(a) Sketch the synthesis of [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COCH₃)] and [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COOH)] complexes starting from [Fe(η⁵-C₅H₅)₂]…

(a) Synthesis of acetylferrocene and ferrocenecarboxylic acid from ferrocene

Step 1, Friedel–Crafts acylation: ferrocene is an electron-rich, aromatic-like sandwich compound and is acylated readily, with acetic anhydride and phosphoric acid (or acetyl chloride and AlCl₃) as the source of the acylium ion CH₃CO⁺. One cyclopentadienyl ring is substituted: Fe(η⁵-C₅H₅)₂ + (CH₃CO)₂O → [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COCH₃)] + CH₃COOH. The acetyl group withdraws electrons and deactivates that ring, so the second acylation goes to the other ring (heteroannular), and mild conditions with limited acylating agent give mainly the monoacetyl compound. Fe remains Fe(II).

Step 2, haloform oxidation: the methyl ketone is oxidised by NaOCl (or NaOBr) in NaOH. The CH₃ group is halogenated to CX₃, and hydroxide cleaves the C–CX₃ bond, giving the carboxylate and CHX₃. Acidification gives [Fe(η⁵-C₅H₅)(η⁵-C₅H₄COOH)].

(b) Spin-only magnetic moments (μ = √[n(n + 2)] BM)

(i) [Fe(H₂O)₅NO]²⁺ (brown-ring complex): written as Fe(I) with NO⁺, d⁷, high-spin, n = 3; μ = √15 = 3.87 BM.

(ii) [Cr(NCS)₆]³⁻: Cr(III), d³, n = 3; μ = √15 = 3.87 BM.

(iii) [V(H₂O)₆]³⁺: V(III), d², n = 2; μ = √8 = 2.83 BM.

(iv) [Co(bpy)₃]²⁺: Co(II), d⁷, high-spin (t₂g⁵e_g²) at room temperature, n = 3; μ = √15 = 3.87 BM. A low-spin d⁷ configuration would give n = 1 and 1.73 BM, but bpy does not produce a field strong enough to force pairing in Co(II) at room temperature.

(c) Beer–Lambert law

For the 1 cm cell, T = 0.10, so A = −log T = 1.0 = εc(1 cm).

For a 0.5 cm cell, concentration and ε are unchanged, so A = 1.0 × 0.5/1 = 0.50. T = 10⁻⁰·⁵ = 0.316 (31.6%).

Light absorbed = 100 − 31.6 = 68.4%.

(d) Transition-state theory and the pre-exponential factor

Theory: reactants A + B are in a rapid equilibrium with an activated complex (transition state) [AB]‡ at the saddle point of the potential-energy surface, and the complex decays to products at the frequency kBT/h along the reaction coordinate:

A + B ⇌ [AB]‡ → products; k = (kBT/h)K‡.

Since K‡ = exp(−ΔG‡/RT) = exp(ΔS‡/R)exp(−ΔH‡/RT), the rate constant is the Eyring equation

k = (kBT/h) exp(ΔS‡/R) exp(−ΔH‡/RT).

Comparing with k = A exp(−Eₐ/RT), and using Eₐ = ΔH‡ + RT for a solution reaction, gives A = e(kBT/h)exp(ΔS‡/R). In statistical terms, A depends on the ratio of partition functions of the complex to those of the reactants.

Superiority over collision theory: collision theory gives A = PZ, where the collision frequency Z treats molecules as hard spheres, and the steric factor P is an empirical adjustment for the orientation requirement and cannot be calculated. In TST, A is given by the entropy of activation, which is worked out from molecular masses, moments of inertia, vibrational frequencies and the geometry of the complex. A tightly ordered transition state has a negative ΔS‡ and a small A (low P), and a loose one has a larger A. So the steric factor is explained, not assumed, and the temperature dependence of A can be predicted. TST also explains solution reactions and solvent effects, through ΔG‡, and gives thermodynamic ideas such as ΔH‡ and ΔS‡ from an Eyring plot of ln(k/T) against 1/T.