Q6
(a) How does the bonding in cyclic phosphazene differ from that of benzene and borazine? (10 marks) (b) What are the limitations of collision theory? How is it explained by transition state theory? (20 marks) (c) Derive an equation for Langmuir's adsorption isotherm. Show that under limiting conditions of pressure, the system follows both first-order and zero-order of adsorption. (20 marks)
हिंदी में प्रश्न पढ़ें
(a) बेंजीन और बोराजीन में आबंधन, चक्रीय फॉस्फाजीन से कैसे अलग है? (10 अंक) (b) संघट्ट सिद्धांत की परिसीमाएं क्या हैं? संक्रमण अवस्था सिद्धांत से इसकी व्याख्या कैसे की जाती है? (20 अंक) (c) लैंगम्यूर अधिशोषण समतापी वक्र के समीकरण को व्युत्पन्न कीजिए। यह भी दिखाइए कि दाब के सीमांत प्रतिबंध के अंदर यह तंत्र प्रथम-कोटि तथा शून्य-कोटि अधिशोषण का अनुसरण करता है। (20 अंक)
Directive word: Derive
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How this answer will be evaluated
Approach
Begin with the directive 'derive' for part (c), the highest-weighted section, while addressing 'how' in part (a) and 'what/why' in part (b). Allocate approximately 20% time to part (a) on bonding comparisons, 40% to part (b) on kinetic theory limitations and transition state explanations, and 40% to part (c) for rigorous derivation of Langmuir isotherm with limiting condition proofs. Structure as: comparative bonding analysis → theory critique with mechanism → mathematical derivation with graphical verification.
Key points expected
- Part (a): Contrast phosphazene's dπ-pπ bonding with benzene's delocalized π-system and borazine's partial aromaticity; note bond length equality in phosphazene vs. bond alternation in borazine; mention skeletal electron counting (6π vs. 6π vs. 6π but different orbital contributions)
- Part (b): List collision theory limitations—ignores molecular orientation, energy distribution assumptions, no account for activation energy details; explain how transition state theory introduces the activated complex, potential energy surface, and thermodynamic formulation of rate constants via partition functions or thermodynamic parameters (ΔH‡, ΔS‡, ΔG‡)
- Part (c): Derive Langmuir isotherm from kinetic equilibrium (rate of adsorption = rate of desorption) or statistical mechanics; define θ = KP/(1+KP); prove low P limit: θ ≈ KP (first-order, Henry's law region) and high P limit: θ ≈ 1 (zero-order, saturation)
- Part (c) continued: Show mathematical steps clearly—start with assumptions (monolayer, uniform surface, no interaction), set up equilibrium expression, solve for surface coverage θ
- Cross-part integration: Connect surface chemistry in (c) to catalytic applications relevant to Indian industry (e.g., Haber-Bosch ammonia synthesis, heterogeneous catalysis in refineries); relate transition state theory in (b) to enzyme kinetics and pharmaceutical development
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 25% | 12.5 | Demonstrates precise understanding of dπ-pπ bonding in phosphazenes (N-P π-backbonding), distinguishes true aromaticity (benzene) from pseudoaromaticity (borazine) and homoaromaticity alternatives; correctly identifies activated complex vs. transition state distinctions in TST; states all Langmuir assumptions explicitly including ideal surface behavior | Identifies basic bonding differences but confuses phosphazene's bonding type or mislabels borazine aromaticity; lists collision theory limitations without explaining their physical origin; states Langmuir equation without proper derivation context or misses key assumptions | Fundamental errors such as claiming phosphazene has pure pπ-pπ bonding like benzene, conflating collision and transition state theories as equivalent, or presenting Freundlich isotherm instead of Langmuir derivation |
| Mechanism / equation | 25% | 12.5 | Presents complete derivation of Langmuir isotherm with clear steps: adsorption rate = kₐP(1-θ), desorption rate = k_dθ, equilibrium setting leading to θ = KP/(1+KP); for (b), explains Eyring equation derivation from statistical mechanics or thermodynamic cycle with proper activated complex treatment | Writes final Langmuir equation correctly but derivation has gaps or skips equilibrium justification; for TST, mentions Eyring equation without derivation; presents correct but unmotivated mathematical steps | Incorrect rate expressions (e.g., first-order in occupied sites for desorption), missing equilibrium condition, or algebraic errors in solving for θ; presents Arrhenius equation as explanation for TST without modification |
| Numerical accuracy | 15% | 7.5 | Correctly performs Taylor expansion for low P limit showing θ ≈ KP (first-order); demonstrates high P limit simplification showing θ → 1 (zero-order); calculates or estimates realistic K values; presents dimensionally consistent equations throughout | States limiting conditions correctly but shows incomplete mathematical justification; presents correct final forms without derivation steps; minor algebraic slips that don't affect final conclusions | Incorrect limiting behavior (e.g., claims zero-order at low P), mathematical errors in expansion, or ignores pressure dependence entirely; presents equations with inconsistent units |
| Diagram / structure | 20% | 10 | Draws clear structures showing (NPR₂)₃ ring with axial/equatorial substituents for phosphazene; benzene with delocalized π-cloud; borazine with alternating B-N bond character; potential energy surface diagram for TST with reaction coordinate, activated complex at saddle point; Langmuir isotherm plot showing approach to saturation with asymptotic behavior | Draws basic ring structures without stereochemical detail; simple energy profile diagram without proper labeling of axes or activated complex; sketches Langmuir curve but misses asymptotic approach or labels axes incorrectly | Missing diagrams for any part; incorrect ring structures (e.g., planar phosphazene without puckering consideration); no PE surface for TST explanation; linear plot instead of hyperbolic isotherm curve |
| Application context | 15% | 7.5 | Cites Indian industrial relevance: phosphazene applications in flame-retardant polymers (defense/aerospace); TST applications in drug design (Indian pharmaceutical industry); Langmuir isotherm in water treatment (Arsenic removal in West Bengal), catalysis (IFFCO ammonia plants), or surface characterization (IIT research); connects theory to practical measurement techniques (BET method extension) | Mentions general applications without Indian specificity; notes catalysis importance without concrete examples; states adsorption is 'important in industry' without elaboration | No application context provided; entirely theoretical treatment disconnected from practical chemistry; irrelevant examples from unrelated fields |
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