(a) Explain the common structural features of two major iron-containing proteins—haemoglobin and cytochrome c present in the human body. Explain the coordination chemistry involved at the central metal atom in case of oxyhaemoglobin and deoxyhaemoglo

Question

(a) Explain the common structural features of two major iron-containing proteins—haemoglobin and cytochrome c present in the human body. Explain the coordination chemistry involved at the central metal atom in case of oxyhaemoglobin and deoxyhaemoglobin. Give the details of the spin states, magnetic moment and oxidation number of central metal ion in both the cases. (10 marks)

(b) Write the ground-state electronic configuration of lanthanides mentioned below:
(i) ₅₉Pr (Praseodymium)
(ii) ₆₃Eu (Europium)
(iii) ₆₄Gd (Gadolinium)
Calculate the predicted effective magnetic moment (μₛ₊ₗ) for the metal ions in +3 oxidation state in the units of Bohr magneton. (10 marks)

(c) Derive a rate expression for a bimolecular surface reaction. Discuss the kinetics of such a reaction, when the gaseous reactants, say A and B, are adsorbed in the following way:
A + B → Product
(i) A and B are sparsely adsorbed.
(ii) A is relatively more strongly adsorbed than B. (10 marks)

(d) Nickel was found to be coordinated with oxygen in the UV-visible spectrum of [Ni(OS(CH₃)₂)₆]²⁺ complex ion. Predict theoretically the number of peaks and assign them to the corresponding electronic transitions. (10 marks)

(e) An ideal gas (V_i = 0.05 L and P_i = 8 atm) is subjected to reversible isothermal expansion (V_f = 0.40 L and P_f = 1 atm) at 25 °C. Calculate the work done, ΔU, ΔH and ΔS for this process. Is the heat (q) same as ΔH in this process? If not, why? (10 marks)

UPSC Answer Check · Accepted Answer

The five parts are linked by the idea that structure fixes electronic state, surface coverage fixes rate, and state functions differ from path functions.

(a) Haemoglobin and cytochrome c. Both haemoglobin and cytochrome c are iron porphyrin proteins. In each, iron is held in a porphyrin ring, mainly through four nitrogen donors, and completes its coordination sphere with axial ligands from the protein. Haemoglobin contains heme b, with a proximal histidine and a distal histidine in the binding pocket; cytochrome c contains heme c, covalently attached to cysteine residues, with axial histidine and methionine ligands. The protein environment controls redox behaviour and ligand binding. Cytochrome c functions by cycling between Fe(II) and Fe(III) during electron transfer, whereas haemoglobin transports O₂ with iron remaining formally Fe(II).

In deoxyhaemoglobin, Fe(II) is five-coordinate: four porphyrin nitrogens plus the proximal histidine, with the distal site vacant. The ligand field is relatively weak, so the d⁶ ion is high-spin, paramagnetic, with μ ≈ √24 = 4.90 BM. In oxyhaemoglobin, O₂ binds at the distal site, making the iron six-coordinate. O₂ acts as a π-acceptor, and Fe→O₂ back-donation increases the splitting; the d⁶ ion becomes low-spin, t₂g⁶, diamagnetic, with μ = 0 BM. In both cases the formal oxidation number of iron is +2, although oxyhaemoglobin has important Fe(III)–superoxide resonance character.

(b) Lanthanide configurations and moments. The ground-state configurations are: Pr, ₅₉Pr: [Xe]4f³6s²; Eu, ₆₃Eu: [Xe]4f⁷6s²; Gd, ₆₄Gd: [Xe]4f⁷5d¹6s². In the +3 state: Pr³⁺ is [Xe]4f², Eu³⁺ is [Xe]4f⁶, and Gd³⁺ is [Xe]4f⁷.

For the requested μₛ₊ₗ expression, Pr³⁺ has S = 1 and L = 5, so μₛ₊ₗ = √[4S(S+1)+L(L+1)] = √[8+30] = √38 ≈ 6.16 BM. Gd³⁺ has S = 7/2 and L = 0, giving μₛ₊ₗ = √[4(7/2)(9/2)] = √63 ≈ 7.94 BM. Eu³⁺ is special: its ground term is ⁷F₀, with J = 0, so the zero-temperature spin–orbital ground-state moment is 0. The accepted room-temperature effective moment is about 3.4 BM because the low-lying ⁷F₁ level is thermally populated; it is not the spin-only 6.93 BM value.

(c) Surface reaction kinetics. For a Langmuir–Hinshelwood surface reaction, A and B first adsorb and then react on the surface: rate = kθ_Aθ_B. Using Langmuir adsorption, θ_A = K_A P_A/(1+K_A P_A) and θ_B = K_B P_B/(1+K_B P_B), so

rate = k K_A K_B P_A P_B / [(1+K_A P_A)(1+K_B P_B)].

If A and B are sparsely adsorbed, K_A P_A ≪ 1 and K_B P_B ≪ 1, so the denominator is approximately 1. The rate becomes rate ≈ k K_A K_B P_A P_B, first order in both A and B. If A is relatively more strongly adsorbed than B, θ_A approaches unity while B remains weakly adsorbed, so θ_B ≈ K_B P_B. The rate then becomes rate ≈ k K_B P_B, independent of P_A and first order in P_B.

(d) Spectrum of [Ni(OS(CH₃)₂)₆]²⁺. In this complex, DMSO coordinates through oxygen, giving an octahedral Ni(II) centre with a d⁸ configuration. For an octahedral d⁸ ion, the ground term is ³A₂g. The theoretically expected spin-allowed d–d transitions are three: ³A₂g → ³T₂g (ν₁), ³A₂g → ³T₁g(F) (ν₂), and ³A₂g → ³T₁g(P) (ν₃). Because O-donor DMSO is a weak-field ligand, Δ_o is relatively small, so the bands lie in the visible/near-UV region. Weak spin-forbidden bands may appear, but the principal theoretical count is three spin-allowed peaks.

(e) Isothermal reversible expansion. For the ideal gas, n = P_iV_i/RT = (8 atm × 0.05 L)/(0.0821 L atm mol⁻¹ K⁻¹ × 298 K) ≈ 0.0163 mol. For reversible isothermal expansion,

w = −nRT ln(V_f/V_i) = −nRT ln(0.40/0.05) = −nRT ln 8.

Using nRT = P_iV_i = 0.40 L atm, w = −0.40 × 2.079 = −0.832 L atm ≈ −84.3 J. Thus the work done by the gas is +84.3 J. For an ideal gas at constant temperature, ΔU = 0 and ΔH = 0, because both depend only on temperature. The entropy change is

ΔS = nR ln(V_f/V_i) = 0.0163 × 8.314 × 2.079 ≈ 0.282 J K⁻¹.

For a reversible isothermal process, q = −w = +84.3 J. The heat is not the same as ΔH here because ΔH = q only at constant pressure with only PV work. This expansion is isothermal but not isobaric; pressure falls from 8 atm to 1 atm, while ΔH remains zero for the ideal gas.

Thus, ligand field and protein environment control spin and magnetism, adsorption coverage controls surface reaction order, and isothermal ideal-gas behaviour fixes ΔU and ΔH while heat and work remain path-dependent.

(a) Explain the common structural features of two major iron-containing proteins—haemoglobin and cytochrome c present in the…

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