Environmental Fate and Transport of Solvent-Stabilizer Compounds - Environmental Investigation and Remediation - page 116

average rate of migration of a chemical in air in response to temperature, pressure, and concentra-
tion gradients exclusive of any chemical movement in response to advection. The air diffusion
constant is sometimes called air diffusivity, often denoted as D a (expressed in units of cm 2 /s).
Temperature affects the air diffusion constant, which affects the volatilization rate.
Values for the air diffusion constant, D a , are not widely available from experimental data.
Methods to estimate D a include empirical equations based on a compound's molecular weight and
specii c gravity. The following equation has been used to estimate D a (USEPA, 2001a):

3/2 2

0.0029( T + 273.16) 0.034 + (1 / MW)(1 - 0.00015MW ) ,

D = (3.1)

a

2

È ˘

(MW/2.5 ) r+

1/3

1.8

Î ˚

where D a is the diffusion coefi cient of the chemical in air (in cm 2 /s), T is the temperature (in °C),
MW is the molecular weight (in g/mol), and is the density (in g/cm 3 ).

A useful index for contrasting vapor densities of single compounds is relative vapor density
(RVD). A compound's RVD is the ratio of the density of dry air saturated with that compound at
25°C and 1 atm total pressure to the density of dry air. The RVD may be calculated by using
Equation 3.2 (Pankow and Cherry, 1996):

ρ

=

( p / 760)MW + [(760 - p )29.0] / 760

(3.2)

RVD ,

29

where p ° is the saturated vapor pressure, MW (in g/mol) is the molecular weight, and 29 g/mol is
the mean molecular weight of dry air. RVD is dependent on temperature, so the temperature at
which the RVD is calculated must also be stated (usually at 25°C). The saturated vapor pressure p °
can be obtained from the Antoine equation. * At a compound's boiling point, RVD

MW/29.
Table 3.1 provides vapor pressure values cited in the literature and estimated values of vapor
pressure, vapor density, and air diffusion constants for 1,4-dioxane and other commonly used solvent
stabilizers likely to be present in vapor degreasing and other solvent wastes. For comparison, data
for the major chlorinated solvents are included.
Chemicals on dry soil partition to the vapor phase according to the parameters in Table 3.1. Once in
the vapor phase, advection causes vapor to move from soil to turbulent air, and diffusion causes upward
movement of vapor into still air (Dragun, 1988). A number of empirical equations are available to
estimate the rate of volatilization of a pure chemical from dry soil. The rates at which chemicals diffuse
at a given temperature are inversely proportional to the square roots of their molecular weights:

=

1/2

D
D

Ê MW ˆ

a

1

= Á . (3.3)

1

˜

MW

Ë ¯

a 2

2

An equation for estimating the rate of vapor generation of a pure chemical from dry soil under
steady-state conditions was proposed by Shen (1981):

1/2

È LDv ˘ Ê W ˆ

Aa c

EPW = 2 ,

(3.4)

Í ˙ Á˜

vA

() p f W

˯

Î ˚

* The Antoine equation describes the relationship between saturated vapor pressure of pure substances and temperature by
the relationship P = 10[ A -( B /( C + T ))], whereby historic convention P is the pressure (in mm Hg), T is the temperature
(in °C), and A , B , and C are the Antoine equation coefi cients available from the National Institute of Standards and
Technology ( http://webbook.nist.gov/chemistry/ ).