Mass Transfer
455
Table 10.10
Diffusion coefficients for different solutes in dilute aqueous solutions at 25 °C
Comoonent
Di GO'9 m2 s''f
D.W flO12
kems-K'f
Oxygen
2.50
7.50
Carbon dioxide
1.96
5.88
Ammonia
2.00
6.00
Acetic acid
1.24
3.72
Methanol
1.60
4.80
Ethanol
1.28
3.84
Lactose
0.49
1.47
Glucose
0.69
2.07
Sucrose
0.56
1.68
“The ratio
(Da rj)/T
, which is approximately constant fo ra given solute-solution system (see Note 10.4) is also listed.
T
is the absolute temperature and
77
is the liquid (here water) viscosity. Data from Perry's Chemical Engineer's Handbook
6
th edition, McGraw-Hill (1984).
Note. 10.4. Estimating molecular diffusivities
Molecular diffusivities can be estimated by a number of different methods. The basis for many of these
methods is the Stokes-Einstein equation. This equation is derived from considering the drag force on a large
sphere, which moves in a solution (see e.g. Cussler, 1997). The diffusivity is found from the expression
D
A
kBT
6
xrjR0
(
1
)
where kfl is Boltzmann’s constant (= 1.380662 1023 kg m2 s"2 K'1), T is the absolute temperature, E is the
viscosity of the solvent and Ro is the radius of a spherical solute molecule. For non-spherical molecules, the
equation can be modified in different ways, e.g. for ellipsoidal molecules
D .
{a2~b2Y2
f
a
In
a+(a2-b2y
(
2
)
where a and b are the length of the major axes of the ellipsoid. Since the Stoke-Einstein equation builds on
the assumption that the diffusing compound is large relative the solvent compounds, it is mainly used to
predict diffusivities for large molecules such as proteins. It may also be used the other way around, i.e. to
predict the size of protein molecule from a measured diffusivity.
For prediction of diffusivities for smaller solute molecules A, diffusing in solvent B, the Wilke-Chang
correlation (Eq. 3), which has a similar structure as the Stoke-Einstein equation, may instead be used (Reid
etal,
1977).
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