(a) Differentiate between T and R conformation of hemoglobin. (10 marks) (b) (i) Describe the structure and bonding in diborane…

(a) T and R states of haemoglobin (10 marks)

Haemoglobin is a tetramer (α₂β₂) that exists in two quaternary states in equilibrium: the T (tense, taut) state, the form of deoxyhaemoglobin, and the R (relaxed) state, the form of oxyhaemoglobin.

• Oxygen affinity: the T state has low affinity for O₂, whereas the R state has affinity about 100 to 300 times higher.
• Salt bridges: in the T state the subunits are held by extra salt bridges and hydrogen bonds between the α₁β₂ and α₂β₁ interfaces and the C-terminal residues (for example His146β to Asp94β, and Arg141α to the neighbouring subunit); in the R state these are broken, and the structure is looser.
• Iron and haem: in the T state the high-spin Fe(II) is five-coordinate and lies about 0.6 Å out of the porphyrin plane (domed), pulled towards the proximal histidine. On binding O₂, Fe becomes low-spin, smaller and moves into the plane, pulling the proximal histidine and the F helix, which triggers the change to R.
• Quaternary structure: the transition from T to R rotates one αβ dimer relative to the other by about 15° and narrows the central cavity.
• 2,3-Bisphosphoglycerate (2,3-BPG): it binds in the central cavity of the T state, cross-linking the two β chains, and stabilises it; it does not fit in the R state, so BPG lowers oxygen affinity.
• Effectors: H⁺ and CO₂ (Bohr effect) stabilise the T state and promote O₂ release in tissues; high O₂ favours R.
• Cooperativity: binding of O₂ to one subunit shifts the equilibrium towards R and raises the affinity of the remaining sites, so the O₂-binding curve is sigmoidal (Hill coefficient about 2.8), unlike the hyperbolic curve of myoglobin. This is described by the concerted (Monod-Wyman-Changeux) model.

(b)(i) Structure and bonding in diborane (10 marks)

Diborane, B₂H₆, has D₂h symmetry with a bridged structure, not an ethane-like structure. Each boron carries two terminal hydrogens, and two hydrogens bridge the two borons. The four terminal B-H bonds (119 pm) and both borons lie in one plane, and the two bridging H atoms (B-H 133 pm) lie above and below it, in a plane perpendicular to the first. The terminal H-B-H angle is about 122°, the B-H-B angle 83° and B···B 177 pm.

Bonding. B₂H₆ has only 12 valence electrons (3 + 3 from B and 6 from H), too few for eight normal two-centre bonds, so it is electron-deficient. Each B is approximately sp³ hybridised. Eight electrons form the four terminal two-centre two-electron (2c-2e) B-H bonds. The remaining four electrons form two three-centre two-electron (3c-2e) bonds, each B-H-B "banana" bond in which two boron sp³ hybrid orbitals and the hydrogen 1s orbital combine to give a bonding, a non-bonding and an antibonding molecular orbital, and the two electrons occupy the bonding one. Each bridge thus has two electrons spread over three atoms, which is why the bridge bonds are longer and weaker than the terminal bonds. The molecule is diamagnetic and reactive, for example it is a strong Lewis acid, and hydrolyses to boric acid and hydrogen.

(b)(ii) Classification of silicates and the three silicates (10 marks)

Silicates are classified by how the SiO₄ tetrahedra are linked, that is by the number of oxygen corners shared between tetrahedra:

• 0 corners shared: orthosilicates (nesosilicates), isolated SiO₄⁴⁻ units (olivine, zircon).
• 1 corner shared: pyrosilicates (sorosilicates), Si₂O₇⁶⁻.
• 2 corners shared: cyclic silicates (SiO₃)ₙ²ⁿ⁻ (beryl, benitoite) and single-chain silicates (SiO₃)ₙ²ⁿ⁻ (pyroxenes).
• 2 and 3 corners shared alternately: double-chain silicates (Si₄O₁₁)ₙ⁶ⁿ⁻ (amphiboles).
• 3 corners shared: sheet silicates (Si₂O₅)ₙ²ⁿ⁻ (micas, clays, talc).
• 4 corners shared: three-dimensional framework (SiO₂ and, with Al replacing some Si, feldspars and zeolites).

The three ions are:

• (1) SiO₄⁴⁻: the orthosilicate ion, a single isolated tetrahedron with no shared oxygen (as in Mg₂SiO₄, olivine).
• (2) Si₂O₇⁶⁻: the pyrosilicate (disilicate) ion, two tetrahedra sharing one common corner oxygen (a Si-O-Si bridge), with six terminal O⁻ (as in Sc₂Si₂O₇, thortveitite).
• (3) Si₃O₉⁶⁻: the cyclic trisilicate ion, three tetrahedra each sharing two corners, forming a six-membered ring (Si₃O₃) with two terminal O⁻ on each Si (as in BaTiSi₃O₉, benitoite).

(c)(i) Magnetic moments of Eu³⁺ and Sm³⁺ (5 marks)

For most Ln³⁺ ions the observed moment agrees with μ = g_J√(J(J + 1)) (Van Vleck formula) because only the ground spin-orbit level is populated. In Sm³⁺ (4f⁵, ground state ⁶H₅/₂) and Eu³⁺ (4f⁶, ground state ⁷F₀) the spin-orbit coupling is small, so the excited J levels (⁶H₇/₂ and ⁷F₁, ⁷F₂ …) lie only a few hundred to about 1000 cm⁻¹ above the ground state, comparable to kT (about 208 cm⁻¹ at 300 K). They are therefore thermally populated at 300 K and contribute to the moment. For Eu³⁺ the formula gives μ = 0 (J = 0), but the observed value is about 3.4 to 3.6 BM; for Sm³⁺ it gives 0.84 BM, whereas the observed value is about 1.5 to 1.6 BM. There is also a temperature-independent (Van Vleck) contribution from mixing of the ground and excited states.

(c)(ii) Decrease in metallic radii from La to Lu (5 marks)

The radii fall steadily from La to Lu (about 187 pm to 174 pm), the lanthanide contraction (3 marks). Along the series the nuclear charge rises by one unit at each step and an electron is added to the inner 4f subshell. The 4f electrons shield the outer 5s, 5p and 6s electrons poorly because of the diffuse, directional shape of f orbitals, so the effective nuclear charge increases and the outer shells contract.

Eu (about 204 pm) and Yb (about 193 pm) are exceptions with much larger metallic radii (2 marks). They have the stable half-filled (4f⁷) and completely filled (4f¹⁴) configurations, and in the metal they contribute only two electrons, not three, to the conduction band (they behave as divalent metals, like the alkaline earths). With fewer bonding electrons the metallic bonding is weaker and the atoms are larger.

(c)(iii) Separation of lanthanides by complex formation (5 marks)

The lanthanides are separated by cation-exchange chromatography with a complexing eluent. A solution of Ln³⁺ is loaded on the top of a column of a cation-exchange resin (a sulfonated polystyrene such as Dowex-50) and the ions are adsorbed. The column is eluted with a buffered solution of a complexing agent such as citrate, EDTA or α-hydroxyisobutyrate at controlled pH.

The stability of the complexes increases with atomic number, since the ionic radius falls and the charge density rises. Heavier lanthanides therefore form stronger complexes, stay in solution more and are held less by the resin, so they are eluted first; lutetium comes off first and lanthanum last. The successive fractions are collected and the separated ions precipitated as oxalates and ignited to oxides. Repeated equilibration along the long column gives high purity (over 99.9%). The method was developed by Spedding and co-workers in the 1940s, and today solvent extraction with tributyl phosphate is used industrially.

(c)(iv) Absence of visible absorption in Ce³⁺ and Yb³⁺ (5 marks)

Ce³⁺ (4f¹) and Yb³⁺ (4f¹³) each have a single 4f electron or hole, so there is only one f-f transition, ²F₅/₂ ↔ ²F₇/₂, which is the spin-orbit splitting of the ²F term. Its energy is small, lying in the infrared (about 2200 cm⁻¹ for Ce³⁺ and about 10 000 cm⁻¹, or 1000 nm, for Yb³⁺), so it does not absorb visible light and the ions are colourless. With no other f-f transitions possible, there is nothing in the visible region.

In the ultraviolet they show intense absorption. For Ce³⁺ this is the 4f¹ → 5d¹ transition, which is Laporte-allowed (parity-changing), and so intense; for Yb³⁺ it is a ligand-to-metal charge-transfer transition, since Yb³⁺ is readily reduced to the stable 4f¹⁴ Yb²⁺. Both occur at high energy in the UV.