The Evolution of Combined Gas Law


By Don Lincoln, Ph.D., University of Notre Dame

Let’s go back in time and take a look at the evolution of gas laws: From Boyle to Charles and from Gay-Lussac to Avogadro, covering the constant progression of gas laws until the discovery of combined gas law.

An illustration showing the evolution of combined gas law.
An illustration showing the evolution of combined gas law. (Image: Fouad A. Saad/Shutterstock)

The study of gases and how their properties relate is one of the earliest quantifiable tests of what eventually became chemistry. If you take a sealed jar of gas and keep the gas from entering or leaving, you can characterize the material in the container by three measurements: the temperature, the volume, and the pressure. In this article, we’re going to learn how most people are taught how these three quantities are related.

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Boyle’s Law: The Pressure Is Inversely Proportional to Volume

The first study of the linkages between the temperature, pressure, and volume of a gas was made in 1662 when Irish chemist Robert Boyle explored the relationship between pressure and volume. He took a J-shaped glass tube filled with air and then poured in liquid mercury. By varying the amount of mercury he poured in, he varied the pressure that the air experienced.

He found that the pressure was inversely proportional to the volume, which is to say, as the pressure increased the volume decreased.

Mathematically, he found that the pressure times the volume equaled a constant. We now call this Boyle’s law and write it as PV=k, where P is pressure, V is volume, and k is a constant. If we double the pressure, then we cut the volume in half.

Boyle is often considered to be the first modern chemist and he was ahead of his time. It was nearly 150 years before the next advance was made.

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Charles’ Law: The Volume Is Directly Proportional to Temperature

In 1787, French chemist Jacques Charles was experimenting on the relationship between the volume and temperature of a gas. What he found was that, if he kept the pressure constant, that the volume of a gas was proportional to the gas’s temperature. If you doubled the temperature of a gas, you doubled its volume. Mathematically, you can write this as volume divided by temperature as a constant. And, by the way, to do this, you need to express the temperature in units of kelvin.

In Fahrenheit, water freezes and boils at 32° and 212° respectively. In Celsius or centigrade, water freezes and boils at 0° and 100°. In the kelvin scale, water freezes at 273.15° and boils at 373.15°. Those two temperatures are 100° apart, just like the Celsius scale, but with a big offset.

The kelvin scale is perhaps sensible because 0° kelvin is the smallest possible temperature, whereas the zero of the other two scales is a bit more arbitrary. Talking about the history of the different temperature scales is very interesting, but it would be off the topic for us. Just remember that for this lecture we’re always going to have to use the kelvin scale.

Gay-Lussac’s Law: Pressure Is Directly Proportional to the Temperature

Charles didn’t publish his work for many years, and it was two decades later in 1802 when French chemist Joseph-Louis Gay-Lussac studied the connection between pressure and temperature that Charles’ work came to light. In fact, it was Gay-Lussac who shared it with the world. What Gay-Lussac found was that the pressure of gas was directly proportional to the temperature. And, again in terms of a formula, he wrote that pressure P, divided by temperature T was a constant. Double the pressure and you double the temperature, and vice versa. And, of course, we need to use kelvin for temperature.

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Avogadro’s Law: The Volume Is Directly Proportional to the Number of Atoms

It was a few years later, in 1811, when Italian chemist Amedeo Avogadro determined that at constant temperature and pressure, the volume of a gas was proportional to the number of atoms in the container. The idea is the same as the others. Double the number of atoms and you double the volume. This is called Avogadro’s law.

Combined Gas Law

An image of, French physicist. Benoît Paul Émile Clapeyron.
French physicist Benoît Paul Émile Clapeyron came up with the combined gas law in 1834. (Unknown/Public domain)

So, these four laws: Avogadro’s law, which connects the number of atoms and volume; Boyle’s law, which compares pressure and volume; Charles’ law, which compares volume and temperature; and the Gay-Lussac law, which compares temperature and pressure, were pieces of what we now call the combined gas law. In 1834, French physicist Benoît Paul Émile Clapeyron combined them together into a single law.

The only way to combine these four laws was if the pressure times the volume divided by the temperature and number of atoms were a constant. That means that if the pressure and volume were increased times two, the temperature would need to be increased by four, or the number of atoms would have to change.

That constant on the right-hand side has a name and a symbol. It’s denoted R and it’s called the ideal gas constant. This allows you to write the relationship between all of these variables in what is called the ideal gas law with an equation of PV=nRT.

P, V, and T are the pressure, volume, and temperature; R is the ideal gas constant; n is the number of gas molecules in volume in a funny unit.

An image showing the combined gas law and other contributory gas laws.
An illustration showing the evolution of combined gas law from the earlier gas laws to PV=nRT. (Image: Fouad A. Saad/Shutterstock)

If you have 6 times 10 raised to the 23rd power number of anything, it’s called a mole. No, it has nothing to do with the nearsighted underground rodent. The term comes from an abbreviation of the German word for molecule.

A mole is basically like the word dozen. You could have a dozen eggs or a dozen pairs of shoes. Similarly, you could have a mole of molecules.

In any event, the symbol n is just the number of molecules of gas you have, divided by that 6 times 10 to the 23rd number. That tells you the amount of molecules you have in units of moles.

So, that’s the ideal gas law: PV=nRT. It just slides off the tongue, PV=nRT.

Common Questions about the Evolution of Combined Gas Law

Q: How was the combined gas law discovered?

In 1834, French physicist Benoît Paul Émile Clapeyron combined the old gas laws into one single law which was called combined gas law.

Q: What does the combined gas law state?

The combined gas law combines the four gas laws: Boyle’s Law, Charles’ Law, Gay-Lussac’s Law, and Avogadro’s law to form ideal gas law. It states that the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant

Q: What does Boyle’s law state?

Boyle’s Law states that the pressure for a gas is inversely proportional to the volume.

Q: What is r in ideal gas law?

R is represented by a universal gas constant. The value of R depends upon the units but is usually displayed in S.I. units, such as R = 8.314 J/mol·K.

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