Lesson 2 - Gas Laws

The universal gas law, and its counterpart the specific gas law, are strictly only applicable for ideal gases. In fact, we may come across these gas laws termed the ‘ideal gas law’. So, what do we mean by an ideal gas?

Perhaps, rather strangely, one definition of an ideal gas is one which behaves according to the ideal gas law.

This definition allows us to mathematically define the behaviour of an ideal gas and compare experimental gas data against the mathematics to test for an ideal gas. However, it does not really help us visualise an ideal gas. At this stage of the course, it is not easy to give a meaningful description of what an ideal gas is.

An ideal gas is a theoretical gas with descriptions of molecular particles and their interactions, which utilises some quite complicated atomic theory.

Instead of concerning ourselves with the ins and outs of the detail of an ideal gas, let us simply consider under what circumstances most brewery gases approach (or approximate to) the behaviour of an ideal gas. These circumstances are as follows:

• Simple gases approximate as ideal gases (think of a simple molecular formula like CO₂). An exception to this is water vapour (steam) which departs quite significantly from ideal gas behaviour.

• Low to moderate pressures such as those experienced in blowers, fans, and low-pressure compressors (e.g. less than 10 bar) and moderate temperatures support ideal gas assumptions.

• High pressures and low temperatures, such as those found in a cryogenic, refrigeration, and gas compression-liquefaction plant (such as brewery CO₂ recovery plant result in a significant departure from ideal gas behaviour).

• Further to the last point, any phase transition of a gas (e.g. condensation) is not modelled at all by the ideal gas equation.

Let us now look at two applications of the universal gas law in defining the concept of molar volume, and the standardised conditions of pressure and temperature.

Molar volume, standard temperature and pressure (STP)

One of the interesting applications of the universal gas law is the concept of molar volume. In this, the gas law is rearranged to give the volume of 1 kmol of gas:

The volume of 1 kmol of an ideal gas is a function only of temperature and pressure. Taking this one step further, at the same temperature and pressure, the molar volume for an ideal gas will be the same. So, if we had a standard for pressure and temperature, we could quantify the standardised molar volume for an ideal gas. Fortunately, we do have such a standard in place – called the ‘standard temperature and pressure’, which is abbreviated to STP. The values of STP are 0°C (273.15 K) and 101,325 Pa.

Therefore, the molar volume at STP is given by:

This suggests that the volume of 1 kmol of an ideal gas at STP is 22.4 m³. This value allows us to quickly estimate the density of a gas, which is described by the ideal gas law, using its molar mass. We can consider this in the worked example below.

Example:

Compare the density of carbon dioxide (CO₂) and oxygen (O₂) at STP using the molar volume concept.

We know that the molar volume at STP is 22.4 m³ and we know that the molar masses of CO₂ and O₂ are 44 and 32 kg/kmol, respectively. The density of both gases is given by:

And:

Let’s now look at another worked example dealing with STP and gas densities.

At STP conditions, what would the mass be of 2.5 L of CO₂?

We determined the density of CO₂ gas at STP conditions above and it was given as:

The mass of 2.5 L of CO₂ at STP would be:

Another way of thinking of this is that 2.5 L of CO₂ at STP has a mass of 5 g.

You should make sure that you are comfortable with this concept of molar volume, STP, and masses and volumes of gases. When we look at dissolved gases in a later lesson, we will be using it again.

We have, so far, learned about ideal gases and the situations where common brewery gases can be considered to approximate to ideal gases. However, we have only considered single ideal gases and the brewing world is also often concerned with gas mixtures (e.g. air and mixtures of CO₂ and N₂). To appreciate the laws by which mixtures behave, we need to consider a variant of the universal gas law, which is called Dalton’s law.