Chemistry • Year 12 • Module 5 • Lesson 13
Temperature & Keq, Colourimetry
Apply Beer–Lambert law and temperature–Keq reasoning to real data sets, calibration curves, and environmental monitoring contexts.
1. Beer–Lambert calibration curve — reading and interpreting data 10 marks
A student prepares five standard solutions of FeSCN2+ and measures their absorbance at 447 nm using a colorimeter with a 1 cm cuvette. The results are plotted below.
(a) Describe the relationship shown in Figure 1.1 between absorbance and [FeSCN2+] and state the Beer–Lambert law that predicts this relationship. 2 marks
(b) Use the calibration curve to estimate [FeSCN2+]eq for the equilibrium sample with absorbance A = 0.60. Show your reading on the graph with a dashed line. 2 marks
(c) Using the best-fit equation A = 0.240c (where c is in units of 10−4 mol L−1), calculate the molar absorptivity ε at 447 nm for a 1 cm path length. Give units. 2 marks
(d) The equilibrium sample was prepared with initial [Fe3+] = 1.00 × 10−3 mol L−1 and initial [SCN−] = 1.00 × 10−3 mol L−1. Using your answer to (b), construct an ICE table for Fe3+(aq) + SCN−(aq) ⇌ FeSCN2+(aq) and calculate Keq. 4 marks
2. Temperature–Keq data table — N2O4 ⇌ 2NO2 9 marks
A student investigates the equilibrium N2O4(g) ⇌ 2NO2(g) at four temperatures. NO2 is deep reddish-brown; N2O4 is colourless. Keq is expressed in terms of concentrations (mol L−1).
| Temperature (°C) | Keq (mol L−1) | Colour intensity of mixture |
|---|---|---|
| 25 | 4.64 × 10−3 | Pale brown |
| 45 | 2.18 × 10−2 | Light brown |
| 65 | 9.47 × 10−2 | Medium brown |
| 85 | 0.371 | Dark reddish-brown |
Source: adapted from NIST Chemistry WebBook thermodynamic data for N2O4/NO2 system.
(a) Describe the trend in Keq as temperature increases from 25°C to 85°C. 1 mark
(b) Use the trend to determine whether the forward reaction N2O4(g) → 2NO2(g) is exothermic or endothermic. Justify your answer. 2 marks
(c) Explain why the colour of the equilibrium mixture becomes darker as temperature increases, linking your answer to the Keq data. 2 marks
(d) Identify the controlled and independent variables in this experiment. 2 marks
(e) Predict whether Keq at 100°C would be greater or less than 0.371. Justify your prediction. 2 marks
3. Australian context — NOx monitoring by colourimetry 5 marks
Read the passage, then answer the question.
The NSW Environment Protection Authority (EPA) monitors nitrogen dioxide (NO2) concentrations in urban air as part of the National Environment Protection Measure for Ambient Air Quality. One analytical method involves collecting air samples in an absorption solution, allowing NO2 to react and form a coloured Griess-type product. The absorbance of this product is measured using a spectrophotometer and compared against a calibration curve of known NO2 concentrations to determine the concentration in the original air sample. The national standard for NO2 is 0.12 ppm (1-hour average). In 2023, sites in Western Sydney recorded occasional exceedances near high-traffic corridors during morning peak hour.
Question: Using your understanding of Beer–Lambert law and colourimetry, explain how the NSW EPA method described above determines the concentration of NO2 in an air sample. In your response, identify the role of the calibration curve, the Beer–Lambert relationship, and discuss one limitation of the method that could affect the accuracy of results at very low NO2 concentrations.
4. Predict and justify 4 marks
The equilibrium CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g) has ΔH° = +206 kJ mol−1. A chemical engineer claims that operating a steam-methane reformer at a higher temperature will produce a higher yield of H2 at equilibrium.
Predict whether the engineer’s claim is correct and justify your prediction in terms of the effect of temperature on Keq for this reaction.
Q1(a) — Beer–Lambert relationship
Absorbance increases linearly (directly proportionally) with [FeSCN2+]; the relationship is a straight line through the origin. This is predicted by Beer–Lambert law A = εlc: for constant ε and l, A ∝ c.
Q1(b) — Reading the calibration curve
[FeSCN2+]eq ≈ 2.5 × 10−4 mol L−1. The dashed lines from A = 0.60 on the y-axis intersect the best-fit line and drop to approximately 2.5 on the x-axis. 1 mark for the correct x-reading; 1 mark for correct units.
Q1(c) — Molar absorptivity
A = εlc ⇒ ε = A/(lc). Gradient of best-fit = 0.240 (absorbance per 10−4 mol L−1). Converting: ε = 0.240 / (1 cm × 1×10−4 mol L−1) = 2400 L mol−1 cm−1. 1 mark for correct working; 1 mark for correct value and units.
Q1(d) — ICE table and Keq calculation
Using [FeSCN2+]eq = 2.5 × 10−4 mol L−1:
- ICE: I: Fe3+ = SCN− = 1.00×10−3; FeSCN2+ = 0. C: −2.5×10−4, −2.5×10−4, +2.5×10−4. E: Fe3+ = SCN− = 7.5×10−4 mol L−1; FeSCN2+ = 2.5×10−4 mol L−1.
- Keq = (2.5×10−4) / [(7.5×10−4)2] = (2.5×10−4) / (5.625×10−7) = 444 (dimensionless).
1 mark: correct ICE table; 1 mark: correct equilibrium concentrations; 1 mark: correct Keq expression; 1 mark: correct numerical answer with working.
Q2(a) — Trend in Keq
Keq increases as temperature increases from 25°C to 85°C (approximately 80-fold increase over the range).
Q2(b) — Exothermic or endothermic?
The forward reaction is endothermic. When temperature increases, Keq increases — meaning more NO2 (product) is present at equilibrium. This is consistent with an endothermic forward reaction: adding heat drives the reaction further to the right (Le Chatelier’s Principle), and the thermodynamic effect is that Keq increases with temperature when ΔH° > 0.
Q2(c) — Colour intensity and Keq
Higher Keq at higher temperatures means a greater proportion of the gas mixture is NO2 at equilibrium. NO2 is reddish-brown; N2O4 is colourless. Greater [NO2]eq means higher absorbance — hence the darker colour. By Beer–Lambert law A = εlc, higher [NO2] gives higher absorbance (greater colour intensity).
Q2(d) — Variables
Independent variable: temperature (°C). Controlled variables: initial amount/concentration of N2O4, total volume (or pressure if using closed vessel), path length, wavelength of light. (1 mark for independent; 1 mark for at least two controlled variables.)
Q2(e) — Prediction at 100°C
Keq at 100°C would be greater than 0.371. The forward reaction is endothermic, so increasing temperature further increases Keq. The trend in the data (Keq approximately doubling or more with each 20°C step) supports this prediction.
Q3 — NOx monitoring by colourimetry
Sample response (5 marks): The absorbed NO2 reacts in the collecting solution to form a coloured product. The absorbance of this coloured product is measured with a spectrophotometer. Because Beer–Lambert law states A = εlc, absorbance is proportional to the concentration of the coloured product (and therefore to [NO2]) for fixed ε and path length. The calibration curve converts the measured absorbance into a concentration by reading across from the absorbance value to the curve and then down to the concentration axis; the curve was prepared by measuring absorbance of known NO2 standards. One limitation is that at very low NO2 concentrations (approaching the detection limit), the absorbance reading may fall below the limit of quantification of the spectrophotometer, where small errors in the instrument reading become large as a percentage of the small true absorbance — reducing accuracy. Other valid limitations: interference from other coloured species in the air sample; deviation from Beer–Lambert law at very low concentrations due to stray light. Award: 1 mark — Beer–Lambert law A ∝ c stated; 1 mark — role of calibration curve correctly described; 1 mark — how concentration is read from calibration curve; 1 mark — identifies a valid, specific limitation; 1 mark — explains how the limitation affects accuracy.
Q4 — Steam-methane reformer prediction
The engineer’s claim is correct. The forward reaction has ΔH° = +206 kJ mol−1 — it is endothermic. For an endothermic forward reaction, increasing temperature increases Keq (more products favoured at the new equilibrium). Therefore, operating at higher temperature shifts the equilibrium further to the right, producing a greater equilibrium yield of H2. 2 marks: identifies forward reaction as endothermic from ΔH° sign; 2 marks: correctly states that higher T increases Keq for an endothermic reaction, therefore higher H2 yield at equilibrium.