Boyle’s Law

I

Introduction

Boyle’s Law, law of chemistry developed by English chemist Robert Boyle that relates changes in the pressure of a gas to changes in its volume. Boyle’s law was developed in the mid-1600s, and it deals with ideal gases. An ideal (or perfect) gas is one in which there is no interaction between the individual molecules, or the smallest particles, of the gas. Boyle’s law states that the pressure (P) of an ideal gas at a constant temperature varies inversely with its volume (V); that is, pressure increases as volume decreases, and vice versa. The pressure of a gas is the amount of force per unit of area that the gas exerts on its container. The volume of the gas is the three-dimensional size of its container. According to Boyle’s law, the product of an ideal gas’s pressure and its volume is constant. The mathematical expression of Boyle’s law is PV = constant. See also Gases.

Boyle’s law is only approximate for real gases, but predicts a gas’s behavior more accurately as the gas behaves more like an ideal gas. Under conditions that minimize contact between gas molecules—low pressure and high temperature, for example—Boyle’s law is useful for studying real gases.

II

Physical Basis for Boyle’s Law

Boyle developed his law through experimentation—examining and measuring systems of gases—but he did not know why gases followed this rule. In the 19th century scientists developed the kinetic theory of gases to explain the behavior of gases. This theory describes a gas as a collection of tiny, hard spheres that interact with each other and with the surface of the gas’s container. These spheres represent the molecules in the gas and behave according to the laws of motion developed by English scientist Sir Isaac Newton in the late 17th century. The kinetic theory is now the most widely accepted explanation of the theory of gas behavior. It describes how interactions between molecules influence gas characteristics such as temperature and pressure. It also explains why gases follow Boyle’s law.

According to the kinetic theory, the pressure of a gas is caused by collisions between gas molecules and the container walls. The temperature of a gas is directly related to the average speed of the gas molecules. In a gas at a constant temperature, the speed of the molecules remains constant. If a scientist reduces the volume of the container, the molecules will have less distance to travel before they hit a container wall. Therefore, the molecules will hit the container wall more often, resulting in a higher pressure. If the volume is increased, the molecules will hit the container walls less often, reducing pressure.

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III

History of Boyle’s Law

Boyle’s work on gases was inspired by Italian astronomer Galileo’s suggestion that vacuums, or regions where no matter was present, might exist. Boyle studied containers filled with air or other gases, and compared them to containers from which the air had been almost totally removed. German inventor Otto von Guericke invented the vacuum pump in 1650, and Boyle used an improved version of Guerike’s device to evacuate containers for his experiments later that decade.

In his experiments, Boyle proved that air was necessary for the transmission of sound and for substances to burn. Boyle believed that the difference between air and a vacuum was evidence that gases had a mechanical atomic structure and behavior. Boyle then investigated the elasticity of air by trapping some air in a tube. He did this by pouring mercury into the open end of a U-shaped tube and sealing the other end of the tube. The mercury trapped a fixed amount of air, no matter how much mercury Boyle used. However, the volume that the air occupied varied as Boyle changed the amount of mercury. If he used more mercury, the air was forced into a smaller volume. By measuring the pressure of the air, Boyle was able to develop the rule later known as Boyle’s law. He published his results in 1660 in a book called The Spring of Air.

The ideal gas law is a more general law than Boyle’s law. It describes how a gas responds to changes in volume, pressure, and temperature. Boyle’s law was an important part of the formulation of the ideal gas law. In the 1780s French chemist Jacques Charles developed Charles’s law, which relates the volume and temperature of a gas. French chemist Joseph Gay-Lussac refined Charles’s law in 1809, and the law became known also as Gay-Lussac’s law. Together, Boyle’s law and Charles’s (or Gay-Lussac’s) law make up the ideal gas law. The ideal gas law states that the product of a gas’s pressure (P) and volume (V) equals the product of the gas’s temperature (T) and a constant called the ideal gas constant (R), for each mole (a certain number of atoms or molecules) of gas. In mathematical terms, the ideal gas law is PV = RT.