Physical Chemistry Third Edition

28.6 Approximate Theories of Transport Processes in Liquids 1189

Particles

being

moved

aside

Vacancy

Moving

particle

Former

position

of moving

particle

Figure 28.17 Motion of a Molecule into a Vacancy in a Liquid.This figure attempts to

illustrate the position of maximum potential energy of a molecule moving from one shell of

neighbors to another.

Diffusion

Diffusion is a process by which molecules of a substance in a mixture move from a

region of higher concentration to a region of lower concentration. It is described quite

accurately by Fick’s law of diffusion, which for diffusion in thezdirection is

Jiz−Di

∂ci

∂z

(28.6-1)

whereJidenotes the diffusion flux, defined as the net amount of substance in moles

passing through unit area of a plane per unit time, and where the concentration of

substanceiis denoted byci. The coefficientDiis called thediffusion coefficient.If

Fick’s law is obeyed,Diis independent of concentration.

We now apply the activated complex theory of Eyring and Polanyi to diffusion in

liquids. In the thermodynamic formulation of the activated complex theory, the rate

constant of a first-order reaction is given by the analogue of Eq. (26.4-16):

k

kBT

h

e−∆G

‡◦/RT

(28.6-2)

where∆G‡

◦

is the standard-state Gibbs energy change per mole to form the activated

complex, excluding motion along the reaction coordinate. We represent our liquid

by a model system that resembles a disordered crystal with fluctuating vacancies, and

assume that a molecule can occasionally move into a vacancy. As it does so, it must push

some neighboring molecules aside, moving through a state of high potential energy, as

depicted schematically in Figure 28.17. This potential energy maximum is analogous

to the maximum along the reaction coordinate for a chemical reaction described in

Section 26.4, and we treat the state of high potential energy as an activated complex.

Consider a two-component liquid system, with a concentration of component 2 that

is smaller for larger values of thezcoordinate. Assume that a vacancy occurs atzz′.