(a) Calculate the e.m.f. of the following electrochemical cell at 25 °C : Pt/H₂₍₁ ₐₜₘ₎|H⁺₍C=0.01 M₎‖Cu²⁺₍C=0.1 M₎|Cu(s) (10 marks)

(b) (i) A certain closed cell foam used as an insulating material is initially filled with polyatomic gas of molecular

Question

(a) Calculate the e.m.f. of the following electrochemical cell at 25 °C : Pt/H₂₍₁ ₐₜₘ₎|H⁺₍C=0.01 M₎‖Cu²⁺₍C=0.1 M₎|Cu(s) (10 marks)

(b) (i) A certain closed cell foam used as an insulating material is initially filled with polyatomic gas of molecular weight ~ 60. Later, the gas diffuses out of the foam and is replaced by dry air (mean molecular weight ~ 30). Assuming that insulating property arises largely from the thermal conductivity of the gas, explain the factors which influence the thermal conductivity of the gas. For each factor, make an argument whether insulating ability increases or decreases. What is the overall effect upon the insulating ability? (10 marks)
(ii) The critical temperature and pressure for NO gas are 177 K and 64 atm, respectively, and for CCl₄, they are 550 K and 45 atm, respectively. Which gas has the smaller values of the van der Waals' constants, a and b? Which is the most nearly ideal in behaviour at 300 K and 10 atm? (10 marks)

(c) Explain the phase diagram of phenol-water system by highlighting the importance of tie lines. (20 marks)

UPSC Answer Check · Accepted Answer

Begin with a brief introduction acknowledging the interconnected nature of physical chemistry principles across electrochemistry, transport phenomena, and phase equilibria. Allocate approximately 15 minutes (20%) to part (a) for precise Nernst equation calculation; 20 minutes (25%) to part (b)(i)-(ii) covering thermal conductivity analysis and real gas comparisons; and 35 minutes (45%) to part (c) requiring detailed phenol-water phase diagram with tie line construction. Conclude by synthesizing how non-ideality manifests across electrochemical, gaseous, and liquid-liquid systems.
- Part (a): Correct identification of half-reactions (H₂ → 2H⁺ + 2e⁻ and Cu²⁺ + 2e⁻ → Cu), application of Nernst equation E = E° - (RT/nF)lnQ with proper substitution of concentrations and partial pressure, yielding Ecell ≈ 0.34 - 0.0591/2 log(0.01²/0.1) = 0.34 + 0.0887 = 0.4287 V
- Part (b)(i): Explanation of thermal conductivity dependence on molecular weight (κ ∝ 1/√M, lower M increases conductivity, worsening insulation), degrees of freedom (polyatomic vs diatomic affecting specific heat and energy transfer), and mean free path; overall conclusion that air replacement degrades insulating performance
- Part (b)(ii): Derivation that smaller Tc and larger Pc indicate smaller 'a' (intermolecular forces) and 'b' (molecular size), hence NO has smaller a and b than CCl₄; NO behaves more ideally at 300K/10atm due to lower Tc and reduced significance of attractive forces at T >> Tc
- Part (c): Construction of temperature-composition phase diagram for phenol-water showing upper consolute temperature (~66°C, 34% phenol), two-phase region below CST, and conjugate solutions; explicit demonstration of tie lines connecting equilibrium liquid compositions and their use in lever rule calculations for phase amounts
- Integration point: Recognition that all parts involve deviation from ideality—electrochemical (activity coefficients), gaseous (van der Waals corrections), and liquid-liquid (partial miscibility)—with practical relevance to materials science and chemical engineering applications in Indian industrial contexts

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless conceptual grasp: for (a) identifies standard hydrogen electrode as reference and correct cell polarity; for (b)(i) correctly relates thermal conductivity to kinetic theory parameters and identifies all three influencing factors; for (b)(ii) accurately interprets critical constants in terms of van der Waals parameters; for (c) correctly identifies phenol-water as partially miscible with upper consolute temperature and explains mutual solubility variation with temperature	Shows basic understanding of most concepts but with minor errors: may confuse anode/cathode designation, misidentify one factor affecting thermal conductivity, or incorrectly relate critical constants to molecular parameters; phase diagram description lacks precision on consolute temperature nature	Fundamental misconceptions present: incorrect cell reaction direction, confuses thermal conductivity with thermal diffusivity, misapplies van der Waals equations, or describes phenol-water as completely miscible or immiscible without temperature qualification
Mechanism / equation	20%	10	Presents all required equations with proper physical meaning: Nernst equation in both forms (natural log and base-10), kinetic theory expression for thermal conductivity with temperature and molecular weight dependence, van der Waals equation and its relationship to critical constants (Tc = 8a/27Rb, Pc = a/27b²), lever rule equation for tie line applications; all equations properly labeled and variables defined	Writes most key equations but with minor omissions: may present Nernst equation without showing concentration term derivation, states thermal conductivity trends without underlying equation, gives van der Waals equation without critical constant relationships, or states lever rule conceptually without mathematical formulation	Missing or incorrect equations: omits Nernst equation entirely, provides irrelevant transport equations, cannot relate critical constants to a and b, or fails to mention lever rule for tie lines
Numerical accuracy	20%	10	Part (a): Correct calculation with all steps shown—E°cell = 0.34 V, Q = [H⁺]²/PCu²⁺ = (0.01)²/0.1 = 0.001, E = 0.34 - (0.0591/2)log(0.001) = 0.34 + 0.08865 = 0.4286 V (or 0.43 V with proper significant figures); Part (b)(ii): Correct quantitative comparison showing NO has a(NO)/a(CCl₄) ≈ (Tc·Pc ratios) indicating smaller values; no calculation errors, proper unit handling, and reasonable significant figures throughout	Correct approach but with arithmetic errors: wrong exponent in Nernst equation (uses n=1 instead of n=2), sign error in log term, or incorrect Q expression; qualitative comparison in (b)(ii) without numerical justification; final answer within 10% of correct value	Major numerical errors: completely wrong Ecell value, incorrect formula application yielding nonsensical results, or omission of numerical work in (a) and (b)(ii) entirely
Diagram / structure	20%	10	Part (c): Neat, labeled phase diagram with temperature (y-axis) vs composition (x-axis, 0-100% phenol), clearly marked upper consolute temperature (~66°C at 34% phenol), dome-shaped two-phase region below CST, single-phase regions above CST and at composition extremes; multiple properly drawn horizontal tie lines at different temperatures with endpoints (conjugate solutions) connected, demonstrating lever rule application; axes labeled with units, curves distinguished	Sketch present but with deficiencies: missing labels on axes or key points, tie lines drawn but not explained, consolute temperature indicated but approximate position wrong, or diagram too small to interpret clearly	No diagram provided, or diagram fundamentally wrong (e.g., shows lower consolute temperature, eutectic behavior, or completely misshaped miscibility gap); tie lines absent or incorrectly drawn vertically
Application context	20%	10	Connects all parts to practical significance: for (a) mentions pH measurement, fuel cells, or corrosion protection relevant to Indian metallurgical industries; for (b)(i) explicitly addresses building insulation, energy efficiency in tropical/subtropical Indian climates, and refrigerant gas selection; for (b)(ii) relates to gas storage, industrial gas handling safety, and process design; for (c) references phenol-water separation in petrochemical/wastewater treatment, pharmaceutical extraction processes, or phenol-formaldehyde resin (Bakelite) manufacturing in Indian chemical industry	Mentions some applications but superficially: generic statements about batteries, insulation, or phase separation without specific Indian/industrial context; may focus on only 2-3 parts while neglecting others	No application context provided; or irrelevant applications cited (e.g., discussing electrochemistry for (c), or phase diagrams for (a)); complete disconnect between theory and practical utility

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