Ideal Gas Law

The volume of a gas changes with temperature, pressure and the number of molecules in the container. Early workers used experimental data to derive Charles Law and Henri’s Law. They recognized that these laws were imperfect in that they did not take into account the volume of the individual gas molecules or any forces of attraction between molecules. A few gases actually did vary slightly from the properties predicted by Charles Law and Henri’s Law. Thus these laws were called ideal gas laws because they describe an “ideal gas” or one with no molecular volume and no attractive forces between molecules. An ideal gas behaves as though gas molecules are only influenced by kinetic energy and by the elastic collisions between molecules or of molecules with the wall of a container.

Later workers combined the two laws into a universal ideal gas law formula, PV=nRT where P is pressure, V is volume, n is the number of molecules (generally expressed in moles), R is a constant dependent on what units of measure are used, and T is the absolute temperature. I require my students to memorize this equation because it can be rearranged algebraically to solve any ideal gas problem. This formula gives valid answers for almost all real gases at the conditions that early chemists were working with and also for most conditions generally encountered in laboratories today. It looses its validity at very low temperatures and very high pressures.

Ideal gas laws predict that any ideal gas will shrink in volume as the temperature is reduced until it reaches a volume of zero at -273.2 degrees Celsius. Of course no real gas can be made to completely disappear, but the ideal gas laws tell us that all molecular motion stops at this temperature which is known as absolute zero. No one has ever been quite able to reach absolute zero. Even if someone reaches absolute zero, scientists believe they can go no lower.

An absolute temperature is a temperature scale using absolute zero as zero. One such scale is the Kelvin scale. To find a temperature in degrees Kelvin, one adds 273.2 to the temperature in degrees Celsius. This is the temperature that must be used in the ideal gas formulas.

Almost all scientists use the universal ideal gas formula and encounter variations that are within experimental error of their equipment. Problems occur when very high pressures or very low temperatures squeeze the molecules into such small volumes that the volume of the gas molecules become significant. Under these conditions, the molecules act as though they are incompressable pebbles. Measurements of volume are much greater than predicted by ideal gas laws. If one increases the pressure, or drops the temperature lower, the gas becomes a liquid. Gas laws no longer apply.

In order to understand how our world behaves, scientists often use assumptions that set up ideal conditions. The theories derived using ideal conditions help us understand science, but are seldom useful in the real world where there are few, if any ideal conditions. As long as one avoids extreme conditions, ideal gas laws are one place where we reality meets ideal conditions. Remember the formula PV = nRT, and you will be able to calculate the changes in temperature, pressure of volume of gases encountered in the laboratory and in real life. The formula works for divers and for pilots. It can also be made to work for you.