., 22.40 cm³, not 22.4 cm³). The second decimal digit should be either a '0' or a '5'.
• Command Words: If asked to "Describe how to perform a titration," ensure you mention rinsing the equipment (burette with acid, pipette with alkali) to prevent contamination and dilution.
• Real-world contexts: Titrations are often used to find the concentration of vinegar (ethanoic acid), the purity of a sample, or the concentration of a commercial cleaning product.
• Table Formatting: In practical exams, always present your results in a clear table with "Initial", "Final", and "Titre" rows/columns, all including units (cm³).

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0620 Theory papers.

Exam-Style Question 1 — Short Answer [6 marks]

Question:

A student performs a titration to determine the concentration of a hydrochloric acid solution. They titrate the hydrochloric acid with a standard solution of sodium hydroxide of known concentration.

(a) State the name of the piece of apparatus used to accurately measure a fixed volume of the sodium hydroxide solution. [1]

(b) Describe how the student would use this apparatus to accurately measure the fixed volume of sodium hydroxide solution. [3]

(c) State the colour change that would be observed at the end-point of the titration if methyl orange indicator is used. [2]

Worked Solution:

(a)

1. A pipette. [This is the apparatus designed for accurate volume measurement.]

How to earn full marks:

• Must state "pipette", not burette, measuring cylinder, etc.

(b)

1. Rinse the pipette with the sodium hydroxide solution. [This ensures the pipette is free from contaminants and pre-conditioned with the solution being measured.]
2. Use the pipette to draw the sodium hydroxide solution up to the mark. [Carefully fill the pipette to the graduation mark.]
3. Slowly release the sodium hydroxide solution into the conical flask until the bottom of the meniscus touches the graduation mark. [Ensure the bottom of the meniscus is level with the mark on the pipette for accurate volume delivery. Do not blow out the last drop.]

How to earn full marks:

• Mention rinsing the pipette.
• Mention filling to the mark.
• Mention the meniscus.

(c)

1. The solution changes from yellow to red. [Methyl orange is yellow in alkaline conditions and red in acidic conditions. The end-point is when the solution just becomes acidic.]

How to earn full marks:

• Must state "yellow to red" in that order.
• Do not accept orange to red.

Common Pitfall: Many students confuse the use of pipettes and burettes. Remember a pipette is used to accurately measure a fixed volume, while a burette is used to deliver a variable volume. Also, be precise with indicator colours; "orange" is not the starting colour for methyl orange in alkaline conditions.

Exam-Style Question 2 — Short Answer [5 marks]

Question:

(a) Define the term 'end-point' in the context of an acid-base titration. [2]

(b) State two properties of a suitable indicator for an acid-base titration. [2]

(c) Suggest a reason why it is important to swirl the conical flask during a titration. [1]

Worked Solution:

(a)

1. The end-point is the point in a titration when the indicator changes colour. [The end-point is signalled by a visible change in the indicator.]
2. Indicating that the acid has completely neutralised the base (or vice versa). [This marks the point of complete reaction based on the indicator's behaviour.]

How to earn full marks:

• Mention the colour change of the indicator.
• Mention the neutralisation of acid and base.

(b)

1. The colour change should be distinct and easily observable. [A clear colour change makes it easy to identify the end-point accurately.]
2. The colour change should occur rapidly with the addition of a single drop of titrant. [A sharp colour change ensures minimal over-titration.]

How to earn full marks:

• Mention the colour change being distinct.
• Mention the colour change occurring rapidly.

(c)

1. To ensure thorough mixing of the reactants. [Swirling ensures the acid and base are well-mixed, so the reaction proceeds efficiently and the end-point is reached accurately.]

How to earn full marks:

• Must mention mixing or reaction.

Common Pitfall: The end-point is not exactly the same as the equivalence point (the theoretical point of perfect neutralisation), but it's the best visual estimate we can get. Also, remember that a good indicator should have a clear and sharp colour change, not a gradual one.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A student wants to determine the concentration of ethanoic acid in vinegar. They titrate 25.0 cm$^3$ of the vinegar solution with a 0.100 mol/dm$^3$ solution of sodium hydroxide. The student performs the titration three times and obtains the following results:

Titration	Initial burette reading (cm$^3$)	Final burette reading (cm$^3$)	Volume of NaOH used (cm$^3$)
1	0.50	26.20	25.70
2	0.20	25.50	25.30
3	0.00	25.20	25.20

(a) Use the student's results to calculate the average volume of sodium hydroxide used in the titration. [2]

(b) The equation for the reaction between ethanoic acid and sodium hydroxide is: $CH_3COOH(aq) + NaOH(aq) \rightarrow CH_3COONa(aq) + H_2O(l)$ Calculate the number of moles of sodium hydroxide used in the average titration. [2]

(c) Deduce the number of moles of ethanoic acid in the 25.0 cm$^3$ of vinegar solution. [1]

(d) Calculate the concentration of ethanoic acid in the vinegar solution, in mol/dm$^3$. [3]

Worked Solution:

(a)

1. Identify concordant titres: 25.30 cm$^3$ and 25.20 cm$^3$ [Concordant titres are those within 0.2 cm$^3$ of each other.]
2. Calculate the average volume: (25.30 + 25.20) / 2 = 25.25 cm$^3$ [Add the concordant titres and divide by the number of concordant titres.]
3. Convert to dm$^3$: 25.25 / 1000 = 0.02525 dm$^3$ [Volume needs to be in dm$^3$ for calculations.]

How to earn full marks:

• Identify the two correct titres.
• Calculate the average correctly: $\boxed{0.02525 \text{ dm}^3}$
• Correct unit conversion.

(b)

1. Use the formula: moles = concentration × volume [This is the relationship between moles, concentration, and volume.]
2. Calculate the moles of NaOH: moles = 0.100 mol/dm$^3$ × 0.02525 dm$^3$ = 0.002525 mol [Substitute the values into the formula.]

How to earn full marks:

• State the formula.
• Calculate the moles correctly: $\boxed{0.002525 \text{ mol}}$

(c)

1. From the equation, the mole ratio of $CH_3COOH$ to $NaOH$ is 1:1. [The balanced equation shows the stoichiometry of the reaction.]
2. Therefore, the number of moles of $CH_3COOH$ is equal to the number of moles of $NaOH$: 0.002525 mol. [Since the ratio is 1:1, the moles are the same.]

How to earn full marks:

• State the correct mole ratio.
• Deduce the correct number of moles: $\boxed{0.002525 \text{ mol}}$

(d)

1. Convert the volume of vinegar to dm$^3$: 25.0 cm$^3$ / 1000 = 0.025 dm$^3$ [Volume needs to be in dm$^3$ for the calculation.]
2. Calculate the concentration of ethanoic acid: concentration = moles / volume [This is the formula to calculate concentration.]
3. Concentration = 0.002525 mol / 0.025 dm$^3$ = $\boxed{0.101 \text{ mol/dm}^3}$ [Substitute the values into the formula.]

Common Pitfall: Remember to only average the concordant titres (those close to each other). Forgetting to convert cm$^3$ to dm$^3$ is a very common mistake, so double-check your units before calculating moles or concentrations. Also, pay close attention to the mole ratio from the balanced equation.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A student investigates the reaction between dilute sulfuric acid and barium hydroxide solution using titration. The student adds 25.0 cm$^3$ of barium hydroxide solution to a conical flask and titrates it with 0.050 mol/dm$^3$ sulfuric acid solution, using methyl orange as an indicator. The student repeats the titration several times and obtains the following concordant results: 24.80 cm$^3$, 25.20 cm$^3$, and 25.00 cm$^3$.

(a) Calculate the average volume of sulfuric acid used in the titration. [1]

(b) Write the balanced chemical equation for the reaction between sulfuric acid and barium hydroxide. [2]

(c) Calculate the number of moles of sulfuric acid used in the average titration. [2]

(d) Deduce the number of moles of barium hydroxide in the 25.0 cm$^3$ of solution. [1]

(e) Calculate the concentration of the barium hydroxide solution in mol/dm$^3$. [3]

Worked Solution:

(a)

1. Calculate the average volume: (24.80 + 25.20 + 25.00) / 3 = $\boxed{25.00 \text{ cm}^3}$ [Add the volumes and divide by the number of volumes.]

How to earn full marks:

• Calculate the average correctly.

(b)

1. $H_2SO_4(aq) + Ba(OH)_2(aq) \rightarrow BaSO_4(s) + 2H_2O(l)$ [Sulfuric acid reacts with barium hydroxide to produce barium sulfate and water.]

How to earn full marks:

• Correct reactants and products.
• Correct balancing of the equation.

(c)

1. Convert cm$^3$ to dm$^3$: 25.00 cm$^3$ / 1000 = 0.025 dm$^3$ [The volume needs to be in dm$^3$ for the calculation.]
2. Use the formula: moles = concentration × volume [This is the relationship between moles, concentration, and volume.]
3. Calculate the moles of $H_2SO_4$: moles = 0.050 mol/dm$^3$ × 0.025 dm$^3$ = $\boxed{0.00125 \text{ mol}}$ [Substitute the values into the formula.]

How to earn full marks:

• Correctly convert cm$^3$ to dm$^3$.
• State the formula.
• Calculate the moles correctly.

(d)

1. From the equation, the mole ratio of $H_2SO_4$ to $Ba(OH)_2$ is 1:1. [The balanced equation shows the stoichiometry of the reaction.]
2. Therefore, the number of moles of $Ba(OH)_2$ is equal to the number of moles of $H_2SO_4$: $\boxed{0.00125 \text{ mol}}$ [Since the ratio is 1:1, the moles are the same.]

How to earn full marks:

• State the correct mole ratio.
• Deduce the correct number of moles.

(e)

1. Convert the volume of barium hydroxide solution to dm$^3$: 25.0 cm$^3$ / 1000 = 0.025 dm$^3$ [Volume needs to be in dm$^3$ for the calculation.]
2. Use the formula: concentration = moles / volume [This is the formula to calculate concentration.]
3. Concentration of $Ba(OH)_2$ = 0.00125 mol / 0.025 dm$^3$ = $\boxed{0.050 \text{ mol/dm}^3}$ [Substitute the values into the formula.]

How to earn full marks:

• Correctly convert cm$^3$ to dm$^3$.
• State the correct formula.
• Calculate the concentration correctly.

Common Pitfall: Make sure you write the balanced equation correctly before determining the mole ratio. Barium sulfate is insoluble and forms a precipitate. Also, remember to include units in your final answer.