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My textbook defines melting point of a solid as the point when the solid vapour pressure is equal to the liquid vapour pressure.

However when I search for solid vapour pressure, I get information on sublimation. This doesn't satisfy me because I know that not all solids sublime easily, but they can melt easily.

So my question is, what is solid vapour pressure? Is it really same as sublimation or is a different phenomenon at work here?

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For a solid to have a vapour pressure we require the solid to be in equilibrium with the vapour i.e. there is a pressure and temperature at which the chemical potentials of the solid and vapour are the same.

If we look at a typical pressure-temperature phase diagram it looks something like this:

Phase diagram

and it is only along the red line that the solid and vapour are in equilibrium, so it is only for this range of pressures and temperatures that the solid has a vapour pressure. But this is exactly the region in which the solid sublimes directly to a vapour without passing through a liquid phase. That's why the solid can have a vapour pressure only if it sublimes.

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  • $\begingroup$ So if we say that a solid sublimes at this point, and we also say that melting point is the point where the solid vapour pressure is equal to the liquid vapour pressure, wouldn't that mean that solids sublime at their melting point? I know this sounds a bit stupid, but I'm confused about this. $\endgroup$
    – Krish Vasa
    Nov 14, 2020 at 6:03
  • $\begingroup$ The only place on the phase diagram where a solid can both sublime and melt is at the triple point. At that point the solid, liquid and vapour are all in equilibrium so the solid has both a melting point and a vapour pressure. At the triple point solid vapour pressure is equal to the liquid vapour pressure, but this happens only at the triple point. $\endgroup$ Nov 14, 2020 at 6:06
  • $\begingroup$ So if we say that this only happens at triple point, how can I justify the definition my textbook gives for melting point? This is because according to my book, it defines 273 K as the melting point for ice by saying that vapour pressure of ice is equal to vapour pressure of liquid water. I know that 273K is not the triple point for water. So how can this be explained? $\endgroup$
    – Krish Vasa
    Nov 14, 2020 at 6:12
  • $\begingroup$ The triple point of water is very close to the melting point of ice. The triple point is at a temperature of 273.16K and the melting point at 1 atm is 273.15K. Maybe your book really means the triple point but because it's so close to the melting point it's just using the term melting point. $\endgroup$ Nov 14, 2020 at 6:15
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    $\begingroup$ The first sentence might more precisely begin "To characterize [or define] a solid's vapour pressure, we require..." All solids have a vapor pressure—in the sense that all solids tend to sublimate into a void—whether they're in an equilibrium setting or not. Vapor pressures of the elements. The common curvature represents an Arrhenius (i.e., exponential) dependence on temperature. $\endgroup$ Nov 14, 2020 at 8:02

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