HSC Exam Practice

Sample response. The equivalence point is the point on a titration curve at which the moles of acid exactly equal the moles of base that have reacted. It is located at the midpoint of the steepest section of the pH jump (the point of inflection of the sigmoid curve, where the rate of pH change per unit volume of titrant is greatest).

Marking notes. 1 mark for defining equivalence point as moles acid = moles base reacted; 1 mark for correctly describing location as midpoint of the steepest section (NOT highest/lowest pH point).

Sample response. For a 0.10 mol/L strong acid (e.g. HCl), the starting pH is ~1.00, because the acid ionises completely: pH = –log(0.10) = 1.00. For a 0.10 mol/L weak acid (e.g. acetic acid, K_a = 1.8 × 10^–5), the starting pH is ~2.87, because the acid ionises only partially: [H⁺] = √(1.8 × 10^–5 × 0.10) = 1.34 × 10^–3 mol/L, pH = 2.87. The difference is caused by the degree of ionisation: the strong acid fully dissociates, producing a high [H⁺]; the weak acid partially dissociates, producing a much lower [H⁺] for the same concentration.

Marking notes. 1 mark for correct starting pH for strong acid (~1) and reason (complete ionisation); 1 mark for correct starting pH for weak acid (>1, partial ionisation); 1 mark for explicitly linking the difference to degree of ionisation / equilibrium position.

Sample response. (1) Strong acid + strong base: EP pH = 7.00 (neutral salt, no hydrolysis). (2) Weak acid + strong base: EP pH > 7 (conjugate base hydrolyses to give OH–). (3) Strong acid + weak base: EP pH < 7 (conjugate acid hydrolyses to give H⁺). (4) Weak acid + weak base: no sharp equivalence point; EP pH is approximately 7 but there is no usable jump.

Marking notes. 1 mark per curve type correctly named with correct EP pH description (= 7, > 7, < 7, or “no sharp EP”). All four required for full marks.

Sample response. In a weak acid + weak base titration, both the acid and base contribute buffer regions that overlap throughout the titration. As a result, there is no sharp pH jump at the equivalence point — the pH changes gradually throughout. Because no narrow pH range corresponds specifically to the equivalence point, no standard colour indicator (which changes over a fixed 2-unit pH range) can reliably signal the endpoint without changing colour well before or after actual equivalence.

Marking notes. 1 mark for stating that dual overlapping buffer regions eliminate the sharp pH jump; 1 mark for explaining that without a sharp jump, no standard indicator can reliably detect the endpoint.

Sample response. Step 1: identify the equivalence point volume V_EP from the curve (midpoint of the steepest section). Step 2: calculate the half-equivalence volume = V_EP/2. Step 3: read the pH from the curve at V_EP/2. At this volume, n(A–) = n(HA) exactly, so the Henderson-Hasselbalch equation gives pH = pK_a + log(1) = pK_a. Therefore pK_a = pH at V_EP/2. K_a = 10^–pKa.

Marking notes. 1 mark for identifying V_EP (midpoint of steepest section) and calculating V_EP/2; 1 mark for stating that pH at V_EP/2 = pK_a with reasoning (n(A–) = n(HA) → log(1) = 0 → pH = pK_a); 1 mark for K_a = 10^–pKa.

Sample response. At the equivalence point of an acetic acid + NaOH titration, all the acetic acid (CH₃COOH) has been converted to sodium acetate (CH₃COO–Na⁺). The acetate ion CH₃COO– is the conjugate base of a weak acid; it undergoes base hydrolysis: CH₃COO– + H₂O ⇌ CH₃COOH + OH–. The production of OH– ions makes the solution basic, driving the pH above 7.00. The exact EP pH (~8.72) is calculated using K_b = K_w/K_a for the acetate ion.

Marking notes. 1 mark for identifying that only CH₃COO– remains at the EP; 1 mark for describing base hydrolysis of CH₃COO– producing OH– (equation not required but equation accepted); 1 mark for concluding that OH– production raises pH above 7 and linking to K_b calculation.

(a) V_EP = 20.00 mL (midpoint of steepest section, as labelled on the curve). EP pH = 8.31 (read from the labelled point). [2 marks: 1 per value]

(b) Half-EP volume = V_EP/2 = 10.00 mL. At 10.00 mL, pH = 3.74 (labelled half-EP on curve). Therefore pK_a = 3.74. K_a = 10^–3.74 = 1.8 × 10^–4. [2 marks: 1 for method / 1 for pK_a and K_a]

(c) n(NaOH) at EP = 0.1500 × 0.02000 = 3.000 × 10^–3 mol. From HCOOH + NaOH → HCOONa + H₂O (1:1 ratio): n(HCOOH) = 3.000 × 10^–3 mol. c(HCOOH) = 3.000 × 10^–3 / 0.02000 = 0.1500 mol/L. [2 marks: 1 for mole calculation / 1 for correct concentration]

(d) Phenolphthalein (pH range 8.3–10.0) is appropriate. The EP pH is 8.31, which falls within phenolphthalein’s transition range. As the titration passes through the sharp jump at 20 mL, phenolphthalein will change from colourless to faint pink precisely at the equivalence point. Methyl orange (pH 3.1–4.4) would change colour in the buffer region at approximately 10–12% neutralisation — completely unsuitable. [2 marks: 1 for naming phenolphthalein with correct range / 1 for justification using EP pH 8.31 within range]

(a) n(propanoic acid) = 0.200 × 0.02500 = 5.00 × 10^–3 mol. V_EP = 5.00 × 10^–3 / 0.200 = 0.02500 L = 25.00 mL. [1 mark]

(b) n(NaOH) added = 0.200 × 0.01500 = 3.00 × 10^–3 mol. Compare: n(NaOH) = 3.00 × 10^–3 < n(HA) = 5.00 × 10^–3 mol. Region: buffer region (0 < V < V_EP). n(HA) remaining = 5.00 × 10^–3 – 3.00 × 10^–3 = 2.00 × 10^–3 mol. n(A–) = 3.00 × 10^–3 mol. pH = pK_a + log(n(A–)/n(HA)) = 4.89 + log(3.00 × 10^–3 / 2.00 × 10^–3) = 4.89 + log(1.50) = 4.89 + 0.176 = 5.07. [3 marks: 1 for region identification; 1 for correct n(HA) and n(A–); 1 for correct pH]

(c) At V_EP = 25.00 mL, all HA → A–. [A–] = 5.00 × 10^–3 / 0.05000 = 0.100 mol/L. K_b(A–) = K_w/K_a = 1.0 × 10^–14 / 1.3 × 10^–5 = 7.69 × 10^–10. [OH–] = √(7.69 × 10^–10 × 0.100) = √(7.69 × 10^–11) = 2.77 × 10^–6 mol/L. pOH = 5.56. pH = 14 – 5.56 = 8.44. [2 marks: 1 for K_b and [OH–] method; 1 for correct pH > 7]

Sample response. The shape, equivalence point pH, and jump size of a titration curve are determined by whether the acid and base are strong or weak — specifically, by the buffer capacity each species provides near the equivalence point.

Strong acid + strong base (e.g. HCl + NaOH): no weak species present, so no buffer capacity exists at any point in the titration. Near the equivalence point, [H⁺] and [OH^–] simultaneously approach 10^–7 mol/L; the logarithmic nature of pH means even a 0.1% excess of either species causes a pH change of ~3 units. The result is the largest jump (~6–8 pH units) of any combination, centred precisely at pH 7.00 (neutral salt, no hydrolysis). Any indicator whose transition range falls within pH 4–10 is suitable.

Weak acid + strong base (e.g. CH₃COOH + NaOH): the weak acid provides a buffer region (HA + A–) before the equivalence point. The buffer resists pH change all the way to near the EP, reducing the jump size to ~4–6 pH units. At the EP, all HA has been converted to A–; A– hydrolyses (A– + H₂O ⇌ HA + OH–), producing OH– and driving EP pH above 7 (~8–9). Phenolphthalein (pH 8.3–10.0) is the appropriate indicator; methyl orange (3.1–4.4) transitions in the buffer region and is unsuitable.

Strong acid + weak base (e.g. HCl + NH₃): no buffer before the EP (strong acid is fully ionised). At the EP, the conjugate acid (NH₄⁺) hydrolyses: NH₄⁺ ⇌ H⁺ + NH₃, producing H⁺ and driving EP pH below 7 (~5–6). A buffer region appears after the EP (excess NH₃/NH₄⁺). Methyl orange (pH 3.1–4.4) or methyl red (4.4–6.2) can be used, as the transition range covers the EP pH below 7.

Weak acid + weak base (e.g. CH₃COOH + NH₃): both species contribute overlapping buffer regions throughout the titration, continuously resisting pH change. There is no sharp equivalence point jump; the pH rises gradually from start to finish. No standard colour indicator can reliably detect the EP — a potentiometric (pH meter) method is required.

In summary: the presence of a weak species introduces buffer capacity near the EP, reduces the jump size, and shifts the EP pH away from 7; the absence of both weak species gives the largest jump at pH 7. These effects directly determine which indicator (if any) can be used.

Marking criteria.

• 1 mark — Correct description of strong/strong: largest jump, EP at pH 7, no buffer region, any mid-range indicator acceptable.
• 1 mark — Correct description of weak acid/strong base: buffer region before EP, EP above 7 (conjugate base hydrolysis), phenolphthalein suitable.
• 1 mark — Correct description of strong acid/weak base: no buffer before EP, EP below 7 (conjugate acid hydrolysis), methyl orange/methyl red suitable.
• 1 mark — Correct description of weak/weak: overlapping dual buffer regions, no sharp jump, no usable standard indicator, pH meter required.
• 1 mark — Explains the mechanism of buffer capacity reducing jump size (HA + A– coexisting moderates pH change near EP) for at least one weak-containing curve.
• 1 mark — Correctly links EP pH to hydrolysis of the conjugate species (conjugate base → EP > 7; conjugate acid → EP < 7) for both weak-containing curve types.
• 1 mark — Provides a synthesising evaluative conclusion: indicator selection must be matched to EP pH (which is determined by the hydrolysis of the salt formed), and no standard indicator works for weak/weak.