Titration Techniques: Your Guide to Volumetric Analysis & Stoichiometry

Hello! Welcome to your study notes on titration and volumetric analysis. Titration is a fundamental quantitative technique used in chemical laboratories to determine the exact concentration of an unknown solution (the analyte) by reacting it with a solution of known concentration (the titrant).

For example, chemists use volumetric analysis to determine the ethanoic acid content in vinegar, test the purity of pharmaceutical samples, or analyse the active carbonate ingredients in antacid tablets.

In this chapter, you will learn the theoretical foundations, standard solution preparation, correct lab glassware techniques, indicator selection, and quantitative stoichiometry calculations for HKDSE Chemistry.


Part 1: The Building Blocks - Key Concepts You Need to Know

Before carrying out titrations, let's review the fundamental quantitative concepts.

1.1 Stoichiometry & The Mole

Stoichiometry describes the quantitative mole relationships among reactants and products in a balanced chemical equation.

For example, in the neutralisation reaction:

\( \text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l) \)

The stoichiometric coefficients indicate that 1 mole of \( \text{HCl} \) reacts with exactly 1 mole of \( \text{NaOH} \) (a 1:1 mole ratio).

Quick Review: The Mole & Molar Mass
  • The Mole: 1 mole of any substance contains \( 6.02 \times 10^{23} \) particles (Avogadro's constant, \( L \)).
  • Molar Mass (\( M \)): The mass per mole of a substance (unit: \( \text{g mol}^{-1} \)). \( \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g mol}^{-1}\text{)}} \).

1.2 Molarity (Molar Concentration) & Dilution

Molarity (\( M \)) is the amount of solute in moles dissolved per \( 1\text{ dm}^3 \) of solution. The standard unit is \( \text{mol dm}^{-3} \) (or M).

\( \text{Number of moles (mol)} = \text{Molarity (mol dm}^{-3}\text{)} \times \text{Volume (dm}^3\text{)} \)

Unit Conversion: Always convert \( \text{cm}^3 \) to \( \text{dm}^3 \) by dividing by 1000: \( \text{Volume in dm}^3 = \frac{\text{Volume in cm}^3}{1000} \).

Dilution Formula

When deionised water is added to dilute a stock solution, the number of moles of solute remains constant:

\( M_1 V_1 = M_2 V_2 \)

where \( M_1 \) and \( V_1 \) are the initial molarity and volume, and \( M_2 \) and \( V_2 \) are the final molarity and total diluted volume.


Part 2: Standard Solutions & Primary Standards

A standard solution is a solution whose concentration is accurately known.

2.1 Primary Standards

A primary standard is a highly pure, stable chemical used to prepare a standard solution directly by accurate weighing and dissolving.

  • Key Criteria for a Primary Standard:
    - High degree of chemical purity (\( > 99.9\% \)).
    - High stability in air (must not be hygroscopic, deliquescent, or react with atmospheric \( \text{O}_2 \) or \( \text{CO}_2 \)).
    - High molar mass to minimise percentage errors during weighing.
    - Readily soluble in water.
  • Common Examples: Anhydrous sodium carbonate (\( \text{Na}_2\text{CO}_3 \)), hydrated oxalic acid (\( (\text{COOH})_2\cdot2\text{H}_2\text{O} \)), potassium hydrogen phthalate.
  • Substances Unsuitable as Primary Standards:
    - Solid \( \text{NaOH} \): Deliquescent (absorbs moisture from air) and absorbs atmospheric \( \text{CO}_2 \) to form \( \text{Na}_2\text{CO}_3 \).
    - Concentrated \( \text{HCl} \): Volatile; loses \( \text{HCl} \) gas readily so its exact concentration changes.
    (Note: Solutions of \( \text{NaOH} \) and \( \text{HCl} \) must be standardised against a primary standard before use.)

2.2 Preparation of a Standard Solution in a Volumetric Flask

  1. Weigh the primary standard accurately on an electronic balance using a weighing boat.
  2. Transfer the solid into a clean beaker and dissolve completely in a moderate volume of deionised water. Rinse the weighing boat into the beaker with deionised water.
  3. Pour the solution into a clean volumetric flask using a filter funnel.
  4. Rinse the beaker, glass stirring rod, and funnel several times with deionised water, transferring all washings into the volumetric flask.
  5. Add deionised water until the liquid level approaches the graduation mark. Use a dropper to add water dropwise until the bottom of the meniscus touches the mark at eye level.
  6. Stopper the flask and invert it repeatedly to ensure thorough mixing.

Part 3: Titration Techniques & Apparatus

3.1 Glassware and Rinsing Rules (Crucial HKDSE Exam Point)

  • Volumetric Pipette: Delivers an accurate, fixed volume (e.g., \( 25.0\text{ cm}^3 \)).
    Rinsing: Rinse with deionised water, then rinse with the solution it is to measure (analyte or standard).
  • Burette: Delivers a variable, precisely measured volume of titrant.
    Rinsing: Rinse with deionised water, then rinse with the titrant solution. Ensure no air bubble is trapped in the jet below the stopcock.
  • Conical Flask: Holds the reaction mixture while swirling.
    Rinsing: Rinse with deionised water ONLY. Never rinse with the analyte solution, as residual analyte would introduce extra moles and lead to an overestimation. Water droplets inside do not alter the number of moles of analyte transferred by the pipette.

3.2 Indicators and Selection

The equivalence point is the theoretical stage where stoichiometric equivalent quantities of acid and alkali have reacted. The end point is the observed experimental stage where the indicator permanently changes colour.

Rules for Indicator Selection:

  • Strong Acid vs. Strong Base: Sharp pH change around pH 4–10. Either Methyl Orange or Phenolphthalein is suitable.
  • Strong Acid vs. Weak Base (e.g., \( \text{HCl} \) vs. \( \text{NH}_3 \)): Equivalence point is acidic (\( \text{pH} < 7 \)). Use Methyl Orange (pH range: 3.1–4.4; colour change: yellow to orange/red).
  • Weak Acid vs. Strong Base (e.g., \( \text{CH}_3\text{COOH} \) vs. \( \text{NaOH} \)): Equivalence point is basic (\( \text{pH} > 7 \)). Use Phenolphthalein (pH range: 8.3–10.0; colour change: colourless to pale pink).
  • Weak Acid vs. Weak Base: No sharp pH change at equivalence point; acid-base titration with an indicator is not suitable.

3.3 Step-by-Step Titration Procedure

  1. Pipette \( 25.0\text{ cm}^3 \) of analyte into a clean conical flask rinsed with deionised water.
  2. Add 2–3 drops of suitable indicator. Place the flask on a white tile to view the colour transition clearly.
  3. Fill the burette with titrant and record the initial reading to 2 decimal places (e.g., \( 0.00\text{ cm}^3 \)).
  4. Perform a rapid trial (rough titration) to locate the approximate end point.
  5. Perform subsequent accurate titrations dropwise near the end point with constant swirling until one drop causes a distinct, permanent colour change.
  6. Repeat until at least two concordant titres (readings within \( \pm 0.10\text{ cm}^3 \) of each other) are obtained. Calculate the average of these concordant titres.

Part 4: Volumetric Stoichiometry Calculations

4.1 Direct Titration Calculation

Example: \( 25.0\text{ cm}^3 \) of an unlabelled \( \text{NaOH}(aq) \) solution required an average concordant titre of \( 22.50\text{ cm}^3 \) of \( 0.100\text{ mol dm}^{-3}\text{ HCl}(aq) \) for complete neutralisation. Calculate the concentration of the \( \text{NaOH} \) solution.

Step 1: Write the balanced chemical equation

\( \text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l) \)

Mole ratio of \( \text{HCl} : \text{NaOH} = 1 : 1 \).

Step 2: Calculate moles of the known standard (titrant)

\( \text{Moles of HCl} = 0.100\text{ mol dm}^{-3} \times \frac{22.50}{1000}\text{ dm}^3 = 2.25 \times 10^{-3}\text{ mol} \)

Step 3: Relate moles using stoichiometric mole ratio

\( \text{Moles of NaOH} = \text{Moles of HCl} = 2.25 \times 10^{-3}\text{ mol} \)

Step 4: Calculate the concentration of the analyte

\( [\text{NaOH}] = \frac{2.25 \times 10^{-3}\text{ mol}}{\frac{25.0}{1000}\text{ dm}^3} = 0.0900\text{ mol dm}^{-3} \)

4.2 Back Titration

Back titration is used when an analyte is insoluble (e.g., \( \text{CaCO}_3 \) in eggshells or limestone), reacts slowly, or is volatile.

  1. A known excess volume of standard acid (e.g., \( \text{HCl} \)) is added to react completely with the insoluble analyte.
  2. The remaining unreacted (excess) acid is then titrated against a standard alkali (e.g., \( \text{NaOH} \)).
  3. Calculation Logic:
    \( \text{Total moles of acid added} = \text{Moles of acid reacted with analyte} + \text{Moles of excess acid unreacted} \)
    \( \text{Moles of acid reacted with analyte} = \text{Total acid added} - \text{Excess acid titrated} \)

Part 5: Limiting Reactants in Stoichiometry

In non-equimolar chemical reactions, the limiting reactant is completely consumed first and governs the maximum theoretical yield of product.

  1. Calculate initial moles of each reactant from given masses or solution volumes.
  2. Divide moles of each reactant by its stoichiometric coefficient in the balanced equation.
  3. The reactant with the lowest mole-to-coefficient ratio is the limiting reactant. All theoretical product yields and reactant consumptions must be calculated from this limiting amount.