Applications of Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 168

equilibrium with it, then the partition constant between air and particulates is

C i a
(W i /C sp ) .

K AP = (4.99)

Note that K AP has units of ng/m 3 .
Traditionally, aerosols are collected using a high-volume air sampler into which a
large volume of air is pulled through a glass fiber filter that retains particulates and
subsequently through a tenax bed that retains the vapors. The filter-retained material
is taken to be W i and the adsorbent-retained solute is taken to be equivalent to C i a .
In our earlier discussion on partitioning into aerosols, we had established that the
fraction adsorbed to particulates in air (

p
i ) is determined by the subcooled liquid
vapor pressure of the compound ( P s ( l ) ). Compounds with small P s ( l ) showed large
values of

φ

p
i . This means that the value of K AP will be correspondingly large.

φ

1 − φ C sp .

p
i

K AP = (4.100)

p
i

φ

The value of K AP has been found to be a sensitive function of temperature. Many
investigators have collected field data and developed correlations of the form

m
T +

log K AP = b , (4.101)

where m and b are constants for a particular compound. Yamasaki, Kuwata, and
Miyamoto (1982), Pankow (1987), Bidleman (1988), and Subramanyam et al. (1994)
have reported correlations (Table 4.15). Pankow (1987) showed theoretically that the
constants in the above equation are given by

=− Δ

H des
2.303 R +

T a
4.606 ,

m (4.102)

log 2.75

10 5 (M a /T a ) 1 / 2
A p t 0

× 1

4.606 ,

b = − (4.103)

where H des is the enthalpy of desorption from the surface (kcal/mol), T a is the

midpoint of the ambient temperature range considered (K), A p is the specific surface
area of the aerosol (cm 2 /

Δ

μ

g), and t 0 is the characteristic molecular vibration time
(10 − 13 -10 − 12 s). Since the value of b is only weakly dependent on molecular weight,
M , the compound specificity on K AP appears through the slope m where

Δ H des is

characteristic of the compound. At a given T , K AP decreases as Δ H des increases. In

general, one can write

10 9 P s ( l )
N s A p RT exp ((

K AP =

H v )/RT) ,

(4.104)

Δ H des − Δ