HSC Exam Practice

Sample response. Ka is the equilibrium constant (Keq) for the specific equilibrium in which a weak acid partially dissociates in water. For HF: Ka = [H¹+][F−] / [HF]. Water is excluded because it is the solvent (a pure liquid); equilibrium expressions exclude pure liquids and pure solids.

Marking notes. 1 mark — Ka defined as Keq for acid dissociation (not described as a different type of constant). 1 mark — correct Ka expression with products over reactants and water absent. 1 mark — water excluded because it is the solvent / pure liquid.

Sample response. Strongest to weakest: HF > acetic acid > carbonic acid. Basis: a larger Ka indicates a greater extent of dissociation (equilibrium lies further to the right), which corresponds to a stronger acid. Ka(HF) = 7.2 × 10−&sup4; > Ka(acetic) = 1.8 × 10−&sup5; > Ka(carbonic) = 4.3 × 10−&sup7;, so HF donates protons most readily at equilibrium.

Marking notes. 1 mark — correct ranking (all three in correct order). 1 mark — larger Ka = stronger acid / more dissociation at equilibrium. 1 mark — at least one Ka value quoted or pKa comparison used correctly.

Sample response. A strong acid (e.g. HCl) has Ka >> 1 and dissociates essentially completely in dilute aqueous solution — no equilibrium is established and essentially no undissociated HA remains. A weak acid (e.g. acetic acid) has Ka << 1 and only partially dissociates — an equilibrium is established with most HA remaining undissociated.

Marking notes. 1 mark — strong acid: Ka >> 1 / essentially complete dissociation + named example (HCl, HNO&sub3;, H&sub2;SO&sub4;, HBr, HI, HClO&sub4;). 1 mark — weak acid: Ka << 1 / partial dissociation / equilibrium established + named example (acetic acid, HF, HCN, carbonic acid, etc.). 1 mark — explicit contrast in equilibrium position (one complete, one partial with most HA remaining).

Sample response. For a conjugate acid–base pair only (e.g. HA and A−), the product Ka × Kb = Kw = 1.0 × 10−¹&sup4; at 25 °C. This is because multiplying the Ka expression by the Kb expression for the conjugate base gives [H¹+][OH−] = Kw. Since Ka × Kb = Kw (a constant), a larger Ka (stronger acid) means Kb = Kw/Ka is smaller — so a stronger acid has a weaker conjugate base.

Marking notes. 1 mark — Ka × Kb = Kw stated; condition: conjugate acid–base pair only. 1 mark — explanation that multiplying Ka and Kb expressions cancels the HA and A− terms to give Kw. 1 mark — stronger acid (larger Ka) ⇒ weaker conjugate base (smaller Kb); weaker acid ⇒ stronger conjugate base (or equivalent inverse reasoning).

Sample response. ΔG° = −RT ln K_eq, where R = 8.314 J mol−¹ K−¹ (the universal gas constant) and T is temperature in Kelvin. A negative ΔG° means K_eq > 1, products are favoured at equilibrium, and the forward reaction is spontaneous under standard conditions. A positive ΔG° means K_eq < 1 and the reverse reaction is favoured.

Marking notes. 1 mark — R identified as 8.314 J mol−¹ K−¹. 1 mark — T must be in Kelvin (not Celsius). 1 mark — negative ΔG° = spontaneous / products favoured; positive ΔG° = non-spontaneous forward / reactants favoured.

Sample response. Ka = 1.8 × 10−&sup5; << 1 indicates that at equilibrium the vast majority of acetic acid molecules remain undissociated (equilibrium lies far to the left). Nevertheless, even a small degree of dissociation in a concentrated solution such as vinegar (~5% acetic acid by volume) produces enough H¹+ ions to give a noticeably acidic taste and pH around 2–3. The equilibrium concentration of H¹+ depends on both Ka and the initial concentration of the acid — a high total concentration of a weak acid can still yield a significant [H¹+].

Marking notes. 1 mark — Ka << 1 ⇒ equilibrium lies far to left, most acetic acid remains undissociated. 1 mark — despite partial dissociation, vinegar contains sufficient CH&sub3;COOH that enough H¹+ is produced to give notable acidity (or pH quoted ~2–3). 1 mark — [H¹+] depends on both Ka and initial concentration of the acid (concentration effect acknowledged).

Sample response. The graph shows a linear (straight-line) positive relationship: as pKa increases, ΔG° increases proportionally. This follows directly from ΔG° = −RT ln Ka and the definition pKa = −log(Ka). Substituting: ΔG° = −RT × (−2.303 pKa) = 2.303RT × pKa. At 25 °C (298 K), the slope = 2.303 × 8.314 × 298 / 1000 = 5.71 kJ mol−¹ per pKa unit. So every one-unit increase in pKa raises ΔG° by ~5.71 kJ mol−¹, explaining the linear graph.

Marking notes. 1 mark — describes linear positive relationship (larger pKa = larger positive ΔG°). 1 mark — connects to ΔG° = −RT ln Ka and pKa = −log Ka (either derivation or statement of proportionality). 1 mark — explicit slope or gradient identified as 2.303RT (~5.71 kJ per pKa unit at 25 °C), or equivalent explanation of why the relationship is linear.

Sample response. Estimate from graph: pKa(HCN) = 9.2, which lies between NH&sub4;¹+ (pKa 9.3, ΔG° +52.8 kJ mol−¹), so estimated ΔG° ≈ +52.3 kJ mol−¹. Calculated: ΔG° = −(8.314)(298) ln(6.2 × 10−¹&sup0;) = −(2477.6)(−21.2) = +52,524 J mol−¹ = +52.5 kJ mol−¹. The estimate and calculated value are in close agreement (<1% difference), confirming the linear ΔG° vs pKa relationship.

Marking notes. 1 mark — reasonable graph estimate in range +50–+54 kJ mol−¹ for pKa ~9.2. 1 mark — correct calculation with T = 298 K, R = 8.314 J mol−¹ K−¹, ln(6.2 × 10−¹&sup0;) ≈ −21.2, ΔG° = +52.5 kJ mol−¹ (±1). 1 mark — comparison noting close agreement and linking to linear relationship or confirming calculated value falls on graph trend.

Sample response. Ka(acetic acid) = 1.8 × 10−&sup5; (given). Kb(acetate) = Kw / Ka = 1.0 × 10−¹&sup4; / 1.8 × 10−&sup5; = 5.6 × 10−¹&sup0;. Acetate is therefore a very weak base.

Marking notes. 1 mark — Kb = Kw/Ka stated with correct substitution. 1 mark — correct answer: 5.6 × 10−¹&sup0; (± acceptable rounding). Award 0 if the relationship Ka × Kb = Kw is not used.

Sample response. ΔG° = −(8.314)(298) ln(1.8 × 10−&sup5;) = −(2477.6)(−10.92) = +27,056 J mol−¹ = +27.1 kJ mol−¹. ΔG° > 0 confirms the forward dissociation of acetic acid is not spontaneous under standard conditions (K<1), consistent with Ka = 1.8 × 10−&sup5; << 1 — at equilibrium, most acetic acid remains undissociated.

Marking notes. 1 mark — correct calculation: ΔG° = +27.1 kJ mol−¹ (±1 kJ mol−¹; penalise if T used in °C). 1 mark — correct interpretation: ΔG° > 0 ⇒ forward reaction not spontaneous; Ka < 1 ⇒ reactants favoured; both ΔG° and Ka cited.

Sample response. For a weak acid, the simplifying assumption is made that the amount of HA that dissociates is so small relative to the initial concentration that [HA]_eq ≈ [HA]_initial (the “5% approximation”). For a strong acid, no such assumption is needed because dissociation is complete — [HA]_eq = 0 by definition, so no equilibrium calculation is required at all.

Marking notes. 1 mark — any valid statement of the simplifying assumption unique to weak acid Ka calculations (e.g. [HA]_eq ≈ [HA]_initial; or equilibrium established vs complete dissociation; or ICE table approximation). Accept any clearly expressed version of the concentration approximation.

Sample response. The claim is incorrect on both counts. Ka and ΔG° are not measures of different things — they are quantitatively and conceptually linked by the equation ΔG° = −RT ln Ka, where Ka is used in place of K_eq for an acid dissociation equilibrium. Ka is itself simply K_eq applied to the specific equilibrium HA(aq) ⇌ H¹+(aq) + A−(aq); it is as much a “physics” quantity as a “chemistry” quantity. Similarly, ΔG° encodes the same equilibrium information as Ka: a positive ΔG° corresponds to Ka < 1 (reactants favoured, weak acid, partial dissociation), and a negative ΔG° would correspond to Ka > 1 (complete dissociation, strong acid). The two quantities are mathematically interconvertible — knowing one allows exact calculation of the other. Separating them into “chemistry” and “physics” is an artificial and misleading distinction. In the Australian context of Great Barrier Reef seawater acidification, carbonic acid dissociation (Ka = 4.3 × 10−&sup7;) has a ΔG° of approximately +36.5 kJ mol−¹ at 25 °C. The positive ΔG° tells a physicist that carbonic acid dissociation is not thermodynamically favoured under standard conditions; the same Ka tells a marine chemist that as CO&sub2; dissolves in reef water, the equilibrium shifts to produce more H¹+ ions, lowering pH and threatening coral calcification. These are not two separate quantities telling two separate stories — they are the same story expressed in different but mathematically equivalent units of the same underlying equilibrium constant. The claim is therefore rejected entirely: Ka and ΔG° are two representations of the same thermodynamic information, and any scientist — chemist or physicist — working on acid equilibria needs to understand both.

Marking notes. 1 mark — identifies that Ka is simply Keq for acid dissociation (not a different type of constant). 1 mark — states the quantitative link ΔG° = −RT ln Ka explicitly. 1 mark — explains that positive ΔG° corresponds to Ka < 1 (reactants favoured, weak acid) and negative ΔG° to Ka > 1 (products favoured, strong acid). 1 mark — rejects the claim that the two are unrelated: they are mathematically interconvertible (knowing one determines the other). 1 mark — rejects the “chemistry vs physics” framing: both quantities describe the same equilibrium information from different angles. 1 mark — Australian context applied correctly: carbonic acid / GBR seawater acidification, or acetic acid in wine, or ammonia in aquaculture; Ka and ΔG° used together to interpret the chemistry. 1 mark — explicit, evidence-based evaluative judgement rejecting the claim (not just describing Ka and ΔG° separately).