HSC Exam Practice

Sample response. K_eq is the ratio of the product of equilibrium concentrations of products to the product of equilibrium concentrations of reactants, each raised to the power of its stoichiometric coefficient, for a given reaction at a specified temperature. The only factor that changes the numerical value of K_eq is temperature.

Marking notes. 1 mark for a correct definition of K_eq (concentrations of products over reactants, raised to stoichiometric coefficients, at equilibrium); 1 mark for stating temperature as the only factor that changes K_eq.

Sample response. The position of equilibrium refers to the relative concentrations of reactants and products present at equilibrium at a given temperature; it can be shifted by changes in concentration, pressure, or temperature. The value of K_eq is a thermodynamic constant that depends only on temperature: it specifies what the ratio of concentrations will be at equilibrium at that temperature. Changing temperature changes K_eq itself — a new equilibrium with a different ratio of product to reactant concentrations. Changing concentration or pressure shifts the position toward the existing equilibrium (Le Chatelier’s Principle) but the ratio at the new equilibrium is still K_eq — unchanged.

Marking notes. 1 mark — defines position of equilibrium as relative concentrations; 1 mark — states K_eq is the equilibrium ratio of concentrations, temperature-dependent only; 1 mark — explicitly contrasts that concentration/pressure changes shift position without changing K_eq, while temperature changes K_eq.

Sample response. The Haber process forward reaction (N₂ + 3H₂ → 2NH₃) is exothermic (ΔH° = −92 kJ mol⁻¹), meaning heat is effectively a product. Increasing temperature adds heat to the system, which by Le Chatelier’s Principle shifts the equilibrium to the left (toward reactants) to consume the excess heat. As a result, less NH₃ is present at the new equilibrium and more N₂ and H₂ remain, so the numerator of the K_eq expression decreases while the denominator increases — the value of K_eq falls. At the thermodynamic level, increasing T increases TΔS°, making ΔG° = ΔH° − TΔS° less negative (more positive), which gives a smaller K_eq via ΔG° = −RT ln K_eq.

Marking notes. 1 mark — identifies forward reaction as exothermic / heat as product; 1 mark — applies Le Chatelier’s Principle correctly (equilibrium shifts left at higher T); 1 mark — links the shift to decreased [NH₃]_eq and therefore decreased K_eq.

Sample response. Beer–Lambert law: A = εlc. A is absorbance (dimensionless); ε is molar absorptivity (L mol⁻¹ cm⁻¹); l is path length (cm); c is concentration (mol L⁻¹). For fixed ε and l, A is directly proportional to c — a straight-line relationship through the origin, which is the basis of the calibration curve.

Marking notes. 1 mark — correct equation A = εlc; 1 mark — correctly identifies at least two variables with correct units; 1 mark — describes A directly proportional to c (linear through origin) for constant ε and l.

Sample response. (1) Prepare a series of calibration solutions with known [FeSCN²⁺] and measure their absorbance; plot absorbance vs [FeSCN²⁺] to obtain the calibration curve (straight line through origin). (2) Prepare an equilibrium mixture from known initial [Fe³⁺] and [SCN⁻]; allow to reach equilibrium. (3) Measure the absorbance of the equilibrium mixture at the same wavelength; use the calibration curve to read [FeSCN²⁺]_eq. (4) Construct an ICE table using initial concentrations and [FeSCN²⁺]_eq to find [Fe³⁺]_eq and [SCN⁻]_eq. (5) Substitute all equilibrium concentrations into the K_eq expression and calculate K_eq.

Marking notes. 1 mark each for any four of the five correctly sequenced steps. The steps need not be numbered but must be in logical order (calibration → equilibration → absorbance measurement → ICE table → K_eq calculation).

Sample response. ΔG° = −RT ln K_eq. When K_eq >> 1 (e.g. K_eq = 10⁴⁰ for H₂ + ½O₂ → H₂O): ln K_eq is a large positive number, so ΔG° is a large negative value — products are strongly thermodynamically favoured and the forward reaction is highly spontaneous under standard conditions. When K_eq << 1 (e.g. K_eq = 10⁻³⁰ for N₂ + O₂ → 2NO): ln K_eq is large and negative, so ΔG° is large and positive — reactants are strongly favoured and the forward reaction is non-spontaneous.

Marking notes. 1 mark — states ΔG° = −RT ln K_eq or correct qualitative form; 1 mark — correctly links K_eq >> 1 to large negative ΔG° (products favoured, spontaneous); 1 mark — correctly links K_eq << 1 to large positive ΔG° (reactants favoured, non-spontaneous). A named example for each is not required but strengthens the response.

Part (a). K_eq increases as temperature increases from 25°C to 85°C, with the increase accelerating at higher temperatures (the relationship is approximately exponential). K_eq increases approximately 80-fold over the 60°C range.

Marking notes (a). 1 mark for correctly describing K_eq increases with temperature. Award the mark if one specific value is quoted.

Part (b). The forward reaction is endothermic. K_eq increases as temperature increases, meaning higher temperature produces more NO₂ at equilibrium. By Le Chatelier’s Principle, adding heat to the system shifts the equilibrium in the direction that absorbs heat — i.e., toward the endothermic direction. Since equilibrium shifts to the right (toward NO₂, products) when temperature increases, the forward reaction must be endothermic (ΔH° > 0).

Marking notes (b). 1 mark — identifies forward reaction as endothermic; 1 mark — applies Le Chatelier’s Principle correctly, linking increasing T to shift toward product and ΔH° > 0.

Part (c). K_eq at 100°C would be greater than 0.371. The forward reaction is endothermic, so further increasing temperature beyond 85°C continues to increase K_eq. Extrapolating the upward trend in Figure 2.1, K_eq at 100°C would be substantially greater than 0.371 (likely in the range 0.6–1.0 based on the trend).

Marking notes (c). 1 mark for stating K_eq > 0.371 AND giving a valid justification (forward reaction is endothermic / upward trend continues / Le Chatelier). The numerical estimate is not required.

Part (a) — [FeSCN²⁺]_eq (1 mark). A = 0.240c ⇒ c = 0.576/0.240 = 2.40 (in units of 10⁻⁴ mol L⁻¹) = 2.40 × 10⁻⁴ mol L⁻¹. 1 mark for correct value and units.

Part (b) — ICE table (3 marks).

Fe³⁺: I = 3.00×10⁻³, C = −2.40×10⁻⁴, E = 2.76×10⁻³ mol L⁻¹.

SCN⁻: I = 1.00×10⁻³, C = −2.40×10⁻⁴, E = 7.60×10⁻⁴ mol L⁻¹.

FeSCN²⁺: I = 0, C = +2.40×10⁻⁴, E = 2.40×10⁻⁴ mol L⁻¹.

1 mark: ICE table structure with correct change signs (Fe³⁺ and SCN⁻ decrease by equal amounts, FeSCN²⁺ increases by same amount — 1:1:1 stoichiometry); 1 mark: correct [Fe³⁺]_eq; 1 mark: correct [SCN⁻]_eq.

Part (c) — K_eq (1 mark). K_eq = (2.40×10⁻⁴) / [(2.76×10⁻³)(7.60×10⁻⁴)] = (2.40×10⁻⁴) / (2.098×10⁻⁶) = 114 (accept 110–120 for rounding). 1 mark.

Part (d) — Assumption (1 mark). The assumption is that both Fe³⁺ and SCN⁻ decrease by the same amount as FeSCN²⁺ increases (1:1:1 stoichiometric change). This holds because the balanced equation for the equilibrium shows a 1:1:1 mole ratio: one mole of Fe³⁺ reacts with one mole of SCN⁻ to produce one mole of FeSCN²⁺.

Sample response. The scientific flaw is the claim that a catalyst increases K_eq. A catalyst does not change K_eq. K_eq is determined by the thermodynamic stability of reactants relative to products (ΔG° = −RT ln K_eq), which depends only on the nature of the substances and the temperature. A catalyst lowers the activation energy of both the forward and reverse reactions equally, so the rates of both reactions increase by the same factor. The system reaches equilibrium faster, but the equilibrium composition — and therefore K_eq — is identical to that reached without a catalyst. While the catalyst does increase the rate of product formation, it equally increases the rate of the reverse reaction, so more product is not present at equilibrium — the statement confuses reaction rate with equilibrium position.

Marking notes. 1 mark — identifies the flaw (catalyst does not change K_eq); 1 mark — explains that K_eq depends only on temperature (ΔG° or thermodynamic stability of substances); 1 mark — explains that a catalyst lowers activation energy of both forward and reverse reactions equally; 1 mark — concludes that equilibrium composition (ratio of concentrations) is unchanged, distinguishing rate from equilibrium position.

Sample response. Colourimetry is an effective and widely used method for determining K_eq in the iron(III) thiocyanate system. The method is based on Beer–Lambert law (A = εlc), which states that absorbance of light by a coloured solution is directly proportional to the concentration of the absorbing species for fixed path length and molar absorptivity. FeSCN²⁺ is intensely red, allowing its equilibrium concentration to be measured accurately from the absorbance of the equilibrium mixture, using a calibration curve constructed from standard solutions. The equilibrium concentrations of the colourless species (Fe³⁺ and SCN⁻) are calculated by ICE table from the known initial concentrations and the measured [FeSCN²⁺]_eq, then substituted into the K_eq expression. This method is directly analogous to colourimetric techniques used in environmental monitoring: the NSW Environment Protection Authority uses absorption spectrophotometry to measure NO₂ concentrations in ambient air, converting absorbance readings of a Griess-type coloured product into quantitative [NO₂] values using a calibration curve — the same Beer–Lambert principle. Despite these strengths, the method has two important limitations. First, Beer–Lambert law assumes ideal dilute solution behaviour — at high concentrations, solute–solute interactions change ε and the A–c relationship becomes non-linear, causing [FeSCN²⁺]_eq and therefore K_eq to be inaccurate. Second, the calibration curve must be prepared at the same temperature as the equilibrium experiment, because ε is temperature-dependent; if the calibration is done at a different temperature, the gradient will not correctly represent the absorbance-to-concentration conversion at the experimental temperature, introducing systematic error in K_eq. A third limitation is that the method is only applicable to equilibrium systems containing a coloured species — it cannot be directly applied to systems where all species are colourless. Overall, colourimetry provides a simple, rapid, and non-destructive means of determining K_eq when a coloured species is present, and its limitations can be managed through careful calibration design.

Marking notes. 1 mark — correctly states Beer–Lambert law and applies it to FeSCN²⁺; 1 mark — describes the role of the calibration curve (absorbance → concentration); 1 mark — describes how [Fe³⁺]_eq and [SCN⁻]_eq are obtained from the ICE table; 1 mark — names a specific Australian environmental or industrial colourimetric application (NSW EPA NO₂ monitoring, or FSANZ food dye testing); 1 mark — first correctly described limitation; 1 mark — second correctly described limitation; 1 mark — overall evaluative statement that correctly qualifies the usefulness of the method (not just lists pros/cons but reaches a judgement). A response that lists only limitations without explaining the principles, or that lists principles without evaluating limitations, cannot score above 5.