log P
V
i ¼ A i À
B i
T þ C i
ð3:5Þ
where,
P
V
i : vapor pressure of compound (kPa)
A i , B i , C i : compound-specific empirical constants
T: temperature (K)
Figure 3.6 shows the vapor pressure of various contaminants as a function of
temperature.
The total vapor pressure of a compound mixture is the sum of the partial pressures
of all the components in the mixture. Thus, the boiling point of this mixture (i.e.,
eutectic point of the azeotropic mixture) is achieved at a lower temperature than any
of the boiling points of any of the separate components (Lupis 1983). Dalton’s law
gives the mole fraction of a component in the gas phase (Eq. 3.6).
y i ¼
P
V
j
P n
j x j P
V
j þ P
V
w
ð3:6Þ
where,
y j : mole fraction of component j in the gas phase (À)
x j : mole fraction of component j in the aqueous mixture (À)
P
V
i : vapor pressure of compound i (kPa)
P
V
j : vapor pressure of compound j (kPa)
P
V
w : vapor pressure of water (kPa)
n: total number of volatile components in the aqueous mixture
140
120
100
Concentration/mol m -3
80
60
40
20
0
20
40
60
80
100
Temperature/°C
120
140
Fig. 3.5 Gas phase TCE (solid line) and PCE (dashed line) concentration as a function of
temperature (Knauss et al. 2000)
3 In Situ Thermal Treatments and Enhancements: Theory and Case Study
159