Topic 8 – The Equation of State for an Ideal Gas

Molecular Kinetic Theory Model

In Topics 8 and 9 we will be looking at how gases behave.  Then in Module 3 we will have a look at the behaviour of solid materials.  In syllabi other than the AQA you may well find that this piece of work is in a completely separate module to mechanics.  However these topics fit quite well with mechanics because you need to understand about collisions to make sense of the Kinetic Theory model.

In mechanics so far we have been looking at big things, like tennis balls, cars, people, to name but a few.  This can be referred to as the macroscopic level.  In this piece of work we will go down to the molecular level, where things are very small.  We call this the microscopic level.

The Ideal Gas

We will be looking at gases and their behaviour under different conditions. The behaviour of ideal gases is quite easily predictable.  However real gases tend to behave slightly differently, especially those that consist of molecules.  So the ideal gas we will consider is:

• monatomic

• at low temperature

• at low pressure.

There is no interaction between the molecules of an ideal gas except for collisions, which are always perfectly elastic. Helium is a good example of an ideal gas.

Ideal Gas Equation

There are three gas laws:

• Boyle's Law

• Charles' Law

• Pressure Law

You are not expected to know them for the examination, but understanding them is useful.  Click HERE to find out more about the Gas Laws.

From the gas laws we can write:

The value of the constant depends on how much gas is being considered.  If we are looking at one mole of gas (which we will define later), then the constant is the universal molar gas constant. This is given the code R and has the value 8.31 J mol^-1 K^-1.

For n moles of a gas, we can write:

Where:

• p - pressure (Pa)

• V - volume (m³)

• n - number of mols

• R - molar gas constant ( 8.31 J mol^-1 K^-1)

• T - Temperature (K)

This is called the equation of state of an ideal gas. In this equation, SI units must be used, i.e. volume in m^-3, pressure in Pa.  Temperature must be in Kelvin (K).  0 K = -273 ^oC.

The temperature quoted in degrees Celsius is commonly set as a bear trap.  Make sure you don't fall into it.

The Mole

The mole is defined as:

 the same number of particles of a substance as there is in 12 g of ¹²C. 

This number is called the Avogadro constant, and is given the codes L or N_A.

L = 6.02 x 10²³ mol^-1

The molar mass M_m is the mass of 1 mole of the substance.  Chemists quote this in grams per mole; for physics we need to convert to kilograms per mole by dividing by 1000 (or multiplying by 10^-3).