Chemistry 2024 Paper I 50 marks Calculate

Q4

(a) A new drug has been synthesized and its phase diagram is explored. It is found that near its triple point, vapour pressure over the liquid (Pl) and over the solid (Ps) are given by : ln Pl = − 3010/T + 13·2 and ln Ps = − 3820/T + 16·1. Calculate the triple point temperature and pressure. Is the new drug solid, gas or liquid at 1 bar, 298 K ? What is ΔHsublimation ? Explain. (15 marks) (b) (i) What is polarography ? Explain the concentration polarization at the electrode. Give the labelled diagram of polarographic cell assembly. (15 marks) (ii) Define concentration cell and mention its types. Justify the statement "Fuel cells are energy conversion devices and not energy storage devices." (5 marks) (c) (i) For the sequential reaction A → B → C, the rate constants are kA = 5 × 10⁶ s⁻¹ and kB = 3 × 10⁶ s⁻¹. Determine the time when the concentration of B is at a maximum. (10 marks) (ii) In acidic condition, benzyl penicillin (BP) undergoes the following reaction : P₁ ← BP → P₂ (with k₁, k₂) and BP → P₃ (with k₃). Imagine while swallowing penicillin, pH of the stomach is ~3. At this pH, and temperature 22°C, the rate constants for the processes are : k₁ = 7·0 × 10⁻⁴ s⁻¹, k₂ = 4·1 × 10⁻³ s⁻¹, k₃ = 5·7 × 10⁻³ s⁻¹. What is the yield of P₁ formation ? (5 marks)

हिंदी में प्रश्न पढ़ें

(a) एक नया ड्रग (दवाई) संश्लेषित किया गया और उसके प्रावस्था आरेख की गवेषणा की गई। यह पाया गया कि इसके त्रिक बिंदु के पास तरल (Pl) और ठोस (Ps) के ऊपर वाष्प दाब दिया गया है : ln Pl = − 3010/T + 13·2 और ln Ps = − 3820/T + 16·1। त्रिक बिंदु तापमान और त्रिक बिंदु दाब का परिकलन कीजिए। क्या नया ड्रग 1 bar, 298 K पर ठोस, गैस या द्रव होगा ? ΔHउर्ध्वपातन क्या है ? समझाइए। (15 अंक) (b) (i) ध्रुवणलेखिकी (पोलैरोग्राफी) क्या है ? इलेक्ट्रोड पर सांद्रता ध्रुवण की व्याख्या कीजिए। ध्रुवणलेखीय सेल समुच्चय का नामांकित आरेख दीजिए। (15 अंक) (ii) सांद्रता सेल को परिभाषित कीजिए और इसकी किस्मों का उल्लेख कीजिए। "ईंधन सेल ऊर्जा परिवर्तन करने वाले यंत्र हैं न कि ऊर्जा को संग्रहित करने वाले यंत्र।" इस कथन को उचित सिद्ध कीजिए। (5 अंक) (c) (i) एक अनुक्रमिक अभिक्रिया A → B → C के लिए, वेग स्थिरांक kA = 5 × 10⁶ s⁻¹ और kB = 3 × 10⁶ s⁻¹ हैं। उस समय को निर्धारित कीजिए जब B का सांद्रण अधिकतम हो। (10 अंक) (ii) अम्लीय अवस्था में, बेंजिल पेनिसिलिन (BP) निम्नलिखित अभिक्रिया देता है : P₁ ← BP → P₂ (k₁, k₂ से) और BP → P₃ (k₃ से)। मान लीजिए पेनिसिलिन को निगलते समय, पेट का pH ~ 3 है। इस pH पर और ताप 22°C पर इन प्रक्रमों के वेग स्थिरांक हैं : k₁ = 7·0 × 10⁻⁴ s⁻¹, k₂ = 4·1 × 10⁻³ s⁻¹, k₃ = 5·7 × 10⁻³ s⁻¹। P₁ की उत्पत्ति की लंबिथ/उपज क्या है ? (5 अंक)

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Directive word: Calculate

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How this answer will be evaluated

Approach

Begin with the directive to calculate, derive, and explain across all sub-parts. Allocate approximately 30% time to part (a) for triple point calculations and phase identification, 35% to part (b) for polarography explanation with diagram and concentration cell theory, and 35% to part (c) for sequential reaction kinetics and parallel reaction yield calculations. Structure as: direct numerical solutions for (a) and (c), conceptual definitions with diagram for (b)(i), and analytical justification for (b)(ii).

Key points expected

  • Part (a): Triple point occurs where Pl = Ps; solve −3010/T + 13.2 = −3820/T + 16.1 to get T_tp = 270.3 K, then P_tp = 0.042 bar; compare 1 bar/298 K with triple point to identify liquid phase; ΔH_sublimation = ΔH_vap + ΔH_fus derived from Clausius-Clapeyron slopes
  • Part (b)(i): Definition of polarography as electrolysis with dropping mercury electrode; explanation of concentration polarization as depletion of electroactive species at electrode surface causing diffusion-controlled current; labelled diagram showing Hg reservoir, capillary, electrolyte solution, reference electrode, and potentiometer
  • Part (b)(ii): Concentration cell definition (E_cell depends only on concentration ratio); types—electrode concentration cell and electrolyte concentration cell; fuel cells convert chemical energy directly to electrical energy (Gibbs free energy change) unlike batteries which store energy
  • Part (c)(i): For sequential reaction A→B→C, time for maximum [B] is t_max = (ln(k_A/k_B))/(k_A - k_B); substitute k_A = 5×10⁶ s⁻¹, k_B = 3×10⁶ s⁻¹ to obtain t_max ≈ 5.1×10⁻⁷ s
  • Part (c)(ii): For parallel reactions, yield of P₁ = k₁/(k₁+k₂+k₃) × 100%; calculate as (7.0×10⁻⁴)/(7.0×10⁻⁴ + 4.1×10⁻³ + 5.7×10⁻³) × 100% ≈ 6.7%

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Demonstrates flawless understanding of triple point definition, phase stability criteria, polarography principles, concentration polarization mechanism, fuel cell thermodynamics, and sequential/parallel reaction kinetics; correctly identifies liquid phase at 298 K/1 bar by comparing with triple pointShows basic understanding of most concepts but confuses triple point with critical point, or misidentifies phase at given conditions; vague explanation of concentration polarization; incomplete justification for fuel cellsFundamental misconceptions about phase equilibria, misidentifies solid/liquid/gas at 298 K; fails to distinguish between energy conversion and storage; confuses sequential with parallel reaction kinetics
Mechanism / equation20%10Correctly writes Clausius-Clapeyron integrated form, derives ΔH_sublimation from vapor pressure equations; explains Ilkovič equation for diffusion current; writes Nernst equation for concentration cells; derives t_max formula for sequential reactions; applies Arrhenius concepts appropriatelyWrites most key equations but misses derivation steps; states Ilkovič equation without context; writes Nernst equation but doesn't apply to concentration cells; uses t_max formula without derivationIncorrect or missing equations; confuses Clausius-Clapeyron with van't Hoff equation; no mention of diffusion current equation; fails to write rate equations for sequential reactions
Numerical accuracy25%12.5Precise calculations: T_tp = 270.3 K (or 269-271 K), P_tp = 0.042 bar (or 0.04-0.045 bar), ΔH_vap = 25.0 kJ/mol, ΔH_sub = 31.8 kJ/mol; t_max = 5.1×10⁻⁷ s; yield of P₁ = 6.7% (or 6.6-6.8%); all unit conversions correctCorrect order of magnitude for most answers but arithmetic errors in 1-2 calculations; incorrect unit conversion for pressure or time; yield calculation shows correct method but wrong final percentageMajor calculation errors; wrong formula application; order of magnitude errors; missing units; fails to calculate more than half the required numerical values
Diagram / structure15%7.5Clear labelled polarographic cell diagram with: dropping mercury electrode (capillary, Hg reservoir), reference electrode (calomel or Ag/AgCl), electrolyte solution, nitrogen inlet for deaeration, potentiometer/galvanometer; shows polarogram (current-voltage curve) with residual, limiting, and diffusion current regionsBasic diagram with mercury drop electrode but missing key labels; no reference electrode shown; or shows conventional voltammetric cell instead of polarographic setupNo diagram provided; or completely incorrect schematic; unlabelled sketch; diagram of wrong technique (e.g., conductometric titration)
Application context20%10Relates triple point to pharmaceutical stability (drug formulation storage); connects polarography to trace metal analysis in environmental/clinical samples (e.g., heavy metal detection in Ganges water); links fuel cells to India's hydrogen energy mission; discusses penicillin degradation kinetics in drug design; cites Indian pharmaceutical industry relevanceGeneric mention of applications without Indian context; states polarography is 'useful in analysis' without specifics; mentions fuel cells for vehicles without energy policy contextNo real-world applications mentioned; purely theoretical treatment; fails to connect any concept to practical chemistry or Indian scenario

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