Environmental Modeling - Mathematics and Statistics for the Environment - page 87

3. Recall that the ideal gas law is

P × V = n × R × T

where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant
(8.31 L⋅kPa/mol⋅K or 0.821 L⋅atm/mol⋅K), and T is temperature. Therefore,

99.2 kPa × 0.250 L = n × 8.31 L⋅kPa/mol⋅K × 298 K

Rearranged:

n = 99.2 kPa × 0.250 L/8.31 L⋅kPa/mol⋅K/298 K

n = 0.0100 mol or 1.00 × 10 -2 mol hydrogen

3.6.2.3 Raoult's Law
Raoult's law states that the vapor pressure of mixed liquids is dependent on the vapor pressures of
the individual liquids and the molar fraction of each present. Accordingly, for concentrated solu-
tions where the components do not interact, the resulting vapor pressure ( P ) of component a in
equilibrium with other solutions can be expressed as

P = x a × P a (3.16)

where
P = Resulting vapor pressure.
x a = Mole fraction of component a in solution.
P a = Vapor pressure of pure a at the same temperature and pressure as the solution.

3.6.2.4 Henry's Law
Henry's law states that the mass of a gas that dissolves in a definite volume of liquid is directly
proportional to the pressure of the gas, provided the gas does not react with the solvent. A formula
for Henry's law is

P = H × x (3.17)

P is the partial pressure of a gas above the solution, H is Henry's constant, and x is the solubility of
a gas in the solution phase.
Henry's law constant ( H ) is a partition coefficient usually defined as the ratio of the concentration
of a chemical in air to its concentration in water at equilibrium. Henry's law constants generally
increase with increased temperature, primarily due to the significant temperature dependency of
chemical vapor pressures. Solubility is much less affected by the changes in temperature that are
normally found in the environment (Hemond and Fechner-Levy, 2000). H can be expressed either
in a dimensionless form or with units. Table 3.1 lists the Henry's law constants for some common
environmental chemicals.

3.7 CHEMICAL TRANSPORT SYSTEMS
In environmental modeling, environmental practitioners have a fundamental understanding of the
phenomena involved with the transport of certain chemicals through the various components of
the environment. The primary transport mechanism at the microscopic level is molecular diffu-
sion driven by concentration gradients; whereas, mixing and bulk movement of the medium are