Chemistry • Year 12 • Module 5 • Lesson 13

Temperature & K_eq, Colourimetry

Synthesise, evaluate, and justify using multi-step data and real-world scenarios. Two extended questions, each 7–8 marks. Band 5–6.

Master · Band 5–6

Question 1 — Colourimetry, ICE table, and experimental evaluation 8 marks

A Year 12 student conducts a NESA-specified investigation of the iron(III) thiocyanate equilibrium:

Fe³⁺(aq) + SCN⁻(aq) ⇌ FeSCN²⁺(aq) ΔH° = −18 kJ mol⁻¹

The student prepares a calibration curve and an equilibrium mixture. Their results are summarised in Table 1 and Figure 1.

Table 1. Experimental data for the FeSCN²⁺ equilibrium investigation.
Parameter	Value
Initial [Fe³⁺]	2.50 × 10⁻³ mol L⁻¹
Initial [SCN⁻]	2.50 × 10⁻³ mol L⁻¹
Initial [FeSCN²⁺]	0 mol L⁻¹
Absorbance of equilibrium mixture (A)	0.74
Calibration gradient (A per 10⁻⁴ mol L⁻¹)	0.240
Path length (l)	1.00 cm
Temperature of experiment	25°C
K_eq measured at 45°C by a second student	186

In your extended response, address all of the following:

Calculate [FeSCN²⁺]_eq at 25°C from the absorbance measurement and calibration gradient.
Construct a complete ICE table for the equilibrium and calculate K_eq at 25°C.
Compare K_eq at 25°C (your calculated value) with K_eq = 186 at 45°C. Use this comparison to determine whether the forward reaction is exothermic or endothermic and justify your answer with reference to ΔH° given above.
Evaluate one source of systematic error in this colourimetry method that could cause the student’s calculated K_eq at 25°C to be inaccurate, and propose how it could be reduced.

Tip: work through points 1–2 numerically before writing your response to 3–4.

Question 2 — Food dye concentration testing and Beer–Lambert law evaluation 7 marks

Food Standards Australia New Zealand (FSANZ) sets maximum permitted concentrations for artificial food dyes in beverages. A food technologist uses colourimetry to test whether a sports drink complies with the permitted maximum of 1.50 × 10⁻⁴ mol L⁻¹ for Allura Red (Red 40), a strongly absorbing dye at 504 nm.

The technologist prepares four calibration standards and plots absorbance vs concentration. The best-fit line has the equation:

A = 1840c (where c is in mol L⁻¹, path length = 1 cm)

Three samples from three batches of the sports drink give these absorbance readings:

Batch	Absorbance (A)	Compliant? (show working)
Batch A	0.228
Batch B	0.285
Batch C	0.264

In your extended response, address all of the following:

Use the Beer–Lambert equation to calculate [Allura Red] for each batch. Show working.
State which batches comply and which do not comply with the FSANZ limit. Justify with calculated concentrations.
The technologist assumes the Beer–Lambert law applies perfectly to this system. Identify and explain two conditions that must hold for Beer–Lambert law to give an accurate concentration measurement from absorbance.
A colleague suggests that colourimetry is more reliable than taste or visual inspection for determining food dye compliance. Evaluate this claim by comparing colourimetry with visual inspection on at least two criteria.

Tip: for part 1, rearrange A = 1840c to find c for each batch first, then compare with 1.50 × 10⁻⁴ mol L⁻¹.

Answers — do not peek before attempting

Question 1 — Marking guide (8 marks)

Part 1 — [FeSCN²⁺]_eq (1 mark):

Calibration: A = 0.240 × (c in 10⁻⁴ mol L⁻¹). Rearranging: c = A / 0.240 = 0.74 / 0.240 = 3.083 × 10⁻⁴ mol L⁻¹ ≈ 3.08 × 10⁻⁴ mol L⁻¹. Award 1 mark for correct calculation with units.

Part 2 — ICE table and K_eq at 25°C (3 marks):

Initial: [Fe³⁺] = [SCN⁻] = 2.50 × 10⁻³ mol L⁻¹; [FeSCN²⁺] = 0.
Change: [Fe³⁺] and [SCN⁻] each decrease by 3.08 × 10⁻⁴; [FeSCN²⁺] increases by 3.08 × 10⁻⁴.
Equilibrium: [Fe³⁺]_eq = [SCN⁻]_eq = (2.50 × 10⁻³) − (3.08 × 10⁻⁴) = 2.19 × 10⁻³ mol L⁻¹.
K_eq = (3.08 × 10⁻⁴) / (2.19 × 10⁻³)² = (3.08 × 10⁻⁴) / (4.796 × 10⁻⁶) = 64.2 ≈ 64.

1 mark: correct ICE table structure with correct change signs; 1 mark: correct equilibrium concentrations; 1 mark: correct K_eq calculation (accept 62–66 depending on rounding).

Part 3 — Comparing K_eq values and ΔH° (2 marks):

K_eq at 25°C ≈ 64; K_eq at 45°C = 186. K_eq increases as temperature increases. For an endothermic forward reaction, K_eq increases with temperature — but ΔH° = −18 kJ mol⁻¹ means the forward reaction is exothermic. For an exothermic forward reaction K_eq should decrease with temperature. Therefore the comparison reveals an inconsistency with the expected pattern: either the experimental K_eq at 25°C is underestimated (due to systematic error), or the K_eq at 45°C measurement is incorrect. A student who notes this inconsistency and correctly identifies the expected direction (K_eq should decrease with T for exothermic forward) should receive full marks. Award: 1 mark for correct K_eq direction statement (increase or decrease with T); 1 mark for linking to ΔH° sign and identifying the expected direction/inconsistency. Note: if a student receives K_eq(25°C) > 186, the data would be consistent with an exothermic forward reaction — accept consistent reasoning either way based on their calculated value.

Part 4 — Systematic error and reduction (2 marks):

Acceptable systematic errors include:

Stray light: light that bypasses the sample reaches the detector, artificially reducing apparent absorbance → [FeSCN²⁺]_eq underestimated → K_eq underestimated. Reduction: use a higher-quality monochromator or narrow bandpass filter.
Calibration curve prepared at a different temperature than the equilibrium mixture: molar absorptivity ε changes slightly with temperature, so the calibration gradient may not accurately represent ε at the equilibrium measurement temperature. Reduction: prepare calibration standards and equilibrium mixtures at the same temperature in a thermostatted water bath.
Incomplete equilibration: if the equilibrium mixture is measured before equilibrium is fully established, [FeSCN²⁺] may differ from the true equilibrium value. Reduction: wait a defined mixing time and verify absorbance is stable before reading.

1 mark: names and explains a valid systematic error; 1 mark: proposes a specific and practical reduction strategy.

Question 2 — Marking guide (7 marks)

Part 1 — Concentrations (2 marks):

c = A / 1840:

Batch A: c = 0.228 / 1840 = 1.239 × 10⁻⁴ mol L⁻¹
Batch B: c = 0.285 / 1840 = 1.549 × 10⁻⁴ mol L⁻¹
Batch C: c = 0.264 / 1840 = 1.435 × 10⁻⁴ mol L⁻¹

1 mark for correct formula/method; 1 mark for all three correct values (accept ±2 in last digit).

Part 2 — Compliance (1 mark):

Limit = 1.50 × 10⁻⁴ mol L⁻¹. Batch A (1.24 × 10⁻⁴): compliant. Batch B (1.55 × 10⁻⁴): non-compliant (exceeds limit). Batch C (1.44 × 10⁻⁴): compliant. 1 mark for all three compliance statements correct and justified with the calculated concentration.

Part 3 — Conditions for Beer–Lambert (2 marks):

Monochromatic light: Beer–Lambert law holds for light of a single wavelength (ε is wavelength-dependent); broad or mixed-wavelength light causes apparent deviations from linearity. The spectrophotometer must use a narrow wavelength band at the absorption maximum.
Low concentration / no scattering or aggregation: at high concentrations, solute–solute interactions can change ε or cause aggregation/precipitation, making the A–c relationship non-linear. The calibration range must cover the concentration range of interest, and concentrations should be low enough that Beer–Lambert linearity holds.
No other absorbing species at the measurement wavelength: other coloured components of the food dye mixture could absorb at 504 nm and add to the measured absorbance, making [Allura Red] appear higher than it actually is.

1 mark per condition correctly stated and explained (max 2); accept any two valid conditions.

Part 4 — Evaluating colourimetry vs visual inspection (2 marks):

The colleague’s claim is correct. Colourimetry is more reliable than visual inspection on multiple criteria:

Quantitative precision: colourimetry gives a numerical concentration (e.g. 1.24 × 10⁻⁴ mol L⁻¹) that can be directly compared to a regulatory limit, whereas visual inspection can only detect gross differences in colour intensity and is highly subjective. Human colour perception varies between individuals and is affected by lighting conditions.
Detection limit: colourimetry can detect concentration differences of a few percent of the Beer–Lambert linear range, while visual inspection cannot reliably distinguish a 1.44 × 10⁻⁴ mol L⁻¹ sample from a 1.55 × 10⁻⁴ mol L⁻¹ sample by colour alone.
Reproducibility: colourimetry readings are instrument-based and reproducible between operators and sessions; visual comparison depends on the individual observer.

1 mark per criterion compared correctly between the two methods (max 2); both criteria must involve a direct comparison not just a description of one method.