Gas Laws and Gas Law Mathematics

When studying the behaviors of gases, one aspect of gases that separates them from the study of solids and liquids is the ability to describe gases with basic mathematical statements, or equations. Over the years, many individuals have added their names to the lexicon of gas laws by developing equations that describe unique relationships between a variety of gas law variables. Boyles Law, Charles Law, Avogadro's Law, and Gay-Lussac's Law are all attempts to describe gases in terms of a set of defining characteristics.

The mathematical description of gases is dependent upon four gas law variables. These variables are:

• Temperature, symbolized as T, and always measured in Kelvin. This term is a direct measure of the temperature, or average kinetic energy, of all the gas particles in the system.
• Pressure, symbolized as P, and measured in a variety of units. Two common units of pressure are the Torr and the Atmosphere. These two pressure units are related to each other by the statement that 760 Torr = 1 Atm.
• Volume, symbolized as V, and measured most frequently in Liters. The volume term does not represent the volume of the gas particles, but represents the volume of the container that the gas could occupy. Even if the gas, such as the atmosphere, is not in a container, the V term will still measure the size of the container that the gas COULD occupy if it were in a container.
• Moles, symbolized as n, and measured in the unit of moles. This term is the measure of the number of objects within the gas phase system.

Any mathematical statement that is used to describe a gas phase system must provide information about all four of these terms.

It turns out that the many individual gas laws that exist can be combined into a single gas law known as the Ideal Gas Law. This law can be written in two different ways. Although the two equations appear to be quite different from each other, they are actually very closely related. The only significant difference between them is when they can each be used.

or	Notice that this version of the equation has only one term for each of the gas law variables. This equation is used in any problem that provides single pieces of information about the variables and asks for information about a single, missing variable. The term R is known as the Ideal Gas Constant and will be discussed later.
	The second version of the equation has two terms for each of the variables. This equation is used when one or more of the variables are changed during a problem. For instance, if presure is changed then there will be two pressure terms, a before and after situation. As a result of the changes in the values of these variables, it is possible to determine a new value for a missing variable.