Unit 2: Advance Basics

Section 7: More Gas Laws

* Gas Stoichiometry
* Dalton's Law of Partial Pessure
* Mole Fraction
* Kinetic Molecular Theory of Gas

Gas Stoichiometry

Standard temperature and pressure (abbreviated STP) is defined as 0 oC and 1
atmosphere. At these conditions the volume of 1 mole of any gas is
approximately 22.42 L. In other words, one mole of oxygen gas will take up
about 22 liters, one mole of nitrogen gas will take up about 22 liters, and
one mole of helium gas will take up (you guessed it) about 22 liters.
Another important equation that is used to determine molecular weight is:
molecular weight = dRT/P, where d (density) is in the units grams per liter.
So if you have the density of a gas, the pressure it's under, and the
temperature, you can calculate its molecular weight.

Dalton's Law of Partial Pressure

In 1803, Dalton summarized his observations in this statement: For a mixture
of gases in a container, the total pressure exerted is the sum of the
pressures that each gas would exert if it were alone. This statement, known
as Dalton's law of partial pressures, can be expressed as follows: Ptotal =
P1 + P2 + P3 + , where the subscripts refer to the individual gases (gas 1,
gas 2, etc.). P1, P2, P3, are called partial pressures.

Mole Fraction

The mole fraction is defined as the ratio of the number moles of a given
component in a mixture to the total number of moles in the mixture. This can
be written as: mole fraction = n1/ntotal = n1/n1 + n2 + n3 +

Kinetic Molecular Theory of Gases

The kinetic molecular theory is a simple model that attempts to explain the
properties of an ideal gas. The postulates of the kinetic molecular theory:

Gases consist of particles, which have the following properties:
1. The particles are so small compared to the distances between them
that the volume of the individual particles can be assumed to be
zero.

2. The particles are in constant motion. The collisions of the
particles with the walls of the container are the cause of the
pressure exerted by the gas.
3. The particles are assumed to exert no forces on each other; they
are assumed neither to attract nor to repel each other.
4. The average kinetic energy of a collection of gas particles is
assumed to be directly proportional to the Kelvin temperature of
the gas.

As expected, real gases do not conform to these assumptions, but they are
accurate in explaining ideal gas behavior.

The average kinetic energy of a gas can be determined if given the
temperature. The equation used is (KE)avg = 1.5 RT, where R is equal to
8.3145 J/K mol (which is also equal to .08026 L atm/K mol, but different
units). Temperature must also be expressed in Kelvin. Temperature can also
be used to determine the root mean square velocity. Symbolized as vrms, root
mean square velocity is equal to (sq. root)(3RT)/M. In this equation R is
equal to 8.3145 J/K mol, T must be Kelvins, and M is the mass of a mole of
gas particles in kilograms. The root mean square velocity is in the units
m/s. Although vrms for oxygen gas at STP is about 500 m/s, the majority of
the O2 molecules are not actually going that fast. Instead, the actual
distribution of the velocities is shown in the graph below.