In this section we will consider several mathematical laws that relate the properties of gases. The gas laws are simple mathematical relationships between the volume, temperature, pressure, and amount of a gas. These laws are derived from experiments involving careful measurements of the relevant gas properties.

A. Boyle’s Law

Robert Boyle discovered that doubling the pressure on a sample of gas at constant temperature reduces its volume by one-half. Reducing the pressure on a gas by one-half allows the volume of the gas to double. From such experiments, he formulated the law now known by his name.

B. Charles’s Law

Boyle’s law depends on the temperature of the system remaining constant. But suppose the temperature changes: How does a change in temperature affect the volume and pressure of a gas?

One of the first quantitative observations of gases at different temperatures was made by Jacques Alexandre Charles in 1787. He studied the volume behavior of gas samples kept at constant pressure as they were heated. He found that a sample of gas at a fixed pressure increases in volume linearly with temperature. By linearly, we mean that if we plot the volume occupied by a given sample of gas at various temperatures, we get a straight line.

C. Gay-Lussac’s Law

You have just learned about the quantitative relationship between volume and temperature at constant pressure. What would you predict about the relationship between pressure and temperature at constant volume?

When the temperature of a sample of gas in a rigid container is increased, the pressure of the gas increases as well. The French chemist Joseph Gay-Lussac (1778-1850) discovered the relationship between the pressure of a gas and its absolute temperature.

Gay-Lussac’s Law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant.

D. Avogadro’s Law

Let us take a balloon containing a certain mass of gas. If we add to it more mass of gas, holding the temperature (T) and pressure (P) constant, the volume of gas (V) will increase. It was found experimentally that the amount of gas in moles is proportional to the volume. That is,

V ∝ n (T and P constant) or V = k n where k is constant of proportionality.

Avogadro’s Law in the form V = k n can be rearranged to

For any two gases with volumes V₁, V₂ and moles n₁, n₂ at constant T and P,

If V₁ = V₂, n₁ = n₂.

Thus for equal volumes of the two gases at fixed T and P, number of moles is also equal. This is the basis of Avogadro’s Law which may be stated as: equal volumes of gases at the same temperature and pressure contain equal number of moles or molecules.

Molar gas volume

It follows as a corollary of Avogadro’s Law that one mole of any gas at a given temperature (T) and pressure (P) has the same fixed volume. It is called the molar gas volume or molar volume.

In order to compare the molar volumes of gases, chemists use a fixed reference temperature and pressure. This is called standard temperature and pressure (abbreviated, STP). At STP we find experimentally that one mole of any gas occupies a volume of 22.4 litres. To put it in the form of an equation, we have

1 mole of a gas at STP = 22.4 litres