# Ideal Gases

**DEAL GASES AND THE IDEAL GAS LAW**

**Kinetic Theory assumptions about ideal gases**

There is no such thing as an ideal gas, of course, but many gases behave approximately as if they were ideal at ordinary working temperatures and pressures. Real gases are dealt with in more detail on another page.

The assumptions are:

- Gases are made up of molecules which are in constant random motion in straight lines.
- The molecules behave as rigid spheres.
- Pressure is due to collisions between the molecules and the walls of the container.
- All collisions, both between the molecules themselves, and between the molecules and the walls of the container, are perfectly elastic. (That means that there is no loss of kinetic energy during the collision.)
- The temperature of the gas is proportional to the average kinetic energy of the molecules.

And then two absolutely key assumptions, because these are the two most important ways in which real gases differ from ideal gases:

- There are no (or entirely negligible) intermolecular forces between the gas molecules.
- The volume occupied by the molecules themselves is entirely negligible relative to the volume of the container.

**The Ideal Gas Equation** The ideal gas equation is:

**pV = nRT**

On the whole, this is an easy equation to remember and use. The problems lie almost entirely in the units. **Exploring the various terms** ** Pressure, p** Pressure is measured in pascals, Pa – sometimes expressed as newtons per square metre, N m

^{-2}. These mean exactly the same thing. Be careful if you are given pressures in kPa (kilopascals). For example, 150 kPa is 150,000 Pa. You must make that conversion before you use the ideal gas equation. Should you want to convert from other pressure measurements:

- 1 atmosphere = 101,325 Pa

- 1 bar = 100 kPa = 100,000 Pa

** Volume, V** This is the most likely place for you to go wrong when you use this equation. That’s because the SI unit of volume is the cubic metre, m

^{3}–

**cm**

*not*^{3}or dm

^{3}. 1 m

^{3}= 1000 dm

^{3}= 1,000,000 cm

^{3}So if you are inserting values of volume into the equation, you first have to convert them into cubic metres. You would have to divide a volume in dm

^{3}by 1000, or in cm

^{3}by a million. Similarly, if you are working out a volume using the equation, remember to convert the answer in cubic metres into dm

^{3}or cm

^{3 }if you need to – this time by multiplying by a 1000 or a million. If you get this wrong, you are going to end up with a silly answer, out by a factor of a thousand or a million. So it is usually fairly obvious if you have done something wrong, and you can check back again.

*The gas constant, R*

A value for R will be given you if you need it, or you can look it up in a data source. The SI value for R is 8.31441 J K^{-1} mol^{-1}.

*The temperature, T*

The temperature has to be in kelvin. Don’t forget to add 273 if you are given a temperature in degrees Celsius.