Acid-Base Titrations

The Five Mandatory Titrations and Primary Standards

Every acid-base titration question in Section A stems from five core practicals:

1. Preparation of a standard solution of sodium carbonate.
2. Standardisation of a hydrochloric acid solution using standard sodium carbonate.
3. Standardisation of a sodium hydroxide solution using standard hydrochloric acid.
4. Determination of the concentration of ethanoic acid in commercial vinegar.
5. Determination of the water of crystallisation in hydrated sodium carbonate (washing soda).

A standard solution is a solution of accurately known concentration. When we make one directly by weighing out a solid and dissolving it to a known volume, that solid must be a primary standard.

A primary standard is a substance that can be obtained in a pure, stable form, of known formula, so that a standard solution can be made by weighing it out accurately and dissolving it in a known volume of water. To work on the balance, it must satisfy strict criteria:

• High purity: it is available in a very pure state (at least 99.9% pure), so the mass weighed out is effectively all target substance.
• Stability: it does not decompose or react with gases in the air.
• Known chemical formula: its relative formula mass can be calculated with certainty.
• Non-hygroscopic: it does not absorb water vapour from the air, which would add unmeasured water weight.
• High relative molar mass: a larger mass must be weighed out on the balance, making the percentage weighing error significantly smaller.
• Solubility: it dissolves completely in water and reacts according to a single, known balanced equation.

Anhydrous sodium carbonate ($\text{Na}_2\text{CO}_3$, relative formula mass 106, molar mass $M = 106\text{ g mol}^{-1}$) is the primary standard for acid-base work. Hydrated sodium carbonate can also serve if weighed rapidly, because the crystals are efflorescent (they lose water of crystallisation to dry air). Other accepted primary standards across the Leaving Certificate include ammonium iron(II) sulfate, potassium dichromate, ethanedioic acid (oxalic acid), and potassium hydrogenphthalate.

Substances that fail these criteria cannot be weighed out directly. Solid sodium hydroxide is deliquescent; it absorbs atmospheric moisture so rapidly that it dissolves in the absorbed water, and it also absorbs carbon dioxide gas. Concentrated hydrochloric acid fumes constantly, losing hydrogen chloride gas and allowing its concentration to drift. We prepare approximate solutions of both and standardise them experimentally.

Preparing a Standard Sodium Carbonate Solution (250 cm³)

1. Accurately weigh roughly $2.65\text{ g}$ of anhydrous $\text{Na}_2\text{CO}_3$ on a clean clock glass using an electronic balance reading to at least $0.001\text{ g}$.
2. Transfer the solid into a beaker containing about $100\text{ cm}^3$ of deionised water. Rinse the clock glass with deionised water into the beaker using a wash bottle so that no solute particles remain on the glass.
3. Stir with a clean glass rod until all crystals dissolve completely.
4. Pour the solution through a clean glass funnel into a $250\text{ cm}^3$ volumetric flask. Rinse the beaker, glass rod, and funnel with deionised water from the wash bottle, draining all washings into the volumetric flask (a quantitative transfer).
5. Add deionised water until the level is just below the graduation mark on the neck.
6. With your eye level with the mark to eliminate parallax error, use a dropper to add deionised water dropwise until the bottom of the meniscus rests exactly on the graduation mark.
7. Stopper the flask firmly, hold the stopper securely, and invert the flask about 20 times to achieve complete mixing and a uniform concentration.

Volumetric Apparatus, Rinsing Rules, and Titration Setup

Accurate and concordant titres depend on rinsing each piece of glassware correctly before use. Rinsing errors systematically shift your recorded volumes.

Describing and Drawing the Titration Set-Up

When asked to draw or describe the titration apparatus, include:

• A burette clamped vertically in a burette clamp attached to a retort stand.
• The stopcock (tap) positioned near the bottom, with a narrow jet below it completely filled with liquid and free of air bubbles.
• A conical flask positioned beneath the burette jet, resting on a white tile to make the first permanent colour change easy to see.
• Burette contents clearly labelled (for example, '$\text{HCl}$ solution of unknown concentration') and conical flask contents clearly labelled (for example, '$25.0\text{ cm}^3$ standard $\text{Na}_2\text{CO}_3$ solution + 2–3 drops methyl orange').
• Associated measuring tools: a $25\text{ cm}^3$ pipette fitted with a safety pipette filler, and a $250\text{ cm}^3$ volumetric flask with a stopper and single graduation mark on its narrow neck.

Filling the Burette and Removing Air Bubbles

Fill the burette using a clean funnel, but remove the funnel immediately after filling. If left in place, drops hanging on the funnel stem can fall into the burette during the titration, making the recorded titre artificially low. Open the tap fully into a waste beaker to fill the narrow jet below the tap and expel any trapped air bubble. If an air bubble dislodges during the titration run, the burette reading drops without that volume entering the flask, making the recorded titre too high.

Meniscus Alignment and Reading Precision

For colourless and pale solutions, read the bottom of the curved meniscus at eye level to eliminate parallax error. For intensely coloured solutions where the bottom is obscured (such as potassium manganate(VII)), read the top of the meniscus, using the identical point for both initial and final readings.

A burette is graduated in $0.1\text{ cm}^3$ divisions and read to the nearest $0.05\text{ cm}^3$. Record all readings to two decimal places ending in $.00$ or $.05$ (for example, $23.45\text{ cm}^3$). Because a titre requires two readings (initial and final), each reading carries an uncertainty of $\pm0.05\text{ cm}^3$, giving a combined reading uncertainty of $\pm0.1\text{ cm}^3$.

A $25\text{ cm}^3$ pipette delivers one fixed volume with an uncertainty of about $\pm0.06\text{ cm}^3$, compared to roughly $\pm0.5\text{ cm}^3$ for a graduated cylinder. A pipette is calibrated to deliver: drain it under gravity, touch the jet tip against the inside neck of the conical flask, and leave the tiny drop trapped in the tip. Never blow that final drop out, or the delivered volume will be too large.

Recording Results and Concordancy

Perform one rough titration to find the approximate end point, followed by accurate runs where titrant is added drop by drop with continuous swirling near the colour change. Accompany each run by rinsing down the inner walls of the conical flask with deionised water; this washes splashed reagents into the mixture without altering the total moles present.

Accurate titres that agree within $0.1\text{ cm}^3$ are concordant. Discard the rough run and average only the concordant values:

Average titre = $(23.45 + 23.45 + 23.45) \div 3 = 23.45\text{ cm}^3$.

Titration Curves, Indicator Theory, and pH Calculations

An acid-base indicator is a weak acid in which the un-ionised molecule ($\text{HIn}$) exhibits a different colour from its conjugate base ($\text{In}^-$):

In acidic solutions, high $[\text{H}^+]$ shifts the position of equilibrium to the left by Le Châtelier's principle, showing Colour A. Adding base removes $\text{H}^+$ ions, pulling the equilibrium to the right and showing Colour B.

The equivalence point represents the stage where stoichiometric amounts of acid and base have reacted in the exact ratio given by the balanced equation. The end point is the stage where the indicator permanently changes colour. An indicator is suitable only when its colour-change pH interval lies entirely within the vertical, steep section of the titration curve.

Why the Equivalence pH is Not Always 7

The salt produced during neutralisation can hydrolyse with water. In a vinegar titration, sodium ethanoate dissociates into ethanoate ions ($\text{CH}_3\text{COO}^-$). These act as a Brønsted-Lowry base, accepting protons from water:

This generation of $\text{OH}^-$ makes the equivalence solution alkaline (pH ~8.7). Phenolphthalein changes colour between pH 8.2 and 10.0, sitting directly across this jump, whereas methyl orange changes between 3.1 and 4.4 and would change long before the equivalence point is reached.

Acid-Base Definitions and pH Relationships

• Brønsted-Lowry acid: a substance that donates a proton ($\text{H}^+$).
• Brønsted-Lowry base: a substance that accepts a proton.
• Conjugate acid-base pair: two chemical species that differ by a single proton. In $\text{CH}_3\text{COOH} + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}_3\text{O}^+$, the conjugate pairs are $\text{CH}_3\text{COOH} / \text{CH}_3\text{COO}^-$ and $\text{H}_3\text{O}^+ / \text{H}_2\text{O}$.
• Strong vs Weak: A strong acid or base dissociates completely in water (such as $\text{HCl}$ or $\text{NaOH}$). A weak acid or base dissociates only partially in water (such as $\text{CH}_3\text{COOH}$ or $\text{NH}_3$).
• Concentrated vs Dilute: 'Concentrated' refers to a high amount of solute per litre of solution; 'strong' refers strictly to the degree of dissociation. Ethanoic acid can be concentrated, but it is always weak.
• Amphoteric: a substance capable of acting as either an acid or a base (such as $\text{H}_2\text{O}$).

Key mathematical relationships:

• For $0.100\text{ mol l}^{-1}\text{ HCl}$: $[\text{H}_3\text{O}^+] = 0.100\text{ mol l}^{-1} \Rightarrow \text{pH} = -\log(0.100) = 1.00$.
• For $0.100\text{ mol l}^{-1}\text{ NaOH}$: $[\text{OH}^-] = 0.100\text{ mol l}^{-1} \Rightarrow [\text{H}_3\text{O}^+] = 1.0 \times 10^{-14} \div 0.100 = 1.0 \times 10^{-13}\text{ mol l}^{-1} \Rightarrow \text{pH} = 13.00$.
• For a weak acid where $K_a = \frac{[\text{H}_3\text{O}^+][\text{A}^-]}{[\text{HA}]}$: $[\text{H}_3\text{O}^+] = \sqrt{K_a \times c}$. For $0.100\text{ mol l}^{-1}$ ethanoic acid ($K_a = 1.8 \times 10^{-5}$), $[\text{H}_3\text{O}^+] = \sqrt{1.8 \times 10^{-5} \times 0.100} = 1.34 \times 10^{-3}\text{ mol l}^{-1} \Rightarrow \text{pH} = 2.87$.

Mandatory Experiments: Standardising Acids and Bases

Volumetric calculations rely on stoichiometric ratios established by the balanced chemical equation.

A diprotic acid or a metal carbonate always introduces a factor of 2 into the mole ratio.

Mandatory Practical 1 & 2: Standardising Hydrochloric Acid

• Purpose: to determine the accurate concentration of an approximate bench $\text{HCl}$ solution using primary standard $\text{Na}_2\text{CO}_3$.
• Apparatus: $50.0\text{ cm}^3$ burette, $25.0\text{ cm}^3$ pipette with filler, $250\text{ cm}^3$ conical flask, white tile, wash bottle.
• Stoichiometry: $\text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{H}_2\text{O} + \text{CO}_2$ (ratio $1 : 2$).
• Method:

1. Pipette exactly $25.0\text{ cm}^3$ of standard $0.050\text{ mol l}^{-1}\text{ Na}_2\text{CO}_3$ solution into a conical flask previously rinsed with deionised water.
2. Add 2 to 3 drops of methyl orange indicator; the mixture turns yellow.
3. Fill the burette with $\text{HCl}$ after rinsing with deionised water and titrant; expel the jet air bubble and adjust to $0.00\text{ cm}^3$.
4. Titrate over a white tile, swirling continuously and washing down flask walls with deionised water.
5. Near the end point, add $\text{HCl}$ dropwise until one drop causes a permanent colour change from yellow to pink/red.
6. Repeat to obtain concordant titres within $0.1\text{ cm}^3$ and calculate their average.

• Gas testing: Effervescence occurs during titration due to $\text{CO}_2$ gas. Bubbling this gas through limewater turns the limewater milky/cloudy due to $\text{CaCO}_3$ precipitate.
• Sources of error: Leaving the funnel in the burette (titre too low); failing to purge the air bubble from the jet (titre too high).

Mandatory Practical 3: Standardising Sodium Hydroxide

• Purpose: to find the accurate concentration of approximate $\text{NaOH}$ using standardised $\text{HCl}$.
• Apparatus and Stoichiometry: $\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}$ (ratio $1 : 1$).
• Method:

1. Pipette $25.0\text{ cm}^3$ of approximate $\text{NaOH}$ solution into a clean conical flask.
2. Add 2 to 3 drops of methyl orange (solution turns yellow).
3. Titrate against standard $\text{HCl}$ from the burette until the yellow changes permanently to pink/red.
4. Obtain concordant titres and calculate the exact concentration of $\text{NaOH}$.

• Safety: Sodium hydroxide is caustic and causes severe chemical burns. Concentrated acids are corrosive. Always wear safety goggles and use a pipette filler; never pipette by mouth.

Titration of an Ammonia Solution

• Reaction: $\text{HCl} + \text{NH}_3 \rightarrow \text{NH}_4\text{Cl}$ (ratio $1 : 1$).
• Apparatus: Burette contains standard $\text{HCl}$; conical flask contains $25.0\text{ cm}^3$ of diluted ammonia solution.
• Indicator: Methyl orange, changing from yellow to pink/red at the end point.
• Gas testing: Ammonia gas released from concentrated stock turns damp red litmus paper blue and produces dense white fumes of ammonium chloride when brought near a glass rod dipped in concentrated hydrochloric acid.

Mandatory Experiments: Vinegar Analysis and Water of Crystallisation

Mandatory Practical 4: Ethanoic Acid in Vinegar

• Purpose: to determine the concentration of ethanoic acid in commercial vinegar in $\text{mol l}^{-1}$, $\text{g l}^{-1}$, and $\%\text{ (w/v)}$.
• Why dilute commercial vinegar: Commercial vinegar is roughly $0.8\text{ to }0.9\text{ mol l}^{-1}$. Titrating $25.0\text{ cm}^3$ directly against $0.100\text{ mol l}^{-1}\text{ NaOH}$ would require well over $200\text{ cm}^3$ of titrant—more than four full burette fillings, creating compounded measurement errors. Diluting the vinegar brings the required titre into the reliable $15\text{ to }25\text{ cm}^3$ range.
• Accurate Dilution Procedure:

1. Rinse a $10.0\text{ cm}^3$ or $25.0\text{ cm}^3$ pipette with deionised water and then with commercial vinegar.
2. Pipette the measured vinegar volume into a clean volumetric flask ($50\text{ cm}^3$, $100\text{ cm}^3$, or $250\text{ cm}^3$).
3. Add deionised water with swirling until the level sits just below the graduation mark.
4. Use a dropper to bring the bottom of the meniscus exactly onto the mark at eye level.
5. Stopper and invert 20 times to achieve complete mixing.
6. Dilution factor $= \frac{\text{Flask volume}}{\text{Pipetted volume}}$ (for example, $\frac{50.0}{10.0} = 5$, or $\frac{250.0}{25.0} = 10$).

• Titration steps: Pipette $25.0\text{ cm}^3$ of diluted vinegar into the conical flask, add 2 to 3 drops of phenolphthalein (remains colourless), and titrate with standard $\text{NaOH}$ from the burette. The end point is reached when a single drop produces a permanent pale pink colour that persists for at least 30 seconds.

Mandatory Practical 5: Water of Crystallisation in Hydrated Sodium Carbonate

• Purpose: to determine the value of $x$ in washing soda crystals, $\text{Na}_2\text{CO}_3 \cdot x\text{H}_2\text{O}$.
• Method:

1. Accurately weigh about $3.5\text{ g}$ of washing soda crystals on a clock glass and dissolve immediately in deionised water, quantitatively transferring into a $250\text{ cm}^3$ volumetric flask made up to the graduation mark.
2. Pipette $25.0\text{ cm}^3$ into a conical flask, add 2 to 3 drops of methyl orange, and titrate against standard $0.100\text{ mol l}^{-1}\text{ HCl}$ from the burette.
3. End point colour change: yellow to permanent pink/red.

• Handling precaution: Washing soda crystals are efflorescent. If left exposed to air before weighing, water of crystallisation escapes, leading to an artificially low value for $x$.

Thermochemistry of Neutralisation and Heat Calculations

Neutralisation is the chemical reaction between an acid and a base forming a salt and water:

Heat of neutralisation is the heat change when one mole of $\text{H}^+$ ions from an acid reacts with one mole of $\text{OH}^-$ ions from a base to form one mole of water, under stated conditions of temperature and pressure. For any strong acid reacting with any strong base, the experimental value is consistently about $-57.2\text{ kJ mol}^{-1}$. It is identical across all strong acid-base combinations because strong species dissociate completely, reducing the net process purely to hydrogen ions combining with hydroxide ions to form water.

Experimental Calorimetry Procedure

1. Measure $50.0\text{ cm}^3$ of $1.0\text{ mol l}^{-1}\text{ HCl}$ into an expanded polystyrene cup using a graduated cylinder or pipette; record its steady temperature.
2. Measure $50.0\text{ cm}^3$ of $1.0\text{ mol l}^{-1}\text{ NaOH}$ into a second container and verify that both solutions are at the identical starting temperature.
3. Add the $\text{NaOH}$ solution quickly to the $\text{HCl}$ in the polystyrene cup, replace the lid, stir continuously with a thermometer, and record the highest temperature reached.

• Why a polystyrene cup: Expanded polystyrene is a thermal insulator with very low heat capacity, minimising heat loss to the surroundings far better than glass.
• Temperature curve: The temperature rises rapidly because neutralisation is exothermic, reaching a maximum once neutralisation finishes, before slowly declining as heat radiates into the surroundings.

Heat produced is calculated using:

where $m$ is the total mass of the combined reaction solution in $\text{kg}$ (taking $100\text{ cm}^3 \approx 0.100\text{ kg}$), $c$ is the specific heat capacity ($4.18\text{ kJ kg}^{-1}\text{ K}^{-1}$), and $\Delta T$ is the temperature increase in $\text{K}$ or $^\circ\text{C}$. The enthalpy change is $\Delta H = -\frac{q}{\text{moles of water formed}}$.

Key terms

Standard Solution

A solution whose concentration is accurately and precisely known.

Primary Standard

A substance that can be obtained in a pure, stable form, of known formula, so that a standard solution can be made by weighing it out accurately and dissolving it in a known volume of water.

Standardisation

The laboratory procedure of determining the exact concentration of a solution by titrating it against a known standard solution.

Equivalence Point

The point during a titration at which stoichiometric amounts of acid and base, as dictated by the balanced equation, have completely reacted.

End Point

The point during a titration at which the indicator changes colour permanently, chosen to coincide with the equivalence point.

Deliquescent

The property of a solid absorbing moisture from the atmosphere until it completely dissolves in the absorbed water.

Efflorescent

The property of hydrated crystals losing their water of crystallisation to the atmosphere when exposed to air.

Conjugate Acid-Base Pair

Two chemical species that differ from each other by the transfer of a single proton.

Heat of Neutralisation

The heat change when one mole of hydrogen ions from an acid reacts with one mole of hydroxide ions from a base to form one mole of water, under stated conditions of temperature and pressure.

Quantitative Transfer

The complete transfer of every particle of a weighed solute into a volumetric flask by washing all contact apparatus with deionised water.