Chemistry 2024 Paper I 50 marks Calculate

Q3

(a) (i) Calculate the coefficient of viscosity of air at temperatures : (I) 298 K and (II) 0 K. Assume that the collision cross-section (πσ²) of air is 0·28 (nm)² and average molar mass of air is 29 g mol⁻¹. (10 marks) (ii) Arrange Boyle's temperature of the gases Ar, CH₄ and C₆H₆ in increasing order. Give reason(s) for the answer. (5 marks) (b) (i) Which of the following liquids has greater surface tension : Ethanol or Dimethyl ether. Explain the answer with reasons. (5 marks) (ii) Calculate the difference in pressure across the liquid-air interface for a water droplet of radius 150 nm. (5 marks) (c) (i) Calculate the change in Helmholtz energy for a reversible isothermal compression of 1 mole of an ideal gas whose volume decreases from 100·0 L to 22·4 L. Assume that temperature is 298 K. (10 marks) (ii) Why does a tyre get hot when air is pumped into it ? Can a tyre be inflated without a rise in temperature ? (5 marks) (iii) Calculate the pressure of O₂ (in atm) over a sample of NiO at 25°C if ΔG° = 212 kJ/mole for the following reaction : NiO (s) ⇌ Ni (s) + ½ O₂ (g) (5 marks) (iv) Estimate the final temperature of one mole of gas at 200·00 atm and 19·0°C as it is forced through a porous plug to a final pressure of 0·95 atm. Given : The Joule-Thomson coefficient (μJT) of the gas is 0·150 K/atm. (5 marks)

हिंदी में प्रश्न पढ़ें

(a) (i) वायु के श्यानता गुणांक का परिकलन तापमान (I) 298 K और (II) 0 K पर कीजिए। मान लीजिए कि वायु का संघट्टन परिक्षेत्र (क्रॉस-सेक्शन) (πσ²) 0·28 (nm)² और वायु का औसत ग्राम अणुक (मोलर) द्रव्यमान 29 g mol⁻¹ है। (10 अंक) (ii) Ar, CH₄ और C₆H₆ गैसों को उनके बॉयल ताप के आधार पर बढ़ते हुए क्रम में व्यवस्थित कीजिए। उत्तर का/के कारण दीजिए। (5 अंक) (b) (i) निम्नलिखित द्रवों में किसका पृष्ठीय तनाव अधिक है : एथेनॉल या डाइमेथिल ईथर। कारणों सहित उत्तर की व्याख्या कीजिए। (5 अंक) (ii) एक पानी की बूंद जिसकी त्रिज्या 150 nm है, के द्रव-वायु अंतरापृष्ठ के आर-पार दाब में अंतर का परिकलन कीजिए। (5 अंक) (c) (i) एक ग्राम अणु (मोल) आदर्श गैस के उष्मतापी समतापी संपीडन में आयतन 100·0 L से घटकर 22·4 L हो जाता है। ऐसी प्रक्रिया के लिए हेल्महोल्ट्ज़ ऊर्जा में परिवर्तन का परिकलन कीजिए। मान लीजिए तापमान 298 K है। (10 अंक) (ii) हवा भरने के समय एक टायर गर्म क्यों हो जाता है ? क्या बिना ताप बढ़ाए, एक टायर को फुलाया जा सकता है ? (5 अंक) (iii) निम्नलिखित अभिक्रिया के लिए 25°C पर NiO के नमूने के ऊपर O₂ के दाब (atm में) का परिकलन कीजिए, यदि ΔG° = 212 kJ/mole है : NiO (s) ⇌ Ni (s) + ½ O₂ (g) (5 अंक) (iv) एक ग्राम अणु (मोल) गैस 200·00 atm और 19·0°C पर, के बलपूर्वक संघ्र झार (पोरस प्लग) से घुसाए जाने पर इसका अंतिम दाब 0·95 atm रह जाता है। गैस के अंतिम तापमान का आकलन कीजिए। दिया गया है : गैस का जूल-थॉमसन गुणांक (μJT) 0·150 K/atm है। (5 अंक)

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Approach

Calculate numerical values for all six sub-parts with systematic working. For (a)(i) apply kinetic theory viscosity formula; for (a)(ii) use TB = a/Rb relation with van der Waals constants. For (b)(i) compare intermolecular forces; (b)(ii) apply Laplace equation. For (c)(i) use ΔA = -nRT ln(V2/V1); (c)(ii) explain adiabatic compression; (c)(iii) use ΔG° = -RT ln Kp; (c)(iv) apply Joule-Thomson cooling. Allocate ~25% time to 10-mark parts, ~12-15% to 5-mark parts, showing all steps with proper units.

Key points expected

  • (a)(i) Viscosity calculation at 298 K and 0 K using η = (5/16) × (MRT/π)^(1/2) / (N_A × σ²) with recognition that viscosity → 0 at 0 K (theoretical limit)
  • (a)(ii) Boyle temperature order: CH₄ < Ar < C₆H₆ based on TB = a/Rb; larger molecules with stronger intermolecular forces have higher TB
  • (b)(i) Ethanol > Dimethyl ether due to hydrogen bonding in ethanol vs dipole-dipole only in ether; surface tension correlates with cohesive energy
  • (b)(ii) Laplace pressure ΔP = 2γ/r for spherical droplet; using γ_water ≈ 72 mN/m gives ΔP ≈ 9.6 × 10⁵ Pa or ~9.5 atm
  • (c)(i) Helmholtz energy change: ΔA = nRT ln(V2/V1) = (1)(8.314)(298)ln(22.4/100) ≈ -3.72 kJ (negative for compression)
  • (c)(ii) Tyre heats due to adiabatic compression (q=0, w = ΔU > 0); isothermal inflation with cooling possible but impractical
  • (c)(iii) Kp = exp(-ΔG°/RT) = p(O₂)^(1/2); solving gives p(O₂) ≈ 4.8 × 10⁻³⁷ atm (extremely small, NiO stable)
  • (c)(iv) Joule-Thomson cooling: ΔT = μ_JT × ΔP = 0.150 × (0.95-200) ≈ -29.9 K; T_final ≈ -10.9°C or 262 K

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%12Correctly identifies that viscosity vanishes at 0 K (quantum limit), recognizes TB depends on a/b ratio, distinguishes H-bonding vs dipole effects, identifies adiabatic nature of tyre inflation, and correctly interprets ΔG° >> 0 for NiO stabilityCorrect basic concepts but confuses Boyle temperature with critical temperature, or misidentifies the thermodynamic process in tyre inflation, or makes sign errors in free energy interpretationFundamental conceptual errors: treats viscosity as temperature-independent, confuses surface tension with viscosity, or believes NiO spontaneously decomposes at 25°C
Mechanism / equation20%12States all key equations: Chapman-Enskog viscosity formula, TB = a/Rb, Laplace ΔP = 2γ/r, ΔA = -∫pdV, ΔG° = -RT ln K, μ_JT = (∂T/∂P)_H with correct thermodynamic derivationsWrites most equations correctly but misses constant factors (e.g., 5/16 in viscosity), or uses approximate forms without justification, or omits derivation stepsWrong equations (e.g., uses ΔG = ΔH - TΔS for equilibrium calculation), or invents non-existent formulas, or applies equations to inappropriate conditions
Numerical accuracy25%15All six calculations with correct significant figures: η(298K) ≈ 1.8 × 10⁻⁵ Pa·s, η(0K) → 0, ΔP ≈ 9.6 × 10⁵ Pa, ΔA ≈ -3.72 kJ, p(O₂) ≈ 10⁻³⁷ atm, T_final ≈ 262 K; proper unit conversions throughoutCorrect methodology but arithmetic errors (factor of 2-10), or wrong powers of 10, or inconsistent units (nm vs m, kJ vs J confusion), or missing one calculationOrder-of-magnitude errors, completely wrong answers (e.g., p(O₂) > 1 atm), or missing numerical working for multiple parts; no unit analysis
Diagram / structure15%9Clear schematic of Joule-Thomson porous plug experiment with throttling process; pressure-volume diagram for isothermal compression; molecular diagram showing H-bonding in ethanol vs ether; well-organized calculation layoutBasic sketches without labels, or disorganized presentation with calculations scattered; missing diagrams for key concepts where visual aid would helpNo diagrams where required; chaotic structure making it impossible to follow which calculation belongs to which sub-part; no clear section headings
Application context20%12Connects to real-world relevance: viscosity in atmospheric science/ISRO launch conditions, tyre pressure safety in Indian highways, NiO in battery cathodes (Ni-MH, Li-ion), Joule-Thomson in gas liquefaction (LNG, cryogenics for ISRO); explains why 0 K viscosity is theoreticalMentions one or two applications superficially (e.g., 'used in industry') without specific Indian or technological context; generic statements about 'importance'No real-world connections; fails to explain physical significance of results (e.g., doesn't comment on impossibly low p(O₂) for NiO decomposition)

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