Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 44

is the so-called virial equation of state ,

PV
RT =

B(T)
V +

C(T)
V 2

1 + +··· . (3.2)

The terms B(T) and C(T) are called second and third virial coefficients.
The definition of an ideal solution is different from that of an ideal gas. For solu-
tions one cannot neglect intermolecular forces. Consider a solvent (

≡

A) containing a

≡

solute ( B). The possible solute-solvent interactions are: A-A, A-B, and B-B. The

solution is considered ideal if the three forces are identical and if there is no volume
change or enthalpy change during mixing. There also exist situations in which there
are so few B molecules among a large number of A molecules that B-B interactions
are negligible. These are considered ideally dilute solutions . For these solutions, we
canapplythelimitingconditions x A →

0.Thelimitingconditionisathermo-
dynamic definition of an ideal dilute solution.A practical definition of dilute solution
in environmental engineering is somewhat less stringent than the thermodynamic
definition.

1, x B →

3.1.1 C ONCENTRATION U NITS IN E NVIRONMENTAL E NGINEERING
Environmental concentrations (air, soil, and water) are expressed in a variety of units
(Appendix 4). Traditional units such as parts per million (ppm), parts per billion
(ppb), and parts per trillion (ppt) are still in use, although these units are inexact and
ofdubiousapplicability.Chemicalthermodynamicistsprefertoworkinmolefraction,
molality, and molarity units.
Mole fraction is defined as the ratio of the moles of a solute to the total moles of
all species including the solvent, that is,

n i

i n i

x i = . (3.3)

Molarity is the moles of solute per liter (dm 3 ) of the solution.
Molality is the moles of solute per kilogram of solvent.
The different concentration units are shown in Table 3.1.

TABLE 3.1
Concentration Units in Environmental Chemistry

Phase Conventional Units Preferred SI Units

mol/m 3 water and mol/dm 3
water

Water or organic solvents mg/L water

μ g/m 3 air mol/m 3 air
Soil or sediment mg/kg solid mol/kg solid
Note: In the aqueous phase, mg/L is equivalent to ppm; in the air phase, another
equivalent unit to

Air

g/m 3 is parts per million by volume (ppmv). See also

μ

Appendix 4.