(a) Which one is more stable between the two isomers? Explain. [(H₃N)₅ Cr – CN – Cr(CN)₅] [(H₃N)₅ Cr – NC – Cr(CN)₅] 10…

These parts connect coordination electronics, bioinorganic oxygen binding, radical chain kinetics and surface adsorption.

(a) Stability of the cyanide-bridged isomers. Cyanide is an ambidentate ligand because it can bind through carbon or nitrogen. The more stable isomer is [(H3N)5Cr–NC–Cr(CN)5]. In this structure the nitrogen end of the bridging cyanide is attached to the ammine-rich chromium centre, while the carbon end is attached to the cyanide-rich chromium centre. Cr(III) is a borderline Lewis acid, but its effective hardness is modified by the surrounding ligands: the [Cr(NH3)5] environment is relatively harder, whereas the [Cr(CN)5] environment is softer because cyanide is a soft donor. The harder nitrogen terminus therefore matches the harder ammine-rich centre, and the softer carbon terminus matches the softer cyanide-rich centre. This HSAB-compatible arrangement gives better orbital overlap and stronger Cr–N and Cr–C interactions. The alternative [(H3N)5Cr–CN–Cr(CN)5] places the harder nitrogen on the softer cyanide-rich centre and the softer carbon on the harder ammine-rich centre, so the donor-acceptor match is poorer and the isomer is less stable.

(b) Hemocyanin active site and function. Deoxyhemocyanin contains two Cu(I) centres, each approximately three-coordinate through histidine imidazole nitrogens, with no peroxide bridge and a Cu–Cu separation of about 4.6 Å. It may be represented as His3Cu(I) ··· Cu(I)His3. Because Cu(I) is d10, deoxyhemocyanin is colourless. On binding oxygen, both Cu(I) centres are oxidised to Cu(II) and O2 is reduced to a peroxo bridge. Oxyhemocyanin has a μ-η²:η² peroxo dicopper(II) core, His3Cu(II)–O–O–Cu(II)His3, in which each copper is coordinated by three histidines and two peroxo oxygen atoms. This form is blue because of ligand-to-metal charge-transfer transitions. Hemocyanin is the iron-free oxygen carrier of many arthropods and molluscs; it reversibly binds and transports oxygen in blood or haemolymph, and in some organisms also stores oxygen. It is not a heme protein and does not function as hemoglobin.

(c) Stationary and branching chain reactions. A stationary chain reaction is one in which the concentration of chain carriers remains constant because the rate of initiation equals the rate of termination; propagation continues at a steady rate, as in the photochemical reaction of H2 with Cl2 under constant light. A non-stationary or branching chain reaction is one in which each cycle produces more radicals than it consumes, so the radical concentration increases with time. If the branching factor α, the ratio of radical production by branching to radical loss, is greater than one, the chain length grows exponentially. A classic example is the H2–O2 system, where H + O2 gives OH + O and O + H2 gives OH + H, multiplying radicals. Explosion occurs when net branching exceeds termination. The necessary conditions are: a temperature high enough for the branching steps to be fast; a pressure between the lower and upper explosion limits, because at low pressure radical loss at walls and impurities dominates, while at high pressure three-body termination and heat removal can suppress net branching; a gas composition within the explosive range; a vessel radius above the critical radius, because a large surface-to-volume ratio enhances radical termination; and absence of inhibitors. When these conditions are met, radical multiplication and heat release reinforce each other, the induction period ends, and the reaction runs away as an explosion.

(d) Steady-state approximation in H2 + Cl2. The steady-state approximation assumes that a reactive intermediate is formed and consumed so rapidly that its concentration remains small and nearly constant, so d[intermediate]/dt is approximately zero. For the photochemical reaction H2 + Cl2 → 2HCl, a chain mechanism is: initiation, Cl2 + hν → 2Cl, with rate Ri = 2Ia; propagation, Cl + H2 → HCl + H (k1) and H + Cl2 → HCl + Cl (k2); termination, 2Cl → Cl2 (kt). Applying the approximation to H gives k1[Cl][H2] = k2[H][Cl2]. Applying it to Cl gives 2Ia + k2[H][Cl2] − k1[Cl][H2] − 2kt[Cl]^2 = 0. Substituting the H steady-state relation cancels the propagation terms and gives [Cl] = (Ia/kt)^1/2. The rate of HCl formation is then k1[Cl][H2] = k1(Ia/kt)^1/2[H2]. Since the absorbed light intensity Ia is proportional to [Cl2] when chlorine is the absorbing species, the rate law becomes rate = k[H2][Cl2]^1/2. If HCl inhibition is included, an additional step H + HCl → H2 + Cl introduces the denominator 1 + (k-1/k2)([HCl]/[Cl2]). The statement that the quantum yield is extremely large is justified: one photon creates two chlorine atoms, and each chlorine atom can propagate many cycles before termination. The quantum yield is therefore the chain length and can be 10^4 to 10^6, which is characteristic of photochemical chain reactions.

(e) Langmuir isotherm and surface kinetics. Let θ be the fraction of surface sites occupied by A. For adsorption A(g) + S ⇌ A-S, the adsorption rate is kaP_A(1 − θ) and the desorption rate is kdθ. At equilibrium, kaP_A(1 − θ) = kdθ, so θ/(1 − θ) = (ka/kd)P_A = KP_A, and θ = KP_A/(1 + KP_A). For competitive adsorption, θ_A = K_A P_A/(1 + K_A P_A + K_B P_B + ...). This isotherm is useful in surface kinetics because the rate of a surface reaction is proportional to the coverages of the reacting species. For a unimolecular surface reaction A* → products, rate = kθ_A = kK_A P_A/(1 + K_A P_A), giving first-order dependence at low pressure and zero-order at high pressure. For a bimolecular Langmuir-Hinshelwood reaction A* + B* → products, rate = kθ_Aθ_B = kK_AK_BP_AP_B/(1 + K_A P_A + K_B P_B)^2. For an Eley-Rideal reaction A(g) + B* → products, rate = kP_Aθ_B = kK_BP_AP_B/(1 + K_B P_B). Thus the pressure dependence of the rate reveals the surface coverage, the strength of adsorption, and whether the rate-determining step is unimolecular, bimolecular on the surface, or a gas-surface collision.

Thus, in each case the observed stability, colour, explosiveness, rate law or kinetic order follows directly from the controlling electronic, radical or surface-coverage mechanism.