(a) The gas-phase reaction between methane (CH₄) and diatomic sulphur (S₂) is given by the following reaction: CH₄ (g) + 2S₂ (g) ———→ CS₂ (g) + 2H₂S (g). At 823 K, the rate constant for this reaction is 1·1 × 10⁻³ m³ mol⁻¹ S and at 898 K, the rate co

Question

(a) The gas-phase reaction between methane (CH₄) and diatomic sulphur (S₂) is given by the following reaction: CH₄ (g) + 2S₂ (g) ———→ CS₂ (g) + 2H₂S (g). At 823 K, the rate constant for this reaction is 1·1 × 10⁻³ m³ mol⁻¹ S and at 898 K, the rate constant is 6·4 × 10⁻³ m³ mol⁻¹ S. Calculate the activation energy for this reaction. [Given: R = 8·3145 J K⁻¹ mol⁻¹] (5 marks)

(b) A dye solution containing 1 g per 100 cc transmitted 60% of the blue light in a cell 1 cm thick. (i) What percentage of light would be absorbed by a solution containing 2 g per 100 cc in the same cell? (ii) What should be the cell thickness so that 90% of the light is absorbed by the original solution? (5 marks)

(c) At 0°C and 1 atm pressure, the volume of nitrogen (N₂) gas required to form a monolayer on a sample of charcoal is 155·5 cm³ gm⁻¹ of charcoal. Calculate the surface area per gram of charcoal. Area of cross-section of a N₂ molecule is 0·160 (nm)². [Given: Nₐ = 6·022 × 10²³ mol⁻¹; Molar volume of gas (at 0°C and 1 atm pressure), Vₘ = 22·414 dm³ mol⁻¹] (5 marks)

(d) From the following data for the decomposition of ammonium nitrite in aqueous solution, show that the reaction is of the first order. | Time (minutes) | 10 | 15 | 20 | 25 | ∞ | |---|---|---|---|---|---| | Volume of N₂ (cc) | 6·25 | 9·00 | 11·40 | 13·65 | 35·05 | (5 marks)

(e) Draw the structure of Ferredoxin protein containing [4Fe – 4S] and find the average oxidation number of iron. (5 marks)

(f) Which complex ion has higher value of crystal field splitting energy (Δ₀)? Justify your answer. (i) [Co(H₂O)₆]³⁺ or [Co(H₂O)₆]²⁺ (ii) [Co(NH₃)₆]³⁺ or [Rh(NH₃)₆]³⁺ (iii) [Co(H₂O)₆]³⁺ or [Co(NH₃)₆]³⁺ (10 marks)

(g) Complete the following reactions: (i) S₄N₄ →[SbCl₅] (ii) XeF₆ →[PtF₅] (iii) B₂H₆ →[NH₃][-120°C] (iv) 8KrF₂ + 2Au → (v) XeOF₄ + XeO₃ → (10 marks)

(h) The magnetic moment of d-block elements arises mainly from the contribution of spin motion of the electrons but in case of f-block elements, it is not valid. Justify the statement. (5 marks)

UPSC Answer Check · Accepted Answer

Solve each sub-part systematically with clear step-by-step calculations and reasoning. Allocate approximately 8-10 minutes per 5-mark sub-part: (a) and (d) require Arrhenius equation and first-order kinetics derivations; (b) and (c) need Beer-Lambert law and surface area calculations; (e) and (g) demand accurate structures and reaction products; (f) and (h) require comparative analysis with proper justifications. Present final answers with appropriate units and significant figures.
- Part (a): Correct application of Arrhenius equation in two-point form: ln(k₂/k₁) = (Ea/R)[(T₂-T₁)/(T₁T₂)] to calculate activation energy ≈ 138-140 kJ mol⁻¹
- Part (b): Application of Beer-Lambert law (A = εcl) showing (i) 84% absorption for doubled concentration, and (ii) 2.15 cm path length for 90% absorption
- Part (c): Calculation of number of N₂ molecules using ideal gas law, then surface area = (number of molecules) × (cross-sectional area) ≈ 670-675 m² g⁻¹
- Part (d): Demonstration of first-order kinetics using k = (2.303/t)log[V∞/(V∞-Vt)] with consistent k values (~0.034 min⁻¹) across time intervals
- Part (e): Cubane-like [4Fe-4S] cluster structure with Fe at alternate corners, S at other corners; average oxidation state calculation showing +2.5 or Fe³⁺Fe²⁺ mixed valence
- Part (f): Systematic comparison: (i) Co³⁺ > Co²⁺ (higher charge), (ii) Rh³⁺ > Co³⁺ (4d > 3d), (iii) [Co(NH₃)₆]³⁺ > [Co(H₂O)₆]³⁺ (NH₃ stronger field); citing spectrochemical series and nephelauxetic effect
- Part (g): Complete reactions: (i) [S₄N₄]²⁺[SbCl₅]₂⁻ adduct, (ii) [XeF]⁺[PtF₆]⁻, (iii) BH₃·NH₃ adducts, (iv) 2[Kr₂F]⁺[AuF₄]⁻, (v) 2XeOF₄ + XeO₃ → 3XeO₂F₂
- Part (h): Explanation of spin-only magnetic moment for d-block (μ = √[n(n+2)] BM) vs. f-block where orbital contribution persists due to less effective quenching by ligand fields and spin-orbit coupling

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding of chemical kinetics (Arrhenius, order determination), photochemistry (Beer-Lambert), surface chemistry (BET method), bioinorganic (ferredoxin), CFT, and main group chemistry across all sub-parts with no conceptual errors	Shows generally correct concepts with minor errors in 1-2 sub-parts, such as confusing activation energy with enthalpy, or misapplying spectrochemical series	Fundamental misconceptions evident, such as using wrong kinetic equation, misunderstanding monolayer coverage, or incorrect oxidation state assignments
Mechanism / equation	20%	10	All equations written correctly: Arrhenius two-point form, Beer-Lambert law, first-order integrated rate law, surface area formula; reaction mechanisms for (g) show proper electron transfer and adduct formation	Most equations correct but missing proper form in 1-2 cases, such as omitting ln vs log distinction, or incomplete reaction products	Incorrect or missing equations, wrong rate law applied, unbalanced reactions, or no mechanistic reasoning provided
Numerical accuracy	20%	10	All calculations precise with correct significant figures: Ea ≈ 138.5 kJ mol⁻¹, 84% absorption, path length 2.15 cm, surface area ~672 m² g⁻¹, k ≈ 0.034 min⁻¹ consistent across intervals; proper unit conversions throughout	Correct methodology with minor arithmetic errors or unit conversion mistakes in 1-2 sub-parts, final answers within 5-10% of correct value	Major calculation errors, wrong formulas leading to absurd answers, no unit awareness, or missing numerical work entirely
Diagram / structure	20%	10	Clear labeled diagram of [4Fe-4S] cubane cluster showing Fe-S bonds, bridging sulfides, and cysteine coordination; proper 3D perspective with bond angles; oxidation states clearly indicated on structure	Recognizable cluster structure but poorly drawn perspective, missing labels, or unclear oxidation state notation; 2D representation without depth	No diagram provided, incorrect geometry (e.g., planar instead of cubane), or structure confused with [2Fe-2S] cluster
Application context	20%	10	Connects ferredoxin to biological electron transfer (photosynthesis, nitrogen fixation); relates CFT comparisons to actual spectral data and Indian research in bioinorganic chemistry; explains industrial relevance of surface area measurements for activated carbon	Brief mention of biological significance without elaboration, or generic statements about importance without specific context	No application context provided, or irrelevant connections that demonstrate misunderstanding of practical significance

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