Page 109 - Separation process principles 2

74 Chapter 3 Mass Transfer and Diffusion

Diffusivity in Liquid Mixtures dilute conditions to more concentrated conditions, exten-
sions of (3-38) have been restricted to binary liquid mixtures
Diffusion coefficients in binary liquid mixtures are difficult
dilute in A, up to and perhaps mols.
to estimate because of the lack of a rigorous model for the
One such extension, which gives reasonably good
liquid state. An exception is the case of a dilute solute (A) of
predictions for small wlute molecules, is the empirical
very large, rigid, spherical molecules diffusing through a
Wilke-Chang ,61 equation:
stationary solvent (B) of small molecules with no slip of the
solvent at the surface of the solute molecules. The resulting
DAB)^ = 7.4 x ~O-~(~M~)'/~T
relation, based on the hydrodynamics of creeping flow to (3-39)
describe drag, is the Stokes-Einstein equation: PB vi6
where the units are cm2/s for DAB; CP (centipoises) for the
solvent viscosity, p~ ; K for T; and cm3/mol for VA, the liquid
molar volume of the solute at its normal boiling point. The
where RA is the radius of the solute molecule and NA is parameter +B is an association factor for the solvent, which
Avagadro's number. Although (3-38) is very limited in its is 2.6 for water, 1.9 for methanol, 1.5 for ethanol, and 1 .O for
application to liquid mixtures, it has long served as a starting unassociated solvents such as hydrocarbons. Note that the
point for more widely applicable empirical correlations for effects of temperature and viscosity are identical to the pre-
the diffusivity of solute (A) in solvent (B), where both A and diction of the Stokes-Einstein equation, while the effect of
B are of the same approximate molecular size. Unfortu- the radius of the solute molecule is replaced by VA, which
nately, unlike the situation in binary gas mixtures, DAB = can be estimated by summing the atomic contributions in
DBA in binary liquid mixtures can vary greatly with compo- Table 3.3, which also lists values of v~ for dissolved light
sition as shown in Example 3.7. Because the Stokes- gases. Some representative experimental values of diffusivity
Einstein equation does not provide a basis for extending in dilute binary liquid solutions are given in Table 3.4.

Table 3.3 Molecular Volumes of Dissolved Light Gases and Atomic Contributions for Other Molecules at the
Normal Boiling Point

Atomic Volume Atomic Volume
(m3/kmol) x lo3 (m3/kmo1) 103
C Ring
H Three-membered, as in
0 (except as below) ethylene oxide
Doubly bonded as carbonyl Four-membered
Coupled to two other elements: Five-membered
In aldehydes, ketones Six-membered
In methyl esters Naphthalene ring
In methyl ethers Anthracene ring
In ethyl esters
Molecular Volume
In ethyl ethers
(m3/kmol) x lo3
In higher esters
In higher ethers Air
In acids (-OH) 02
Joined to S, P, N N2
N Brz
Doubly bonded c12
In primary arnines co
In secondary amines co2
Br H2
Cl in RCHCIR' H2O
C1 in RC1 (terminal) H2S
F NH3
I NO
S N20
P so2

Source: G. Le Bas, The Molecular Volumes of Liquid Chemical Compounds, David McKay, New York (1915).