Environmental Modeling - Mathematics and Statistics for the Environment - page 86

■ EXAMPLE 3.5
Problem: Calculate the volume of 0.333 mol of gas at 300 K under a pressure of 0.950 atm.

Solution:

= ×× =

nRT
P

0.333 mol × 0.0821 Latm/molK 300 K

0 959

⋅ ⋅ ×

V = 863 . L

. atm

Most gases in environmental systems can be assumed to obey this law. The ideal gas law can be
viewed as arising from the kinetic pressure of gas molecules colliding with the walls of a container
in accordance with Newton's laws, but there is also a statistical element in the determination of the
average kinetic energy of those molecules. The temperature is taken to be proportional to this aver-
age kinetic energy; this invokes the idea of kinetic temperature.

3.6.2.2 Dalton's Law
Dalton's law states that the pressure of a mixture of gases is equal to the sum of the pressures of all
of the constituent gases alone. Mathematically, this can be represented as

P Total = P 1 + P 2 + … + P n (3.14)

where
P Total = Total pressure.
P 1 , … = Partial pressure.

and

= ××

nRT
V

Partial P (3.15)

where n j is the number of moles of component j in the mixture.
Note: Although Dalton's law explains that the total pressure is equal to the sum of all of the pres-
sures of the parts, this is only absolutely true for ideal gases, but the error is small for real
gases.

■ EXAMPLE 3.6
Problem: The atmospheric pressure in a lab is 102.4 kPa. The temperature of a water sample is 25°C
at a pressure of 23.76 torr. If we use a 250-mL beaker to collect hydrogen from the water sample,
what are the pressure of the hydrogen and the moles of hydrogen using the ideal gas law?

Solution:

1. Make the following conversions—A torr is 1 mm of mercury at standard temperature. In
kilopascals, that would be 3.17 (1 mmHg = 7.5 kPa). Convert 250 mL to 0.250 L and 25°C
to 298 K.

2. Use Dalton's law to find the hydrogen pressure:

P Total = P Water + P Hydrogen

102.4 kPa = 3.17 kPa + P Hydrogen

P Hydrogen = 99.23 kPa