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

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:

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 $H_2SO_4$.

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.

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

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.