With the compression factor, pV/nRT, the variables in the denominator can be determined quite accurately but it is not so true for pressure and volume.
With assumptions we make about ideal gases (zero molecular volume & no attractions between molecules) this is not true for real gases and these have an effect on both pressure and volume.
- THE VOLUME PROBLEM
- The kinetic molecular theory for ideal gases assumes the particles have negligent intrinsic volume. The distance between particles is so large compared with the particle size that particles are treated as point objects.
- For a real gas, this assumption is not true. The molecules themselves do take up a proportion of space in the container. The space in the container available for gas particles to move around in, is less than the measured volume of the container.
- The problem gets worse as more gas is compressed into the container - as the gas gets more compressed, the proportion of the total volume that the molecules themselves take up increases. So if the pressure is low, the volume taken up by the actual molecules IS insignificant compared with the total volume of the container.
- THE PRESSURE PROBLEMAnother assumption of the Kinetic Theory for ideal gases is there are no intermolecular forces between molecules. This is wrong for every real gas.
- If there weren't any intermolecular forces, it would be impossible to condense the gas into a liquid. Even helium, with the weakest of all intermolecular forces, can be turned into a liquid if the temperature is low enough.The effect of intermolecular forces For a gas molecule located in the middle of the gas mixture, there is no net effect. It will be attracted to some extent to all other molecules around it, but, on avg, those attractions will cancel each other out. Attractions from behind a molecular, tending to slow it down, will be cancelled by attractions from in front of it, tending to speed it up.
- The gas molecule in the centre here (marked in green) is experiencing intermolecular forces but it will just continue to move in the same direction as the same speed.
- However if the molecule is about to hit the wall of the container, there aren't as many gas molecules in front of it, and the net attraction is backwards into the body of the gas. The molecule will slow down just before it collides into the wall. If it slows down, it will not the wall as hard, and so exerts less pressure.
- Overall effect - measured pressure is less than it would if the gas was ideal. Hence if you put the measured pressure into the expression PV/nRT, the compression factor you calculate will be less than it would be if the gas was ideal. This is why, under some conditions, graphs of compression factors drop below the ideal value of 1. This effect is noticeable at lower temperatures.
- At lower temperatures, the molecules are moving more slowly on average. Any pull they experience back into the gas will have relatively more effect on a slow moving particle than a faster one. i.e. Intermolecular attractions are more dominant than the molceular volume effect. PV/RT ratio < 1.
- At higher temperatures, where the molecules are moving a lot faster due to great kinetic energy, any small pull back into the body of the gas doesn't do much and is hardly going to be noticeable on the molecule. At high temperatures, the effect of intermolecular forces is negligible and hence high temperatures gives a higher pressure for real gases than an ideal gas would - due to molecular volume contribution to pressure outweighing intermolecular forces. PV/RT ratio > 1.
Another effect concerning intermolecular forces - as pressure increases
, the molecules are forced more closely together - intermolecular forces become more important - as pressure increases, at first the value of the compression factor falls but it soon rises up again. Why? Because at this point, the effect of the size of the molecules starts to become more important - and as pressure increases even more, this effect becomes dominant.