Real Gases, Saturated Vapor; Crystalline and Amorphous Solids
Why water boils cooler on a Tian Shan peak, why a bathroom mirror fogs up, and why glass has no true melting point
Big Idea: The ideal-gas model of the previous topic ignores two facts about real molecules: they attract one another and they take up space. When a gas is squeezed or cooled these facts matter, the gas turns into a liquid, and above the liquid there sits a saturated vapor in dynamic balance with it. The same molecular forces, frozen into place, build the ordered lattice of a crystal or the frozen jumble of an amorphous solid like glass.
By the end of this topic you will be able to:
- explain why real gases deviate from the ideal-gas law at high pressure and low temperature,
- describe evaporation and condensation as a two-way molecular traffic,
- define saturated vapor and state why its pressure depends only on temperature,
- connect boiling to saturated vapor pressure and explain why water boils below 100 °C in the mountains,
- calculate absolute and relative humidity and find the dew point,
- explain the critical temperature above which a gas cannot be liquefied by pressure alone,
- contrast crystalline and amorphous solids by their order, melting behaviour and anisotropy.
1. From the ideal gas to real gases
In the last topic you used the ideal-gas equation of state pV = νRT. That model rests on two assumptions: gas molecules have no volume of their own, and they do not attract one another between collisions. For ordinary air at room temperature and normal pressure those assumptions are excellent - the molecules are tiny and far apart, so the errors are less than a percent.
A real gas is a gas in which we can no longer ignore these two facts. Deviations from the ideal-gas law become large in exactly two situations:
- High pressure. When the gas is strongly compressed, the molecules are packed close together. The space they physically occupy is no longer negligible compared with the container, so the gas is harder to compress than the ideal law predicts.
- Low temperature. When the gas is cold, the molecules move slowly. Now the weak attraction between molecules (the same intermolecular force that holds liquids together) has time to pull them together, lowering the pressure below the ideal value and eventually causing the gas to condense into a liquid.
The van der Waals picture: a more accurate equation for a real gas adds two corrections to pV = νRT: it subtracts a small volume b for the space the molecules occupy, and it adds an internal-pressure term a/V2 for the pull between molecules. You do not need the full formula this year, but keep the idea: real molecules have size and stickiness, and both matter when the gas is dense.