# Ideal gases and pressure

1. Feb 11, 2017

### rashida564

I read from a website that Most gases behave like ideal gases at many temperatures and pressures.
and we have learned that the gases behave like ideal one only in high temperature and low pressure . so which one is true .

2. Feb 11, 2017

### Staff: Mentor

Depends on the accuracy you are interested in. In general, ideal gas equation fails for low temperatures and high pressures, when the assumptions behind the ideal gas theory (can you list them?) no longer hold. But it is not like we can point to a given PT combination and say - that's where the gas stops to behave like an ideal one. If you look for a precision high enough no gas is ideal. If you are interested just in ballpark values - every gas is "ideal enough" even close to the boiling point.

3. Feb 11, 2017

### rashida564

the particles don't occupy any space.
they collide with each other elastically.
they don't have intermolecular force between them .

4. Feb 11, 2017

### Staff: Mentor

Perfect.

Try to think how it translates into the real gas. For example: first assumption is equivalent to "volume occupied by the molecules is negligible compared to the gas volume". Can you think how well that holds for the gas at low temperature and high pressure? How well that holds for low pressure and high temperature?

At what ranges do the intermolecular forces work? When are they important - when the molecules are squeezed and close to each other, or when the molecules are separated and dispersed?

Do you see how it makes the gas behavior to change with PT? And do you see that the change must be gradual?

5. Feb 11, 2017

### Staff: Mentor

If you want to get an idea of how well (or poorly) the ideal gas law applies to your particular gas at its pressure and temperature, start out by calculating the "reduced pressure" and "reduced temperature" of the gas. The reduced pressure is the actual pressure divided by the critical pressure of the gas and the reduced temperature is the actual (absolute) temperature divided by the critical temperature of the gas. Then find (in a thermo book) the generalized graph based on the "law of corresponding states," showing the so called compressibility factor z plotted as a function of the reduced pressure and the reduced temperature. For the real gas, the law will be PV=znRT. So, the deviation of z from 1.0 will tell you the degree of inaccuracy incurred by using the ideal gas law. The graph applies to all gases (to a good approximation).

6. Feb 12, 2017

### rashida564

the first assumption will hold at high temperature and low pressure because it will occupy a small volume compare to the whole volume,and that is because at high temperature and low pressure the particle will be far from each other . so we can Ignore intermolecular force "because as the distance increase the force will decrease " 2-also we can neglect the force due to the high KE of the particles .