Page 114 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 97

The diffusion coefficient of a compound can be estimated using the dif-
fusion coefficient of another compound of similar species, their molecular
weights, and the following relationship:

= (3.27)
D 1 MW 2
D 2 MW 1
As shown in Equation (3.27), the diffusion coefficient is inversely propor-
tional to the square root of its molecular weight. The heavier the COC, the
harder it is for it to diffuse through the fluid. Temperature also has an influ-
ence on the diffusion coefficient. From Equation (3.26), we can see the dif-
fusion coefficient in water is proportional to the temperature and inversely
proportional to the fluid viscosity. The water viscosity (μ ) decreases with
w
increasing temperature and, consequently, the diffusion coefficient increases
with temperature and the following relationship applies:


D 0 @T 1 =  T 1  µ @T 2  (3.28)
w
 µ @T
D 0 @T 2   T 2    w 1  

Example 3.16: Estimate the Diffusion Coefficient
Using the LeBas Method
Estimate the diffusion coefficient of toluene in a dilute aqueous solution at
20°C using the LeBas method.

Solution:
(a) The formula of toluene is C H CH . It consists of a benzene ring
6
3
5
(six carbon member) and a methyl group.
Viscosity of water at 25°C = 0.89 cP (from Table 3.2)
T = 275 + 20 = 293K
Molal volume is determined from the sum of the volume incre-
ments (Table 3.7)
C = (14.8)(7) = 103.6
H = (3.7)(8) = 29.6
Six-membered ring = −15.0
So, V = 103.6 + 29.6 − 15.0 = 118.2 cm /g mole
3
(b) Use Equation (3.26) to find the diffusion coefficient:
−
×
7
5.06 10 (293)
2
D 0 = = 0.95 10 − 5 cm /s
×
(0.89)(118.2) 0.6