Page 115 - Materials Chemistry, Second Edition

98 Practical Design Calculations for Groundwater and Soil Remediation

Example 3.17: Estimate the Diffusion Coefficient
at Different Temperatures
The diffusion coefficient of benzene in a dilute aqueous solution at 20°C is
1.02 × 10 cm /s (Table 3.6). Use this reported value to estimate:
2
−5
• The diffusion coefficient of toluene in a dilute aqueous solution at 20°C
• The diffusion coefficient of benzene in a dilute aqueous solution at
25°C

Solution:
(a) The MW of toluene (C H CH ) is 92, and the MW of benzene
5
6
3
(C H ) is 78.
6
6
Use Equation (3.27):
−
×
5
(1.02 10 ) 92
D 1
= =
D 2 D 2 78
So the diffusion coefficient of toluene at 20°C = 0.94 × 10 cm /s
−5
2
(b) Viscosity of water at 20°C = 1.002 cP (from Table 3.2)
Viscosity of water at 25°C = 0.89 cP (from Table 3.2)
Use Equation (3.28):
(1.02 10 )× − 5 =   293   0.89  
 
0
D @298 K  298   1.002 
So the diffusion coefficient of benzene at 25°C = 1.17 × 10 cm /s
2
−5
Discussion:
1. The diffusion coefficient of toluene estimated from that of ben-
zene is 0.94 × 10 cm /s, which is essentially the same as that
−5
2
from the LeBas method, 0.94 × 10 cm /s (Example 3.16).
2
−5
2. The diffusion coefficient of benzene at 25°C is about 15% larger
than that at 20°C.
Example 3.18: Relative Importance of Molecular
Diffusion and Hydraulic Dispersion

Benzene from USTs at a site leaked into the underlying aquifer. The hydrau-
lic conductivity of the aquifer is 500 gpd/ft and it has an effective porosity
2
of 0.4. The groundwater temperature is 20°C. The dispersivity is found to be
2 m. Estimate the relative importance between the hydraulic dispersion and