Chemistry 2021 Paper I 50 marks Explain

Q3

(a) A drop of water, 0·4 cm in radius, is split up into 125 tiny drops. Find the increase in surface energy. [γwater (surface tension of water) = 72 dynes/cm ] (10 marks) (b) What are ion-selective electrodes? How is glass electrode used in the determination of pH of a given solution? (20 marks) (c) (i) Draw and explain the graph of enthalpy of vapourization from the triple point (Tp) to the critical point (Tc). (10 marks) (ii) A thermally insulated box is separated into two compartments (volumes V₁ and V₂) by a membrane. One of the compartments contains an ideal gas at temperature T, the other is empty (vacuum). The membrane is suddenly removed, and the gas fills up the compartments and reaches the equilibrium. What is the final temperature of the gas? Show that the gas expansion process is irreversible. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) पानी की एक बूंद, जिसकी त्रिज्या 0·4 cm है, 125 बहुत छोटी बूंदों में विपाटित हो गई है। पृष्ठीय ऊर्जा में वृद्धि का पता लगाइए। [γजल (जल का पृष्ठीय तनाव) = 72 dynes/cm ] (10 अंक) (b) आयन-वरणात्मक इलेक्ट्रोड क्या हैं? दिए गए विलयन का pH निर्धारित करने के लिए कांच के इलेक्ट्रोड को कैसे प्रयोग में लाया जाता है? (20 अंक) (c) (i) वाष्प एन्थैल्पी का ग्राफ/आलेख त्रिक बिंदु (Tp) से क्रांतिक बिंदु (Tc) तक खींचकर उसकी व्याख्या कीजिए। (10 अंक) (ii) एक उष्मारोधी बॉक्स को एक झिल्ली के द्वारा दो कक्षों (आयतन V1 और V2) में अलग किया/बांटा गया है। एक कक्ष में आदर्श गैस तापमान T पर अंतर्विष्ट है (समाई है) और दूसरा कक्ष रिक्त (निर्वात) है। जब झिल्ली को एकाएक हटा दिया गया, तो गैस ने कक्षों को भर दिया और साम्यावस्था में पहुंच गई। गैस का अंतिम तापमान क्या है? प्रदर्शित कीजिए कि गैस का प्रसरण अनुक्रमणीय प्रक्रम है। (10 अंक)

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Directive word: Explain

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Approach

Begin with a brief introduction linking surface phenomena, electrochemistry, and thermodynamics as core physical chemistry topics. For part (a), apply the surface energy formula with proper unit conversion from CGS to SI or consistent use of dynes/cm; for (b), define ion-selective electrodes with emphasis on glass electrode mechanism and Nernst equation application; for (c)(i), sketch the enthalpy of vaporization curve showing its decrease from Tp to Tc with proper labeling; for (c)(ii), prove T_final = T_initial using Joule-Thomson expansion concepts and demonstrate entropy increase for irreversibility. Allocate approximately 15-20% time to (a), 35-40% to (b), 20% to (c)(i), and 25% to (c)(ii), ensuring all numerical derivations show intermediate steps.

Key points expected

  • Part (a): Conservation of volume to find radius of small drops (r = R/5 = 0.08 cm), calculation of initial and final surface areas, application of ΔE = γ × ΔA = 4πγ(n·r² - R²) yielding 4πγ × 4R² = 16πγR² = 579.6 ergs or ~58 μJ
  • Part (b): Definition of ion-selective electrodes (ISEs) as membrane electrodes responding selectively to specific ions; glass electrode construction (Ag/AgCl internal reference, thin glass membrane, internal buffer); Nernst equation E = E° - 0.0591 pH at 25°C; calibration using standard buffers (pH 4, 7, 10) and temperature compensation
  • Part (c)(i): Enthalpy of vaporization (ΔHvap) decreases from maximum at triple point to zero at critical point; curve shape concave downward due to weakening intermolecular forces; mention of Watson correlation or Trouton's rule context; proper axes labeling (T on x-axis, ΔHvap on y-axis)
  • Part (c)(ii): Free expansion of ideal gas into vacuum; ΔU = 0 implies T_final = T_initial for ideal gas; calculation of entropy change ΔS = nR ln[(V₁+V₂)/V₁] > 0 proving irreversibility; mention that real gases show Joule-Thomson cooling
  • Integration: Recognition that parts (a) and (c)(ii) both involve energy considerations but with different constraints (surface vs. bulk thermodynamics), while (b) connects electrochemical potential to chemical potential concepts

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies surface energy as work needed to create unit area; defines ISEs by selective ion permeability not redox potential; recognizes ΔHvap→0 at Tc due to liquid-gas distinction vanishing; states free expansion is isothermal for ideal gas but irreversible due to entropy generationBasic definitions correct but confuses surface tension with surface energy units; describes glass electrode operationally without membrane potential mechanism; sketches ΔHvap trend correctly but omits physical reason for zero at Tc; states T_final=T_initial without ΔU=0 justificationConfuses surface energy with bulk internal energy; describes pH meter as whole instead of glass electrode specifically; draws ΔHvap increasing or constant; claims T_final changes or invokes incorrect gas law application
Mechanism / equation20%10Writes complete surface energy equation with area change derivation; presents Nernst equation with proper constants and glass electrode potential equation E_glass = E°_glass + (RT/F)ln a_H+; explains ΔHvap temperature dependence via Clausius-Clapeyron or similar; derives ΔS = nR ln(V_f/V_i) for irreversibility proofStates area ratio formula for (a) without showing volume conservation step; writes Nernst equation but with sign errors or missing temperature term; mentions Clapeyron equation for (c)(i) without integration; states entropy increases without derivationMissing or incorrect equations throughout; no derivation of small drop radius; no Nernst equation; no entropy calculation for irreversibility proof
Numerical accuracy20%10Part (a): Correctly finds r = 0.08 cm, calculates ΔA = 4π(125×0.0064 - 0.16) = 4π×0.64 = 8.042 cm², ΔE = 72×8.042 = 579 ergs = 5.79×10⁻⁵ J or 57.9 μJ with proper unit handling; Part (c)(ii): Explicitly shows T_final = T with numerical entropy value if volumes givenCorrect method but arithmetic errors (e.g., wrong power of 10 in radius calculation); correct final formula but substitution errors; omits unit conversion or leaves in mixed unitsMajor calculation errors (e.g., linear instead of cubic root for radius); order of magnitude wrong; no numerical work shown
Diagram / structure20%10Clear labeled diagram for (c)(i) showing ΔHvap vs T curve from Tp to Tc with correct concave shape, asymptotic approach to zero at Tc, and comparison with sublimation enthalpy; schematic of glass electrode with all components labeled; before/after diagram for free expansion in (c)(ii)Sketch present for (c)(i) but missing labels or incorrect curve shape; glass electrode described textually without diagram; free expansion described without visual representationNo diagrams where required; or completely incorrect diagrams (e.g., linear ΔHvap, wrong axes)
Application context20%10Cites Indian context: use of glass electrodes in Ganga water quality monitoring by CPCB; surface energy relevance to monsoon cloud droplet formation; mentions ISRO studies on cryogenic fuel behavior near critical points; connects free expansion to vacuum technology in Indian research institutionsGeneric applications mentioned (pH measurement in labs, cloud physics) without Indian specificity; no real-world context for thermodynamics partsNo applications cited; or irrelevant applications (e.g., industrial processes not connected to principles)

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