Chemistry 2022 Paper I 50 marks Solve

Q4

(a) By using the following given data, find that under what conditions is H₂ in the state corresponding to N₂ at 126 K and 1 atm ? | Gas | Tc/K | Pc/atm | |---|---|---| | H₂ | 33 | 13 | | N₂ | 126 | 39 | (10 marks) (b) The vapour pressure of water at 363·2 K is 529 torr. Use the Clausius-Clapeyron equation to determine the average value of molar heat of vaporization, ΔH̄, of water between 363·2 K and 373·2 K. [R = 8·314 J mol⁻¹ k⁻¹] (10 marks) (c) Consider two liquids A and B such that A has half of the surface tension and twice the density of B. If liquid A rises to a height of 2·0 cm in a capillary, what will be the height to which liquid B will rise in the same capillary. (10 marks) (d) Write down the basic principle of polarography. With the help of a neat typical polarogram discuss the significance of halfwave potential, diffusion current and limiting current. (10 marks) (e) Determine the percentage of ionic character (bond polarity) of BrCl and comment on the nature of Br–Cl bond. (Dipole moment of BrCl = 1·42×10⁻³⁰ cm, bond length, d_Br–Cl = 214×10⁻¹⁴ m, charge of an electron = 1·6×10⁻¹⁹ C) (10 marks)

हिंदी में प्रश्न पढ़ें

(a) निम्नलिखित दिए गए आंकड़ों के आधार पर पता लगाएं कि कौन सी शर्तें हैं, जिन पर H₂, N₂ (126 K, 1 atm) की संगत अवस्था में हो ? | गैस | Tc/K | Pc/atm | |---|---|---| | H₂ | 33 | 13 | | N₂ | 126 | 39 | (10 अंक) (b) 363·2 K पर जल का वाष्पदाब 529 torr है । क्लॉजियस-क्लेपेरॉन समीकरण का प्रयोग करके जल की वाष्पन की मोलरऊष्मा, ΔH̄, का औसत मूल्य 363·2 K और 373·2 K के बीच में निर्धारित करें । [R = 8·314 J mol⁻¹ k⁻¹] (10 अंक) (c) मान लीजिए दो द्रव A और B हैं, जिनमें A का पृष्ठीय तनाव आधा और घनत्व B से दुगुना है। यदि द्रव A 2·0 cm की ऊँचाई तक एक केशिका में चढ़ता है, तो द्रव B, उसी केशिका में कितनी ऊँचाई तक चढ़ेगा ? (10 अंक) (d) ध्रुवणलेखिकी (पोलेरोग्राफी) का मूल सिद्धांत लिखें। विशुद्ध प्ररूपी (विशिष्ट) ध्रुवणलेख (पोलेरोग्राम) की मदद से अर्धतरंग विभव, विसरण धारा और सीमांत धारा के महत्व/सार्थकता की व्याख्या करें। (10 अंक) (e) BrCl में आयनी लक्षण (आबंध ध्रुवता) की प्रतिशतता को ज्ञात करें और Br–Cl आबंध की प्रकृति पर टिप्पणी करें। (BrCl का द्विध्रुव आघूर्ण = 1·42×10⁻³⁰ cm, आबंध लंबाई d_Br–Cl = 214×10⁻¹⁴ m, इलेक्ट्रॉन का आवेश = 1·6×10⁻¹⁹ C) (10 अंक)

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Approach

This is a multi-part calculation and descriptive problem requiring systematic solving of five independent sub-parts. Allocate approximately 20% time to each part: for (a) apply reduced variables and law of corresponding states; for (b) use integrated Clausius-Clapeyron equation with proper unit conversion; for (c) apply capillary rise formula with given ratios; for (d) explain polarography principle with labeled diagram; for (e) calculate % ionic character using dipole moment formula. Present each part clearly with given data, formula, substitution, and final answer with units.

Key points expected

  • For (a): Apply law of corresponding states using reduced temperature (Tr = T/Tc) and reduced pressure (Pr = P/Pc) to find H₂ conditions equivalent to N₂ at 126 K, 1 atm; calculate Tr(N₂) = 1.0, Pr(N₂) = 0.0256, then find T(H₂) = 33 K and P(H₂) = 0.333 atm
  • For (b): Apply integrated Clausius-Clapeyron equation ln(P₂/P₁) = (ΔHvap/R)(1/T₁ - 1/T₂) with P₁ = 529 torr at 363.2 K, P₂ = 760 torr at 373.2 K; solve for ΔHvap ≈ 40.6 kJ/mol
  • For (c): Use capillary rise formula h = 2γcosθ/(ρgr); establish ratio hA/hB = (γA/γB)×(ρB/ρA) = (1/2)×(2/1) = 1; thus hB = hA = 2.0 cm (or 4.0 cm if angle differs)
  • For (d): State Ilkovic equation principle; draw typical polarogram with S-shaped curve showing residual, limiting, and diffusion currents; explain E½ as characteristic identification potential, id as concentration-proportional, il as total limiting current
  • For (e): Calculate % ionic character = (μobserved/μionic)×100 = (1.42×10⁻³⁰)/(1.6×10⁻¹⁹ × 2.14×10⁻¹⁰)×100 ≈ 4.15%; comment on predominantly covalent nature with slight polarity

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies: law of corresponding states for (a), Clausius-Clapeyron for phase equilibria in (b), capillary action and surface tension relationships in (c), electrochemical principles of polarography including dropping mercury electrode in (d), and electronegativity difference with dipole moment theory in (e)Identifies most concepts correctly but shows minor confusion in one part, such as misstating the law of corresponding states or confusing limiting current with diffusion currentFundamental conceptual errors in multiple parts, such as applying wrong thermodynamic law, misunderstanding polarography principle, or incorrect interpretation of % ionic character formula
Mechanism / equation20%10Writes all required equations correctly: Tr = T/Tc, Pr = P/Pc for (a); integrated Clausius-Clapeyron with proper logarithmic form for (b); h = 2γcosθ/(ρgr) for (c); Ilkovic equation id = 607nD¹/²m²/³t¹/⁶c for (d); μionic = e×d and % ionic character formula for (e)Writes most equations correctly but has minor errors such as wrong sign in Clausius-Clapeyron or missing cosθ term in capillary equationMissing or seriously wrong equations, such as using ideal gas law instead of reduced variables, or completely omitting Ilkovic equation in polarography discussion
Numerical accuracy25%12.5All calculations accurate with proper significant figures: (a) T = 33 K, P = 0.333 atm; (b) ΔHvap ≈ 40.6 kJ/mol; (c) hB = 2.0 cm or 4.0 cm with clear reasoning; (e) % ionic character ≈ 4.1-4.2%; proper unit conversions throughoutCorrect method but arithmetic errors in 1-2 parts, such as wrong temperature conversion, incorrect logarithm calculation, or misplaced decimal in dipole moment calculationMajor calculation errors in multiple parts, wrong order of magnitude answers, or complete absence of numerical working for calculative parts
Diagram / structure15%7.5Neat, labeled polarogram for (d) showing: potential (E) on x-axis, current (i) on y-axis, residual current region, rising portion, half-wave potential (E½) marked, diffusion current plateau (id), and limiting current (il); clear indication of dropping mercury electrode setupSketch present but missing key labels such as E½ or confusing id with il; or diagram drawn for wrong conceptNo diagram for (d), or completely unrecognizable sketch with no labels; failure to understand that only part (d) requires diagram
Application context20%10Connects to practical relevance: corresponding states for gas liquefaction and cryogenics (relevant to Indian space program ISRO cryogenic engines), Clausius-Clapeyron for distillation and meteorology, capillary action for soil science and petroleum recovery, polarography for trace metal analysis in environmental monitoring (Ganga water quality), % ionic character for predicting reactivity of interhalogen compoundsBrief mention of one or two applications without elaboration, or generic statements not specific to the contextNo application context provided; purely theoretical treatment without any real-world connection to Indian industry, environment, or research

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