Page 59 - Materials Chemistry, Second Edition

42 Practical Design Calculations for Groundwater and Soil Remediation

pressure and temperature; the Clausius-Clapeyron equation is commonly
used. This equation assumes that the enthalpy of vaporization is indepen-
dent of temperature and is expressed as

1 P sat ∆H vap  1 1 
ln sat =−  −  (2.16)
2 P R  T 1 2 T 

where P is the vapor pressure of the compound as a pure liquid, T is
sat
the absolute temperature, R is the universal gas constant, and ΔH vap is the
enthalpy of vaporization, which can be found in chemistry handbooks and
references such as Lide [8]. Table 2.1 lists the values of the universal gas con-
stant in various units.
The Antoine equation, which describes the relationship between vapor
pressure and temperature, is widely used and has the following form:

B
ln P sat = A − (2.17)
+
TC
where A, B, and C are the Antoine constants, which can be found in chemis-
try handbooks such as Reid, Prausnitz, and Poling [9].
For an ideal solution, the vapor–liquid equilibrium follows Raoult’s law as:

x
A P = (P vap )( A ) (2.18)

where
P = partial pressure of compound A in the vapor phase
A
P vap = vapor pressure of compound A as a pure liquid
x = mole fraction of compound A in the solution
A
The partial pressure is the pressure that a compound would exert if all
other gases were not present. This is equivalent to the mole fraction of the
compound in the gas phase multiplied by the entire pressure of the gas.
Raoult’s law holds only for ideal solutions. In the dilute aqueous solutions
commonly found in environmental applications, Henry’s law, which will be
discussed in the next section, is more suitable.

Example 2.24: Vapor Concentration in Void with
Presence of Free Product
Benzene leaked from a UST at a site and entered the vadose zone. Estimate
the maximum benzene concentration (in ppmV) in the pore space of the sub-
surface. The temperature of the subsurface is 25°C.