(a) Draw the molecular orbital (MO) diagram of NO molecule. The experimental bond dissociation energy of NO is 626 kJ mol⁻¹ while that of NO⁺ is 1047 kJ mol⁻¹ — rationalize it. NO can also act as a reactive radical — how ? 20

(b) Calculate the diffu

Question

(a) Draw the molecular orbital (MO) diagram of NO molecule. The experimental bond dissociation energy of NO is 626 kJ mol⁻¹ while that of NO⁺ is 1047 kJ mol⁻¹ — rationalize it. NO can also act as a reactive radical — how ? 20

(b) Calculate the diffusion limiting current for the oxidation of an organic compound at an electrode in a quiescent solution. Assume six electrons are involved in the reaction and the thickness of diffusion layer is taken as 0.05 cm in an unstirred solution.

Given :
(i) Concentration of organic compound, Corganic = 10⁻² mole litre⁻¹
(ii) Diffusion coefficient of organic compound, Dorganic = 2 × 10⁻⁵ cm² sec⁻¹ 10

(c) The level of conductivity in a decimolar aqueous solution of calcium nitrate, which is a strong electrolyte, is measured as σ = 26·2 mS cm⁻¹ at 25°C. Calculate the molar conductivity of the electrolyte, that of calcium ions and the transport numbers of the two types of ions present in the solution, with the data given below.

Molar conductivity at infinite dilution in an aqueous solution at 25°C :

(i) λ₊⁰ (mS m² mol⁻¹)
Ca²⁺ 11·9

(ii) λ₋⁰ (mS m² mol⁻¹)
NO₃⁻ 7·14 10

(d) Suppose we redefine the standard state as Pressure, P = 2 atm. Find the new standard ΔG°f values of each substance :

(i) HCl (g)

(ii) N₂O (g)

Explain the results in terms of the relative entropies of reactants and products of each reaction.

Given : Standard free energy of formation at 25°C :

(i) ΔG°HCl = –95.3 kJ mol⁻¹

(ii) ΔG°N₂O = +103.7 kJ mol⁻¹ 10

UPSC Answer Check · Accepted Answer

Begin with a concise introduction stating that the question spans molecular orbital theory, electrochemistry, and thermodynamics. Allocate approximately 40% of effort to part (a) given its 20 marks—draw the MO diagram first, then explain bond order changes and radical character. Spend 20% each on parts (b), (c), and (d), showing all calculation steps with proper units. For (b), apply the Ilkovic equation for diffusion-limited current; for (c), use Kohlrausch's law and ionic mobility relationships; for (d), apply the pressure correction to standard Gibbs free energy using ΔG = ΔG° + RTln(P/P°). Conclude by summarizing how theoretical frameworks connect across physical chemistry domains.
- Part (a): Correct MO diagram for NO (11 valence electrons) showing σ2s, σ*2s, σ2p, π2p, π*2p, σ*2p energy levels with proper electron filling; bond order calculation (NO = 2.5, NO⁺ = 3) explaining higher BDE of NO⁺; explanation of unpaired electron in π*2p orbital conferring radical reactivity
- Part (b): Application of Ilkovic equation i_d = nFAD^(1/2)C/δ or equivalent diffusion-limited current expression; correct unit conversions (litre to cm³, time consistency); final calculation yielding ~0.186 mA or equivalent with proper significant figures
- Part (c): Molar conductivity Λ_m = κ/C calculation (26.2 mS cm⁻¹ / 0.1 mol L⁻¹ = 262 mS cm² mol⁻¹ or 26.2 mS m² mol⁻¹); application of Kohlrausch law Λ_m = ν₊λ₊ + ν₋λ₋ to find individual ionic conductivities; transport numbers t₊ = λ₊/Λ_m and t₋ = λ₋/Λ_m
- Part (d): Correct application of ΔG°(new) = ΔG°(old) + RTln(P_new/P_old) = ΔG°(old) + RTln(2) for each gas; recognition that gases with higher entropy (more complex molecules like N₂O vs HCl) show larger corrections; explanation that ΔG°f becomes more positive for products when standard pressure increases
- Part (a) bonus: Mention of NO's biological significance as signaling molecule (e.g., vasodilation) connecting radical chemistry to physiological function; reference to NO's role in atmospheric chemistry
- Cross-part synthesis: Demonstration of how thermodynamic driving forces (part d) relate to electrochemical potentials (part c) and kinetic limitations (part b) in real chemical systems

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	Demonstrates flawless understanding across all four parts: correctly identifies NO as 11-electron system with bond order 2.5, recognizes diffusion-limited current as mass-transport controlled, applies Debye-Hückel-Onsager or Kohlrausch concepts appropriately for strong electrolytes, and correctly interprets pressure dependence of chemical potential for gases	Shows basic understanding of most concepts but makes minor errors such as incorrect electron count in MO diagram, confusion between molar and equivalent conductivity, or incorrect sign in pressure correction term	Fundamental misconceptions evident: treats NO as 10-electron system, confuses activation control with diffusion control, applies Ostwald dilution law to strong electrolyte, or fails to recognize that ΔG° depends on standard state definition
Mechanism / equation	20%	10	Writes all key equations correctly: MO energy level expressions, Ilkovic or Fick's law-based current equation, Kohlrausch law of independent ionic migration, and pressure-dependent Gibbs free energy relation; shows clear logical flow from first principles	Writes most equations correctly but misses some details like stoichiometric coefficients in Kohlrausch law or uses approximate form of Ilkovic equation without justification	Equations largely incorrect or missing; confuses anodic and cathodic current directions, uses Arrhenius equation instead of diffusion equation, or applies Nernst equation inappropriately to non-equilibrium situations
Numerical accuracy	25%	12.5	All calculations precise with correct unit handling: diffusion current ~0.186 mA (or 1.86×10⁻⁴ A), molar conductivity 26.2 mS m² mol⁻¹ (or 262 S cm² mol⁻¹), transport numbers t(Ca²⁺)≈0.41 and t(NO₃⁻)≈0.59, and ΔG° corrections of +1.72 kJ mol⁻¹ for each gas at 2 atm	Correct methodology but arithmetic errors or unit conversion mistakes (e.g., missing factor of 10³ for mS to S, or incorrect diffusion layer thickness handling); final answers within order of magnitude	Calculations fundamentally flawed: wrong formulas applied, orders of magnitude incorrect, or no numerical working shown despite calculative parts carrying 30 marks
Diagram / structure	15%	7.5	Clear, labeled MO diagram showing relative energy levels of 2s and 2p orbitals, proper s-p mixing effects for NO (heteronuclear diatomic), correct electron filling with distinction between bonding and antibonding orbitals, and explicit marking of the unpaired electron in π*2p	Diagram present but lacks key labels or shows symmetric MO diagram inappropriate for heteronuclear diatomic; energy levels qualitatively correct but missing σ2p/π2p ordering specific to NO	No diagram provided, or diagram shows atomic orbitals without molecular orbital construction, incorrect electron count, or energy levels violating Aufbau principle
Application context	15%	7.5	Effectively connects theoretical concepts to practical significance: NO's role in environmental chemistry (smog formation, acid rain) and biochemistry (signal transduction); relevance of diffusion-limited currents in electroanalytical techniques like voltammetry; industrial importance of conductivity measurements for water quality; implications of standard state redefinition for high-pressure industrial processes	Mentions some applications but superficially; limited connection between calculated quantities and real-world measurement techniques or chemical phenomena	No contextualization provided; treats question as purely mathematical exercise without recognizing physical significance of any calculated quantity

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