# Does unsaturated vapor obey Pressure law?

My textbook says unsaturated vapor obeys Charles and Boyle's law. So I think it should obey pressure law too. But from a certain temperature to dew point at unsaturated state, the mass of vapor remains constant and so the pressure. Therefore, lowering the temperature (volume is constant) doesn’t lower the pressure.So it's not obeying pressure law. Am I right? Or do I have any misconception here?

## 1 Answer

It depends on what accuracy level you are interested in.

These 2 laws are isobaric and isothermal special cases of the ideal gas state equation

$$pV=nRT$$

which is not valid for real "permanent" gases nor for vapours of volatile liquids.

Ideal gas laws as the two mentioned ones expect that gas molecules have zero volume and that there are no attractive forces between molecules of vapour.

The attractive forces between vapour molecules can be very significant. The vapour molar volume at given $$T$$ and $$p$$ can be for high temperature and pressure significantly smaller than for an ideal gas.

These laws can be used as ideal gas approximation without significant error if real gas behaviour does not differ too much from ideal gas.

This condition is rarely satisfied at high temperature and pressure, but the deviation may be acceptable at low temperature and pressure.

If we consider the most familiar van der Waals' state equation:

$$(p + \frac{a}{{V_\mathrm{m}}^2})(V_\mathrm{m}-b)=RT$$

it must be clear there is deviation from both laws.

• The part about the superheated vapor not obeying the ideal gas law at temperatures close to the saturation point does not seem generally correct. I calculated the z-factor for water vapor from the saturated steam tables, and it was very close to 1 at vapor pressures at least up to 1 bar. Commented Oct 22, 2022 at 14:58
• I have not said anything about superheated vapour. Only that, by other words, vapour partial pressure converging to saturated vapour pressure means diverging from ideal gas behaviour. Commented Oct 22, 2022 at 15:00
• What about saturated vapor satisfying the ideal gas law? See the remainder of my previous comment. Commented Oct 22, 2022 at 15:02
• For saturated vapour pressure, pV < nRT due significant attraction forces. But it is interesting, when finding time, I would review that. Commented Oct 22, 2022 at 15:04
• You could as well ask if nitrogen follows ideal gas laws. It depends on what accuracy you expect. Commented Oct 22, 2022 at 15:09