Page 113 - Separation process principles 2

78 Chapter 3 Mass Transfer and Diffusion

Table 3.7 Limiting Ionic Conductances in Water at 25OC, in EXAMPLE 3.8
(~/cm~)(~/cm)(~-e~uiv/cm~)
Estimate the diffusivity of KC1 in a dilute solution of water
Anion A- Cation it at 18.5"C. The experimental value is 1.7 x lop5 cm2/s. At concen-
trations up to 2N, this value varies only from 1.5 x lo-' to
OH- 1.75 x lop5 cm2/s.
C1-
Br- SOLUTION
1-
At 18S°C, T/334~ = 291.7/[(334)(1.05)] = 0.832. Using Table
NO;
3.7, at 25"C, the corrected limiting ionic conductances are
ClO,
HCO, A+ = 73.5(0.832) = 61.2 and A- = 76.3(0.832) = 63.5
HCO,
CH3C0, From (3-47),
C1CH2C0,
CNCH2C0,
CH3CH2CO;
which is close to the experimental value.
CH3(CH2)2CO,
C6H5CO;
HC204
Diffusivity of Biological Solutes in Liquids
(;)c20;-
(;)so;- For dilute, aqueous, nonelectrolyte solutions, the Wilke-Chang
( :)F~(CN)~- equation (3-39) can be used for small solute molecules of
( :)F~(CN)~- liquid molar volumes up to 500 cm3/mol, which corresponds
to molecular weights to almost 600. In biological applica-
Source: Poling, Prausnitz, and O'Connell [2].
tions, diffusivities of water-soluble proteiil macromolecules
having molecular weights greater than 1,000 are of interest.
where T and p~ are in kelvins and centipoise, respectively. In general, molecules with molecular weights to 500,000
As the concentration of the electrolyte increases, the diffu- have diffusivities at 25°C that range from 1 x to
sivity at first decreases rapidly by about 10% to 20% and 8 x cm2/s, which is two orders of magnitude smaller
then rises to values at a concentration of 2 N (normal) that than values of diffusivity for molecules with molecular
approximate the infinite-dilution value. Some representative weights less than 1,000. Data for many globular and fibrous
experimental values from Volume V of the International protein macromolecules are tabulated by Sorber [lo] with a
Critical Tables are given in Table 3.8. few diffusivities given in Table 3.9. In the absence of data,
the following semiempirical equation given by Geankoplis
[ll] and patterned after the Stokes-Einstein equation can be
Table 3.8 Experimental Diffusivities of Electrolytes in Aqueous
Solutions used:

Concentration, Diffusivity, DAB,
Solute Mom Temperature, "C cm2/s x lo5
HCl where the units are those of (3-39).
HN03
Also of interest in biological applications are diffusivities
of small, nonelectrolyte molecules in aqueous gels contain-
H2S04 ing up to 10 wt% of molecules such as certain polysaccha-
KOH
rides (agar), which have a great tendency to swell. Diffusiv-
ities are given by Friedman and Kraemer [12]. In general,
the diffusivities of small solute molecules in gels are not less
NaOH
than 50% of the values for the diffusivity of the solute in
NaCl
water, with values decreasing with increasing weight percent
of gel.
KC1
Diffusivity in Solids

Diffusion in solids takes place by different mechanisms de-
MgS04 pending on the diffusing atom, molecule, or ion: the nature
Ca(N03)2
of the solid structure, whether it be porous or nonporous,