# Gas Laws and Applications (Worksheet)

“...it was as though scales fell from my eyes, doubt vanished, and was replaced by a feeling of peaceful calm.”

Lothar Meyer, upon hearing Avogadro’s hypothesis

It took chemists a long time to understand the nature of gases. Perhaps this was because of the ephemeral quality of gases or because experiments with gases required more sophisticated equipment that did experiments with solids or liquids. Nonetheless, once the Italian chemist Amedeo Avogadro (1776–1856) determined the true nature of gases, the mystery was solved and a more complete understanding of the atomic and molecular essence of matter was possible. This was Avogadro’s great contribution to chemistry, as Lothar Meyer so dramatically declared in the quote above. This unit explores the physical nature of gases, the laws governing the behavior of gases, and applications of gases from air bags to ozone depletion.

## The Gas Laws and the Ideal Gas Equation

Because scientists like the Irish chemist Robert Boyle (1627–1691), the French chemist Jacques Charles (1746–1823), and Avogadro could easily observe the macroscopic gas properties of mass, pressure, volume, and temperature, they provided the data which eventually led scientists to understand what a gas must be like at the particulate level. These pioneers summarized their observations into a set of equations which are the foundation for the ideal gas equation. All of the other gas equations can be derived from the ideal gas equation, so it is important to understand it well.

At low pressure (less than 1 atmosphere) and high temperature (greater than 0°C), most gases obey the ideal gas equation:

PV = nRT

Each quantity in the equation is usually expressed in the following units:

• P = pressure, measured in atmospheres
• V = volume, measured in liters
• n = amount of gas, measured in moles
• T = absolute temperature, measured in kelvins
• R = the ideal gas constant, which has a value of 0.0821 L atm/mol K

The ideal gas law was originally developed based on the experimentally observed properties of gases, although it can also be derived theoretically. It expresses the relationships among the pressure, volume, temperature, and amount of a gas. When Boyle and Charles studied the properties of gases in the seventeenth and eighteenth centuries, they studied the relationship between two of the variables, holding the others constant. Consequently, we have a set of simplified gas laws upon which the ideal gas law is based.

## Boyle’s Law (1662)

At a given temperature and number of moles of gas, Boyle's Law states that the pressure and volume of a gas are inversely proportional. In the form of an equation,

PV = constant

## Charles’ Law (1787)

At a given pressure and number of moles of gas, Charles' Law states that the volume and temperature of a gas are directly proportional. In the form of an equation,

VT = constant

At a given temperature and pressure, Avogadro's Law states that the volume and mass (number of moles, n) of a gas are directly proportional. In the form of an equation,

Vn = constant

Notice how the time line develops. The gas laws evolved over a period of nearly 150 years. During this time, scientists were struggling in an attempt to understand the particulate nature of matter, and it was Avogadro who finally made the breakthrough by recognizing the relationship between the macroscopic properties of gases and the particulate nature of matter.

In order to standardize the literature about experiments with gases, scientists have adopted a convention whereby gas properties are often expressed at a set of conditions known as standard pressure and temperature (STP), defined as exactly 1 atmosphere and 273.15 K.

## The Kinetic/Molecular Theory of Gases

Textbooks similarly state the details of the kinetic-molecular theory albeit somewhat differently. However, they usually summarize the same major points. Write a brief summary of the kinetic-molecular theory of gases, as presented in your textbook.