Lesson 2 - Gas Laws

The universal gas law stems from combining the laws of Boyle, Charles, and Gay-Lussac to form the combined gas law. This is a great form of an equation and helps us to really understand the influences of pressure, volume, and temperature. The extension to the combined gas law, which takes account of the quantity of gas, is the universal gas law which is probably the most powerful gas law in practice.

Before we get into the universal gas law in detail, we need to consider a different way of dealing with gas quantities.

The mole

The chemical mole, not the small furry animal!

Unlike a brewing recipe, which is largely based on the concept of mass, e.g. kilograms of malt and hops, chemistry is based on the number of molecules which would take part in a reaction. It may have been some time since we learned about this concept so let’s refresh ourselves by considering something we use every day – water.

Consider one of the most common chemical molecular equations, to which we again owe thanks to Joseph Gay-Lussac for its existence. This is the formation of water (H₂O) from hydrogen (H₂) and oxygen (O₂):

At a molecular level, we need two molecules of hydrogen and one of oxygen to form two molecules of water; this has nothing to do with mass.

We cannot say it takes two kg of hydrogen and one kg of oxygen to form two kg of water. Why? Does (2 + 1) = 3 kg of reactants form 2 kg of water? We would not be conserving mass, and where did the spare 1 kg of reactant go?

In chemistry, and when using the universal gas law, we need to consider the number of molecules, but how do we do this? Have you ever seen a molecule balance or set of scales in a laboratory? No, because they do not exist. Fortunately, however, the chemists have a conversion for us. However, the conversion is not a constant that we are more familiar with, e.g. we know that we can convert kilograms into tonnes by dividing by 1,000. Rather, the conversion is based on the chemical formula of the gas. Let us have a look at this.

If we consider a gas, like oxygen, we know its formula is O₂. This means it exists as a molecule consisting of two atoms of oxygen. To determine the conversion factor between kg and mole, we need to do the following:

1. Determine the molecular mass of the atoms which the molecule is made up of, in this case oxygen. Molecular mass is the mass of a mole of that substance, so, the molecular mass of oxygen (only one atom O) is 16 g/mole (this number is found in the periodic table).

2. Take note of how many atoms are in the molecule. In this case, two oxygen atoms in one molecule of O₂, so one mole of O₂ will have a mass of (2 x 16) = 32 g/mole.

3. As we are dealing with large quantities of gas in brewing, we utilise g/mole as a conversion. We can use a unit kg/kmol, which is 1,000 times larger. So, for an oxygen molecule, this becomes 32 kg/kmol (In the SI system, we abbreviate mole, or kmole, as a unit to mol or kmol.)

With this approach, we can convert between kmol to kg or kg to kmol.

The molecular masses of common brewing gases are as shown in the table below.

Table: Molecular masses of common brewing gases