Physical Chemistry Third Edition

470 10 Transport Processes

The Temperature Dependence of Diffusion and Viscosity

Coefficients in Liquids

Diffusion coefficients and viscosities in liquids depend more strongly on temperature

than on gases. It is found experimentally that diffusion coefficients in liquids are usually

well described by the formula

DD 0 e−Ea,d/RT (10.4-5)

whereRis the ideal gas constant andTis the absolute temperature. The quantityD 0

is a parameter that is nearly temperature-independent, andEa,dis called the molar

activation energyfor diffusion. Liquid viscosities are usually well described by the

formula

ηη 0 eEa,η/RT (10.4-6)

whereEa,ηis the molar activation energy for viscous flow.

An elementary explanation of Eq. (10.4-5) is as follows: If a molecule in a liquid

pushes past some of its nearest neighbors and moves into the next cage, the potential

energy of the system rises as the molecule passes between the “cage” molecules, as

depicted in Figure 10.8.

If we identifyεaas a minimum energy required to break out of a cage (a molecular

activation energy), then from the Boltzmann probability distribution of Eq. (9.3-42)

we see that the probability for a molecule to have this energy is

(probability)∝e−εa/kBTe−Ea/RT (10.4-7)

wherekBis Boltzmann’s constant and where the molar activation energyEaNAvεa.

It is therefore reasonable that a diffusion coefficient in a liquid would obey Eq. (10.4-5)

withEadroughly equal to the molar activation energy required to move into the

next cage.

Particles

being

moved

aside

Vacancy

Moving

particle

Former

position

of moving

particle

Figure 10.8 Motion of a Molecule into a Vacancy in a Liquid.