Page 110 - Separation process principles 2

3.2 Diffusion Coefficients 75

Table 3.4 Experimental Binary Liquid Diffusivities for Solutes, equation with experimental values for nonaqueous solutions.
A, at Low Concentrations in Solvents, B For a dilute solution of one normal paraffin (Cs to C32) in
another (C5 to C16),
Diffusivity,
Solvent, Solute, Temperature, DAB,
B A K cn12/s x lo5

Water Acetic acid
Aniline
Carbon dioxide where
Ethanol
Methanol
Ethanol Ally1 alcohol
Benzene
and the other variables have the same units as in (3-39).
Oxygen
For general nonaqueous solutions,
Pyridine
Water
Benzene Acetic acid
Cyclohexane
Ethanol
n-Heptane where 9 is the parachor, which is defined as
Toluene
n-Hexane Carbon tetrachloride
Methyl ethyl ketone
Propane When the units of the liquid molar volume, v, are cm3/mol
Toluene and the surface tension, a, are g/s2 (dyneslcm), then the units
of the parachor are ~m~-~'~~/s'"-mol. Normally, at near-
Acetone Acetic acid
ambient conditions, 9 is treated as a constant, for which an
Formic acid
extensive tabulation is available from Quayle [g], who also
Nitrobenzene
Water provides a group-contribution method for estimating para-
chors for compounds not listed. Table 3.5 gives values of
From Poling et al. [2]. parachors for a number of compounds, while Table 3.6 con-
tains structural contributions for predicting the parachor in
the absence of data.
EXAMPLE 3.5
The following restrictions apply to (3-42):
Use the Wilke-Chang equation to estimate the diffusivity of aniline 1. Solvent viscosity should not exceed 30 cP.
(A) in a 0.5 mol% aqueous solution at 20°C. At this temperature,
2. For organic acid solutes and solvents other than water,
the solubility of aniline in water is about 4 g/100 g of water or
0.77 mol% aniline. The experimental diffusivity value for an infi- methanol, and butanols, the acid should be treated as a
nitely dilute mixture is 0.92 x cm2/s. dimer by doubling the values of gA and VA.
3. For a nonpolar solute in monohydroxy alcohols, val-
SOLUTION ues of vg and 9g should be multiplied by 8pB, where
the viscosity is in centipoise.
p,~ = p,~~o 1.01 CP at 20°C
=
UA = liquid molar volume of aniline at its normal boiling Liquid diffusion coefficients for a solute in a dilute binary
point of 457.6 K = 107 cm3/mol system range from about lop6 to lop4 cm2/s for solutes of
molecular weight up to about 200 and solvents with viscos-
= 2.6 for water MB = 18 for water T = 293 K
ity up to about 10 cP. Thus, liquid diffusivities are five orders
From (3-39), of magnitude less than diffusivities for binary gas mixtures
at 1 atm. However, diffusion rates in liquids are not neces-
sarily five orders of magnitude lower than in gases because,
as seen in (3-3, the product of the concentration (molar den-
This value is about 3% less than the experimental value for an infi- sity) and the diffusivity determines the rate of diffusion for a
nitely dilute solution of aniline in water. given concentration gradient in mole fraction. At 1 atm, the
molar density of a liquid is three times that of a gas and, thus,
More recent liquid diffusivity correlations due to Hayduk the diffusion rate in liquids is only two orders of magnitude
and Minhas [7] give better agreement than the Wilke-Chang lower than in gases at 1 atm.