Where the question number is enclosed in a button, e.g. , you can obtain help or comments about the question by clicking it.

2. In solution the mechanism for a bimolecular reaction between species A and B may be written

What is meant by the species {AB} appearing in this mechanism?
Derive an expression for the rate constant of a reaction in solution in terms of the elementary processes shown above. Hence explain under what conditions such a reaction would be expected to be diffusion-controlled.

The diffusion-controlled rate constant for a bimolecular reaction between species A and B in solution (expressed in dm³mol^-1s^-1) can be written as k_D = 4000πr_ABD_ABN_Af(U) where r_AB is the encounter distance (expressed in m), D_AB = D_A + D_B is the relative diffusion coefficient (in m²s^-1) and f(U) is some function of the interaction potential energy, U, between the reactants, evaluated at the encounter distance. For reactions between neutral species, f(U) can be set to unity.

(a) A typical diffusion coefficient for a small molecule in aqueous solution is D_A = 2.0 × 10^-9m²s^-1. Use this value to estimate the diffusion-controlled rate constant for a reaction involving neutral species, assuming an encounter distance of 0.5 nm.

(b) Diffusion-controlled rate constants typically decrease with increasing solvent viscosity and often have activation barriers (typically between 10 kJ mol^-1 and 20 kJ mol^-1). Comment on this observation.
For a reaction between ions in solution

where the Coulomb potential can be written as

where z_A and z_B are the reactant charge numbers, ε_R is the relative permittivity, and e²/4πε₀ = 2.307 × 10^-28 J m.

(c) Sketch the variation of f(U) with U/k_BT, and use it to explain qualitatively the effect charge has on the diffusion rate constant. Note that e^x = (1 + x +..) for small x.

(d) Calculate f(U) for the reaction between solvated electrons and singly charged cations in hexane and in water at 300 K, given the relative permittivities of hexane and water are 1.89 and 78.5 respectively, and assuming an encounter distance of 0.5 nm. Comment on the result you obtain.

3. Comment on the following:

(a) For a number of ion-ion reactions in solution there exists a correlation between the entropy of activation, the volume of activation and the dependence of the reaction rate on pressure.

(b) For a series of electron transfer reactions it is sometimes possible to measure rate constants that decrease as the Gibbs energy of the reaction becomes more negative.

(c) Addition of an inert electrolyte accelerates some ion-ion reactions and decelerates others.

(d) In acid catalysed reactions addition of an inert electrolyte sometimes causes an increase in the rate of reaction.

(e) Estimate the encounter distance for the reaction of H⁺ and OH^- in water at 300 K from the following data: diffusion coefficients, D(H⁺) = 9.1 x 10 ^-9 m² s ^-1 , D(OH^-) = 5.2 x 10 ^-9 m² s^-1 ; rate constant = 1.4 x 10¹¹ dm³ mol ^-1 s^-1. Comment on your answer.