Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 45

3.1.2 D ILUTE S OLUTION D EFINITION
Let us consider a dilute solution of A in solvent B. If we consider a fixed volume V
(m 3 ) of ideal dilute solution, then addition of A and removal of B does not affect the
total volume, and hence the above expression can be rewritten in terms of molarity as

C A
C A +

x A = . (3.4)

C B

For dilute solutions C A C A /C B . For aqueous solutions C B

is the molar density of water, which we designate

C B , and hence x A ∼

55.5 mol/dm 3 ). Thus, mole
fraction is proportional to molarity in a dilute aqueous solution. Relationships similar
to the above can be derived for solutions in gases and solids.

ρ w ( =

E XAMPLE 3.1 C ALCULATION OF C ONCENTRATIONS IN AN E NVIRONMENTAL
M ATRIX

Problemstatement : Calculate the mole fraction, molarity, and molality of the following
solutes in water: (a) ethanol, 2 g in 100 mL water; (b) chloroform, 0.7 g in 100 mL water;
(c) benzene, 0.1 g in 100 mL water; and (d) hexachlorobenzene, 5 × 10 − 7 g in 100 mL
water.
Solution : First obtain the density and molecular weight of the compounds from standard
CRCtables.Thencalculatethevolumeofeachcompoundandthereforethetotalvolume
of the solution. The final results are tabulated below:

Mole

Molecular Molarity Fraction Molality

(g/cm 3 ) (mol/dm 3 )

Compound ρ Weight (mol/kg)

7.5 × 10 − 3

Ethanol 0.79 46 0.420 0.430

1.0 × 10 − 3

Chloroform 1.48 119 0.058 0.058

2.3 × 10 − 4 Benzene 0.87 78 0.013 0.013

1.7 × 10 − 8 3.1 × 10 − 10 1.7 × 10 − 8 Hexachlorobenzene 1.57 285

Note that only for ethanol the molality is different from molarity. At very low mole
fractions, molarity and molality are identical. Since the molarities are all less than
2.773 mol/dm 3 , the solutions can be considered ideal.

3.2 FUGACITY
The concept of fugacity is an invaluable tool in constructing equilibrium models
for the F&T of chemicals in the environment (Mackay, 1991). Fugacity is derived
from the Latin word fugere , which literally means toflee . Thus, fugacity measures the
escapingorfleeing tendencyofamoleculefromaphase.Ifthefugacityofacompound
is the same in two phases, then the molecule is said to be in equilibrium with both
phases. Chemical potential, although a useful quantity, is somewhat awkward to use
since it can only be estimated indirectly. For example, in Chapter 2 we noted that