Gases are the simplest state of matter because the relatively large distances between molecules and the high kinetic energy relative to the intermolecular forces cause the molecules to behave in simple, predictable ways. The behavior of gases were the very first physical properties to be reduced to mathematical form (gravity was second), and it was the simplicity of the relationships that prompted later scientists to develop mathematical models for more complex phenomena. Since the equations found to predict the properties of gases (like those with gravity) did so well, they were referred to as "Laws" in the traditional literature. Nature does, of course, have her "Laws", it's just that they are usually like Russian nesting dolls with a law at one level giving way to new complexity at another level. We will see this in our discussion of gases.
In Previous notes we have discussed the role of Evangelista Torricelli (1608 - 1647), Galileo's assistant in the discovery of the barometer. At about the same time Robert Boyle (1626 - 1691), the son of the Earl of Cork was beginning his examination of the behavior of air. In addition to his numerous observations on the properties of air and speculations of the nature of chemical change, Boyle was the first person to use the term "chemist" to describe his activities.
Boyle used a simple apparatus to examine the relationship between pressure and volume. In this apparatus, a small volume of air was trapped in a glass tube by mercury. A flexible tube connected this tube to a small reservoir of mercury that could be raised or lowered relative to the trapped gas volume. The difference in height of the interior and exterior mercury levels is, of course, the pressure relative to the pressure of the atmosphere. Boyle was able to demonstrate that:
V x P = constant
or that the volume and pressure are inversely proportional. This relationship is called Boyle's Law. This is illustrated by the figure below:
While Boyle observed that there was an additional relationship between temperature and volume he did not examine it in detail and it remained for the Frenchman, Jacques Charles (1746 - 1823) to report in 1787 that:
V = (constant)T
or that volume is directly proportional to temperature. Charles was inspired by the development of hot air balloons in France at this time.
Somewhat later on in 1848, the English scientist William Thompson, who was later raised to the Peerage as Lord Kelvin, recognized that a graph of volume vs. temperature for any gas resulted in a straight line that intersected the temperature axis at -273.15oC. This temperature later became known as absolute zero and was used as the basis for an absolute temperature scale. Temperature units corresponding to the Centigrade scale in this measure are called Kelvins.
We have not discussed the origin of the idea of temperature, or of the various temperature scales. The interested student should explore the web site on Celsius that may be reached by clicking here.
Following in the French tradition, Joseph Lewis Gay-Lussac (1778 - 1850 ) carried out a number of experiments on the properties and reactions of gases, resulting in his law of combining volumes that formed the basis for modern concepts of stoiochiometry. Gay-Lussac's ideas directly influenced the Italian, Amedeo Avogadro (1776 - 1856) to propose in 1811 that equal volumes of gases at the same temperature and pressures contained the same number of molecules. Unlike the other ideas presented here, Avogadro's ideas were more theoretical and (at the time) speculative, and were not accepted by the scientific community that was just then struggling with the implications of Dalton's atomic theory. Some years later during a conference on atomic weights in 1860, Pavesi, an Italian chemist, distributed to the participants a set of class notes that had been prepared by his colleague Stanislao Cannizzaro (1826 - 1910) in which Avogadro's ideas were clearly and convincingly set forth. The notes were in the form of a pamphlet titled "Sunto di un Corso di Filosofia Chimica" ("Epitome of a Course in Chemical Philosophy"). The simplicity and usefulness of these ideas were then apparent and Avogadro's hypothesis was firmly accepted by the scientific community.
Another way of stating Avogadro's idea mathematically is to write:
V = (constant)n
where n is the number of molecules. We now express n in terms of the unit "mole" which contains one Avogadro number of molecules, atoms or particlles. Avogadro's number itself was not first measured until a student of Rutherford collected the helium formed by alpha particles from a sample of radium. Knowing the pressure of the helium gas and the number of alpha decays over time of the sample, the student was able to obtain an estimate of Avogadro's number. Increasingly sophisticated experiments over the years have now set this number as 6.023 x 1023.
Combined Gas Law
If we combine the observations of Boyle, Charles, and Avogadro we find a single expression with four variables and one unified constant that we write as:
PV = nRT
In chemistry we use the following units for these quantities:
Students in engineering will find this equation in their studies as well, but they will use English (actually now American) units including a different temperature scale called Rankine based on Farenheit degrees and not Centigrade degrees.