(a) 'All the F atoms appear indistinguishable in the ¹⁹F NMR spectrum of sp³d hybridized PF₅ molecule.' Explain how. (10…

(a) Why all five F atoms of PF₅ look equivalent in ¹⁹F NMR

Static structure. P uses sp³d hybrids, and PF₅ is a trigonal bipyramid (D₃h) with two kinds of fluorine:

• 2 axial F, with P–F = 158 pm and three 90° neighbours;
• 3 equatorial F, with P–F = 153 pm and 120°/90° neighbours.

A rigid molecule would therefore give two ¹⁹F signals in a 2 : 3 ratio, each split into a doublet by ³¹P (I = ½).

Observation. Only one ¹⁹F environment is seen: a single doublet, with a large ¹J(P–F) of the order of 900 Hz.

Explanation: Berry pseudorotation

• Two equatorial F–P–F angles open from 120° towards 180°, while the two axial fluorines bend together from 180° towards 120°.
• The molecule passes through a square-pyramidal (C₄v) transition state, with the third equatorial F as the "pivot" at the apex.
• It then relaxes to a new trigonal bipyramid in which the former axial F are equatorial and two former equatorial F are axial.
• No bond breaks and the molecule does not rotate as a whole. The barrier is only about 16 kJ mol⁻¹.
• Using different pivots in successive steps permutes all five fluorines. At room temperature (and even far below) this happens about 10⁵ times or more per second, far faster than the NMR timescale.
• Each ¹⁹F nucleus therefore spends equal time in axial and equatorial sites, and the spectrometer records only their time-averaged chemical shift.

Evidence that the exchange is intramolecular: the P–F coupling (the doublet) survives, so fluorines never leave phosphorus. For PF₅ the exchange stays fast even at the lowest accessible temperatures. In slower systems (e.g. some substituted phosphoranes), cooling "freezes out" separate axial and equatorial signals, which coalesce on warming.

The "indistinguishability" is thus a dynamic, NMR-timescale effect. Structurally, on an instantaneous timescale (electron diffraction), the axial and equatorial bonds remain different.

(b)(i) Dispositions of ClF₃ and its shape

Cl has 7 valence electrons; 3 bond to F, leaving 2 lone pairs. Five electron pairs give an sp³d trigonal-bipyramidal arrangement, and the two lone pairs (LP) can be placed in three ways. Only repulsions at 90° are significant, and their order is LP–LP > LP–BP > BP–BP.

• (i) Both LP axial: 90° contacts LP–LP 0, LP–BP 6, BP–BP 0. ClF₃ would be trigonal planar.
• (ii) One axial, one equatorial: LP–LP 1, LP–BP 3, BP–BP 2. ClF₃ would be pyramidal-like.
• (iii) Both LP equatorial: LP–LP 0, LP–BP 4, BP–BP 2. ClF₃ is T-shaped.

Reasoning

• (ii) is the least stable: it alone has the most severe interaction, a 90° LP–LP repulsion.
• Of the remaining two, (iii) has fewer 90° LP–BP repulsions (4 against 6). Its extra two BP–BP contacts are the weakest kind.
• In (iii) the lone pairs also occupy the roomier equatorial sites: 120° apart, with only two 90° neighbours each instead of three.
• (iii) is therefore the most favoured disposition.

Shape

• The atoms define a T-shaped molecule: two axial F and one equatorial F, with the two lone pairs in the equatorial plane.
• The lone pairs push the axial F slightly towards the equatorial F, so ClF₃ is a "bent T": F(ax)–Cl–F(eq) = 87.5° rather than 90°.
• The axial Cl–F bonds (169.8 pm) are longer than the equatorial one (159.8 pm), which is typical of hypervalent 3-centre–4-electron axial bonding.
• The molecule is polar (μ ≈ 0.6 D).

(b)(ii) Structure and bonding of B₂H₆

Structure (D₂h)

• Each B carries two terminal H atoms (Ht), and the two B atoms are joined by two bridging H atoms (Hb), one above and one below the B···B axis.
• The four Ht lie in one plane; the B(μ-H)₂B ring lies in the perpendicular plane.

Geometry:

• B–Ht = 119 pm; B–Hb = 133 pm;
• B···B = 177 pm;
• Ht–B–Ht ≈ 122°; Hb–B–Hb ≈ 97°.

Bonding (hybridisation approach)

• Electron count: B₂H₆ has only 2 × 3 + 6 × 1 = 12 valence electrons. That is too few for the 8 two-electron bonds a classical ethane-like structure would need, so the molecule is electron-deficient.
• Hybridisation: each B is sp³ hybridised, with 3 electrons distributed over four hybrid orbitals.
• Terminal bonds: two sp³ hybrids on each B overlap with H 1s orbitals to give four ordinary 2-centre–2-electron B–Ht bonds, using 8 electrons.

Bridge bonds: the remaining two hybrids on each B (one containing 1 electron, one empty) point towards the bridging positions.

• At each bridge, one sp³ hybrid from B₁, one from B₂ and the 1s orbital of Hb combine into three molecular orbitals: bonding, non-bonding and antibonding.
• Only the bonding MO is occupied, by 2 electrons. This is a 3-centre–2-electron (3c–2e) B–H–B "banana" bond.
• The two bridges use the remaining 4 electrons.
• Result: 12 electrons = 4 × 2 (terminal) + 2 × 2 (bridges). All bonding orbitals are filled even though the molecule is electron-deficient.

Consequences:

• The bridge bonds are longer and weaker than the terminal bonds.
• Diborane is readily cleaved by Lewis bases, e.g. B₂H₆ + 2NMe₃ → 2H₃B·NMe₃.
• IR shows separate terminal and bridge B–H stretches.
• There is no direct B–B bond.

(c) Principles behind the separation of the lanthanides

All Ln³⁺ ions have the same charge, similar outer electronic structure and, because of the lanthanide contraction, only slowly changing radii (La³⁺ 103 pm → Lu³⁺ 86 pm). Every classical method therefore exploits small, systematic differences in size and basicity, magnified by repetition, or a rare difference in oxidation state.

(i) Repeated fractional crystallisation

• Principle: the solubilities of analogous salts change slightly and regularly with ionic radius.
• Method: a mixture is partly crystallised. The crystals are enriched in the less soluble member and the mother liquor in the more soluble one.
• Repetition: the operation is repeated in a systematic scheme, with crystals moving one way and liquors the other, often thousands of times. The process was historically used to obtain pure elements.

Salts used:

• double magnesium nitrates, 2Ln(NO₃)₃·3Mg(NO₃)₂·24H₂O, for the light (cerium-group) lanthanides;
• bromates and ethyl sulfates for the heavier ones.
• Limitation: extremely slow. Separating neighbours such as Tm/Yb once needed thousands of recrystallisations.

(ii) Solvent extraction (the modern industrial method)

• Principle: Ln³⁺ is distributed between an aqueous phase and an immiscible organic phase containing a complexing extractant. The distribution coefficient is D = [Ln]org/[Ln]aq.

Extractants:

• tri-n-butyl phosphate (TBP) from nitrate solution;
• di(2-ethylhexyl)phosphoric acid (D2EHPA) in kerosene.
• Why it separates: D changes regularly across the series. With D2EHPA, extraction increases with atomic number because the smaller, more highly charged heavy ions bind more strongly.
• Separation factors: those between neighbours are small (about 1.5–2.5), so hundreds of counter-current mixer–settler stages are used, followed by selective stripping with acid.
• Industrial practice: this is how monazite-derived rare earths are separated commercially, for example by IREL (India) Ltd at its Rare Earths Division, Aluva, Kerala.

(iii) Fractional precipitation

• Principle: the solubility products of Ln(OH)₃ (and of oxalates and double sulfates) vary with basicity and size. Basicity decreases from La to Lu as the ions get smaller: Ln(OH)₃ becomes less basic and less soluble.

Method: a small amount of precipitant is added to the mixed solution, e.g. dilute NH₃ or NaOH, or a controlled amount of oxalate.

• The least basic (heavier) hydroxides precipitate first, leaving the more basic lighter ones (La, Ce, Pr) in solution.
• The precipitate and filtrate are treated again, repeatedly.
• Group separation: sodium or potassium double sulfates give a coarse split. Those of the Ce group are sparingly soluble; those of the Y group are soluble.

(iv) Change of oxidation state (the most efficient chemical method, where applicable)

A few lanthanides have accessible non-+3 states, which give them sharply different chemistry:

Cerium: Ce³⁺ is oxidised to Ce⁴⁺ (by KMnO₄, NaOCl, H₂O₂ in alkali, or electrolytically). Ce⁴⁺ is much smaller and far less basic.

• It hydrolyses and precipitates as CeO₂·xH₂O or basic salts at pH around 3, where Ln³⁺ stays in solution.
• Alternatively, it is selectively extracted by TBP.
• A single step removes most of the cerium from a mixture.

Europium (also Sm and Yb): Eu³⁺ is reduced to Eu²⁺ (by zinc amalgam in a Jones reductor), stabilised by its half-filled 4f⁷ shell.

• Eu²⁺ behaves like Sr²⁺/Ba²⁺: it is precipitated as insoluble EuSO₄ while Ln³⁺ remain in solution.
• Sm²⁺ and Yb²⁺ can be obtained similarly with sodium amalgam.

(Ion-exchange chromatography, which uses complexing eluents such as citrate or EDTA, is the other major modern method. It is not asked for here.)