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 C 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 urms, 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 urms 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.