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Inquiry Question 5: How are acids and bases defined and how do they behave in aqueous solution?

Conduct an investigation to perform titrations of strong acid and strong base, weak acid and strong base, and weak base and strong acid, and analyse the data to determine concentration, pH at the equivalence point, and appropriate indicator selection

A focused answer to the HSC Chemistry Module 5 dot point on titrations. The four titration curve shapes, equivalence vs end point, indicator selection rules, calculating unknown concentrations from titration data, and worked HSC past exam questions.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-22

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
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In plain English

A titration is a controlled "add-a-little-at-a-time" experiment. You know exactly how much of one solution (the titrant) you are adding from a burette, and your job is to work out how much of the other solution (the analyte) was there to begin with. The indicator is just a colour-coded alarm: it is chosen so that its colour flips at (almost) the same moment the acid and base have exactly cancelled each other out, which chemists call the equivalence point. That "almost" matters. Because a strong acid meeting a strong base produces a neutral salt, the alarm should go off at pH 7. But if a weak acid reacts with a strong base, the leftover salt is slightly basic, so the true cancel-out point sits above pH 7, and you need an indicator whose colour flips up there instead, otherwise you stop adding titrant too early and under-report the concentration. Picking the wrong indicator is like setting a smoke alarm's sensitivity wrong: it will still go off, just not exactly when you needed it to.

What this dot point is asking

NESA wants you to interpret titration data, distinguish equivalence point from end point, recognise the four canonical titration curve shapes, select an appropriate indicator, and calculate an unknown concentration from titration data. The shape of every curve is set by the acid-base chemistry of the species involved and the pH math you used earlier in the module. Expect a 5-7 mark calculation in Section II that often combines stoichiometry with indicator justification.

The answer

Titration basics

A titration is a volumetric analysis in which a solution of known concentration (the titrant, usually in the burette) is added gradually to a solution of unknown concentration (the analyte, usually in a conical flask) until the reaction is complete.

The equivalence point is reached when stoichiometrically equivalent moles of acid and base have been mixed. The end point is when the indicator changes colour. Good experimental design makes these coincide.

Calculation pattern

For an acid-base titration with 1:1 stoichiometry:

c_{\text{unknown}} = \frac{c_{\text{titrant}} \times V_{\text{titrant}}}{V_{\text{unknown}}}

For diprotic acids or bases, include the stoichiometric ratio. For example, $H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + 2H_2O$ : moles of NaOH equals 2 times moles of $H_2SO_4$ .

Titration calculation checkpoints

Core formula: $n = cV$ (moles equals concentration times volume in litres), applied to the titrant first, then converted to moles of analyte using the balanced equation's mole ratio.
1:1 acid/base pairs (e.g. $HCl + NaOH$ ): moles of titrant equals moles of analyte directly.
Diprotic pairs (e.g. $H_2SO_4 + 2NaOH$ ): divide (or multiply) by the mole ratio from the balanced equation before finding concentration.
Indicator selection rule: choose an indicator whose colour-change pH range straddles the equivalence pH of that specific titration, not just "any indicator that changes colour near 7".
Equivalence pH by curve type: strong/strong $\approx 7$ ; weak acid/strong base $> 7$ ; weak base/strong acid $< 7$ .

Comparing titration curves

The shape of a titration curve depends on the strengths of the acid and base involved. The table below traces pH against the fraction of titrant added (acid being titrated with base), making the differences explicit.

Volume added	Strong acid / strong base	Weak acid / strong base	Weak base / strong acid
0%	~1.0	~2.9	~11.1
50% (mid-point)	~1.5	4.74 (= $pK_a$ )	9.26 (= 14 - $pK_b$ )
100% (equivalence)	7.0	8.7	5.3
150%	~12.5	~12.5	~1.5

Note that the 50% point of a weak acid (or weak base) titration occurs at $pH = pK_a$ (or $pH = 14 - pK_b$ ). This is the heart of the buffer region (see buffer systems). After equivalence, all three curves converge toward the pH of the excess titrant.

The upper line is strong acid / strong base (steep, equivalence pH 7). The lower line is weak acid / strong base (gentler approach, buffer plateau around $pK_a$ = 4.74, equivalence pH 8.7).

Why each curve has the equivalence pH it does

Strong acid / strong base (HCl + NaOH). Equivalence pH 7 because the salt (NaCl) does not hydrolyse. The transition is very steep, so several indicators work.

Weak acid / strong base ( $CH_3COOH$ + NaOH). Equivalence pH > 7 because the conjugate base ( $CH_3COO^-$ ) hydrolyses water to give $OH^-$ . The buffer plateau in the middle of the curve is exploited for buffer preparation.

Weak base / strong acid ( $NH_3$ + HCl). Equivalence pH < 7 because the conjugate acid ( $NH_4^+$ ) hydrolyses water to give $H_3O^+$ .

Weak acid / weak base. No sharp transition. No indicator gives a reliable end point. Not used quantitatively in HSC.

Indicator selection rule

Choose an indicator whose colour change range straddles the equivalence pH. If the equivalence pH is 8.7 (weak acid / strong base), phenolphthalein (8.3-10.0) brackets it; methyl orange (3.1-4.4) would change far too early.

Common HSC indicators

Indicator	pH range	Use
Methyl orange	3.1 to 4.4	Weak base / strong acid
Methyl red	4.2 to 6.3	Weak base / strong acid
Bromothymol blue	6.0 to 7.6	Strong acid / strong base
Phenolphthalein	8.3 to 10.0	Weak acid / strong base, also strong/strong

An owned illustrative curve for the third canonical shape, weak base titrated with strong acid, shows the mirror-image pattern: the curve starts high, has a buffer plateau at $pH = 14 - pK_b$ , and crosses equivalence below pH 7.

Worked example

A 20.0 mL sample of HCl of unknown concentration was titrated against 0.0500 mol/L NaOH. The average titre was 18.75 mL. Calculate the HCl concentration and identify a suitable indicator.

Step 1: Balanced equation.

HCl + NaOH \rightarrow NaCl + H_2O

1:1 stoichiometry.

Step 2: Moles of NaOH used.

n(NaOH) = 0.0500 \times 0.01875 = 9.375 \times 10^{-4} \text{ mol}

Step 3: Moles of HCl.

n(HCl) = 9.375 \times 10^{-4} \text{ mol}

Step 4: Concentration.

c(HCl) = \frac{9.375 \times 10^{-4}}{0.0200} = 0.0469 \text{ mol/L}

Step 5: Indicator. This is a strong acid / strong base titration. The equivalence pH is 7, and the steep transition allows several indicators. Bromothymol blue (pH 6.0 to 7.6) is the most precise choice because its range straddles pH 7. Phenolphthalein also works because the curve is steep enough that the colour change occurs within 1 mL of equivalence.

Examples in context

Example 1. Quality control of NSW commercial vinegars. Food chemists at the NSW DPI laboratory in Cobbitty test commercial vinegars against the food standards code, which requires ethanoic acid concentrations between 4 and 8 percent by mass. A pipetted 25 mL sample is titrated against standardised 0.100 mol L $^{-1}$ NaOH with phenolphthalein as indicator. The titre is multiplied by the molar mass of ethanoic acid and divided by sample volume to give the percentage. The curve is a weak acid / strong base shape with equivalence pH near 8.7, so phenolphthalein straddles the colour change. Methyl orange would mark an end point well before equivalence and falsely understate the acid content.

Example 2. NSW HSC depth study titration of aspirin tablets. A common Stage 6 depth study involves crushing a 300 mg aspirin tablet, dissolving in ethanol, and back-titrating against 0.0500 mol L $^{-1}$ NaOH. Aspirin (acetylsalicylic acid) behaves as a weak acid with $pK_a$ around 3.5. The chosen indicator is phenolphthalein because the equivalence pH sits well above 7 after the conjugate base hydrolyses. Students who use methyl orange typically report a "tablet content" of only 60 percent of the stated 300 mg, falling foul of the marker. The depth study lets candidates see firsthand why indicator range and equivalence pH must align.

Try this

Q1. Define the equivalence point and the end point of a titration, and state the criterion for choosing an indicator that makes them coincide. [3 marks]

Cue. Equivalence is stoichiometric mole balance; end point is when indicator changes colour; choose an indicator whose pH range straddles the equivalence pH.

Q2. A 25.0 mL sample of $H_2SO_4$ is titrated to equivalence with 32.50 mL of 0.150 mol L $^{-1}$ NaOH. Calculate the concentration of the sulfuric acid. [3 marks]

Cue. Apply $n(NaOH) = cV$ then divide by 2 for the 1:2 stoichiometry $H_2SO_4 + 2NaOH$ ; divide by the acid volume in litres.

Q3. A weak acid HA of unknown concentration is titrated with 0.100 mol L $^{-1}$ NaOH. The pH at the half-equivalence point is 4.74 and the equivalence point pH is 8.72. (a) State the $pK_a$ of HA. (b) Name a suitable indicator and justify the choice. (c) Sketch how the curve would change if a strong acid were used instead. [1+2+2 marks]

Cue. (a) $pK_a = 4.74$ . (b) Phenolphthalein (8.3 to 10.0) straddles equivalence pH 8.72. (c) Strong acid / strong base curve is steeper, equivalence pH 7, no buffer plateau.

Exam-style practice questions

Practice questions written in the style of NESA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2021 HSC5 marksA 25.0 mL sample of vinegar (containing ethanoic acid, CH₃COOH) was titrated against 0.100 mol/L NaOH. The mean titre was 22.40 mL. Calculate the concentration of ethanoic acid in the vinegar and identify a suitable indicator for the titration. Justify your indicator choice.

Show worked answer →

A 5 mark answer needs the stoichiometry, the concentration calculation, the indicator name, and a justification linked to the equivalence pH.

Equation.

CH_3COOH + NaOH \rightarrow CH_3COONa + H_2O

One mole of acid reacts with one mole of base.

Moles of NaOH used.

n(NaOH) = 0.100 \times 0.02240 = 2.24 \times 10^{-3} \text{ mol}

Moles of acid in the 25.0 mL sample. From 1:1 stoichiometry, $n(CH_3COOH) = 2.24 \times 10^{-3}$ mol.

Concentration of ethanoic acid.

c(CH_3COOH) = \frac{2.24 \times 10^{-3}}{0.0250} = 0.0896 \text{ mol/L}

Indicator. This is a weak acid / strong base titration, so the equivalence pH is above 7 (the conjugate base $CH_3COO^-$ is basic). The salt $CH_3COONa$ hydrolyses, giving an equivalence pH around 8.7.

Phenolphthalein (colour change pH 8.3 to 10.0) is appropriate because its colour change range straddles the equivalence pH. Methyl orange (pH 3.1 to 4.4) would change colour too early and give a falsely low titre.

Markers reward (1) the balanced equation, (2) correct stoichiometric calculation to 3 sig figs, (3) identifying the curve type, (4) naming an indicator with its pH range, (5) explicit justification linking range to equivalence pH.

2018 HSC3 marksDistinguish between the terms equivalence point and end point in an acid-base titration.

Show worked answer →

The equivalence point is the point in a titration at which stoichiometrically equivalent amounts of acid and base have been added. For a 1:1 reaction, moles of acid added equals moles of base. The equivalence point is a property of the chemistry of the titration.

The end point is the point at which the indicator changes colour. It depends on the indicator chosen, not on the chemistry alone.

A well-chosen indicator has its colour change range straddling the equivalence pH, so the end point coincides closely with the equivalence point. A poorly chosen indicator can make the end point occur before or after the equivalence point, giving an inaccurate titre.

Markers reward (1) a clear definition of each, (2) the contrast that equivalence is stoichiometric and end point is indicator-dependent, (3) the connection (a good indicator makes them approximately coincide).

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation3 marksState the criterion for choosing a suitable indicator for a titration, and identify a suitable indicator for a strong acid titrated with a strong base.

Show worked solution →

Criterion. Choose an indicator whose colour change pH range straddles the equivalence pH of the titration.

Strong acid / strong base. The equivalence pH is 7, and the pH jump through equivalence is very steep (roughly pH 4 to pH 10 within a fraction of a drop), so several indicators work. Bromothymol blue (pH 6.0 to 7.6) is the most precise choice because its range is centred closest to pH 7; phenolphthalein (8.3 to 10.0) also works because the transition is steep enough to still fall within about 0.05 mL of equivalence.

Marking criteria: 1 mark for stating the straddle criterion, 1 mark for naming a valid indicator, 1 mark for justifying the choice with its pH range and the equivalence pH.

foundation3 marksA 20.0 mL sample of

NH_3(aq)

of unknown concentration is titrated to equivalence with 27.85 mL of 0.120 mol/L HCl. Calculate the concentration of the ammonia solution.

Show worked solution →

Step 1: balanced equation (1:1 stoichiometry).

NH_3 + HCl \rightarrow NH_4Cl

Step 2: moles of HCl used.

n(HCl) = 0.120 \times 0.02785 = 3.342 \times 10^{-3} \text{ mol}

Step 3: moles of $NH_3$ (1:1 ratio).

n(NH_3) = 3.342 \times 10^{-3} \text{ mol}

Step 4: concentration.

c(NH_3) = \frac{3.342 \times 10^{-3}}{0.0200} = 0.167 \text{ mol/L}

Marking criteria: 1 mark for correct moles of HCl, 1 mark for correctly applying the 1:1 ratio, 1 mark for the final concentration to 3 significant figures with units.

core5 marksA 2.10 g sample of impure sodium carbonate (

Na_2CO_3

M = 106.0

g/mol) is dissolved in water and titrated against 0.200 mol/L HCl, using methyl orange indicator, requiring 32.60 mL to reach the end point. Calculate the percentage purity of the sodium carbonate sample, to 3 significant figures.

Show worked solution →

Step 1: balanced equation (2:1 stoichiometry, HCl to carbonate).

Na_2CO_3 + 2HCl \rightarrow 2NaCl + H_2O + CO_2

Step 2: moles of HCl used.

n(HCl) = 0.200 \times 0.03260 = 6.520 \times 10^{-3} \text{ mol}

Step 3: moles of $Na_2CO_3$ (divide by 2 for the 2:1 ratio).

n(Na_2CO_3) = \frac{6.520 \times 10^{-3}}{2} = 3.260 \times 10^{-3} \text{ mol}

Step 4: mass of pure $Na_2CO_3$ reacted.

m = n \times M = 3.260 \times 10^{-3} \times 106.0 = 0.34556 \text{ g}

Step 5: percentage purity.

\% \text{ purity} = \frac{0.34556}{2.10} \times 100 = 16.5\%

Marking criteria: 1 mark for the balanced equation with correct 2:1 ratio, 1 mark for correct moles of HCl, 1 mark for correctly halving to get moles of carbonate, 1 mark for the mass calculation, 1 mark for the final percentage to 3 significant figures. Note methyl orange is appropriate here because excess $CO_2$ /carbonic acid depresses the equivalence pH below 7 for this weak-base-type analyte.

core5 marksThe titration curve below is an owned illustrative curve of pH against volume of 0.100 mol/L HCl added to 25.0 mL of

NH_3(aq)

. Using features of the curve, identify (a) the approximate equivalence point volume, (b) the equivalence pH, and (c) a suitable indicator, justifying your choice.

Show worked solution →

Reading the curve: The steep vertical drop crosses the volume axis at approximately 25.0 mL, and the curve's inflection (mid-point of the vertical drop) sits at approximately pH 5.3.
(a) Equivalence volume: Approximately 25.0 mL of HCl, read from the midpoint of the steep vertical section of the curve.
(b) Equivalence pH: Approximately 5.3, below 7, because the ammonia is a weak base and its conjugate acid $NH_4^+$ hydrolyses water to produce $H_3O^+$ : $NH_4^+ + H_2O \rightleftharpoons NH_3 + H_3O^+$ .
(c) Indicator: Methyl red (pH 4.2 to 6.3) or methyl orange (pH 3.1 to 4.4) are suitable because their ranges straddle or sit just below the equivalence pH of 5.3; methyl red is the more precise choice as its range is centred closer to 5.3. Phenolphthalein (8.3 to 10.0) would be unsuitable because the colour change would occur well after equivalence, giving a falsely high titre.

Marking criteria: 1 mark for reading the equivalence volume from the curve, 1 mark for reading/stating the equivalence pH, 1 mark for identifying it as a weak base / strong acid curve shape, 1 mark for naming a suitable indicator, 1 mark for justifying with the pH range vs equivalence pH.

exam6 marksEvaluate the reliability of using a titration with a visual indicator, compared with a pH meter, to determine the equivalence point of a weak acid / strong base titration.

Show worked solution →

This is a 6-mark EVALUATE: markers reward a balanced judgement backed by chemistry, not just a list of pros and cons.

Band 6 plan.

Define what "reliability" means here: getting a consistent, accurate estimate of the true equivalence point across repeated trials.
Visual indicator: relies on the analyst's colour perception at the end point, which can vary between observers and is affected by lighting; for a weak acid / strong base curve, the pH transition, while still fairly steep, is less abrupt than strong/strong, so the indicator's finite colour-change RANGE (e.g. phenolphthalein 8.3 to 10.0) means the observed end point may sit slightly off the true equivalence pH of 8.7, introducing a small systematic error.
pH meter: gives a continuous, numerical pH reading, allowing the equivalence point to be identified precisely as the inflection point (point of steepest gradient) on a plotted curve, independent of observer colour perception; this removes the indicator-range error and improves both accuracy and reproducibility between trials.
Practical trade-offs: a pH meter requires calibration (buffer solutions of known pH) before use, is more expensive apparatus, and is slower to set up than a simple indicator; a school laboratory doing many repeat titrations for an average titre may still prefer an indicator for speed once a suitable one has been validated against pH-meter data.
Judgement: a pH meter is more reliable for precisely locating the equivalence point of a weak acid / strong base titration because it removes the indicator's inherent range error and observer bias, but a properly chosen indicator remains an acceptable, faster method once its suitability has been confirmed.

Model answer (excerpt). A pH meter improves reliability because it locates the true equivalence point as the inflection of the curve, independent of any single indicator's finite colour-change range; for the weak acid / strong base case, phenolphthalein's range of 8.3 to 10.0 sits close to, but not exactly on, the equivalence pH of 8.7, so a visual end point can drift slightly from trial to trial depending on how the observer judges the first faint colour change. A calibrated pH meter removes this observer-dependent error and allows the inflection point to be read directly from plotted data, but at the cost of calibration time and equipment expense, so a validated indicator remains a reasonable, faster choice for routine repeat titrations once its suitability has been confirmed against pH-meter data.

Marker's note: top-band answers (1) explicitly link the indicator's finite pH RANGE (not just "human error") to the systematic error against a weak acid/strong base curve, (2) explain why a pH meter locates the inflection point precisely, (3) weigh a genuine practical trade-off (calibration time/cost) rather than treating the pH meter as strictly superior in every respect, and (4) end with an explicit judgement.