# Question about vapor pressure in solids and liquids

I've been reading about vapor pressure and it's a bit confusing. For example when water is in equilibrium between the solid and liquid phase, my textbook says that the vapor pressure is equal between the two.

Now I know this might sound stupid for someone who knows much more than me, but why is there vapor pressure in the equilibrium between a solid and a liquid?

Do the molecules with high kinetic energy go directly from the solid to the vapor form?( same thing with liquid). If not I don't know what that vapor pressure means in this case.

I only understand it in the case of equilibrium between liquid and gas.

Also note that I'm talking of the equilibrium between solid and liquids in water so the temperature would be increasing from 0 celsius up until it's fully a liquid

• the T maintains zero Celsius until the ice phase vanishes. Jun 15, 2023 at 20:21

First, your assumption about molecules going from solid directly to gas (vapor) is correct. This is called sublimation. Though many substances melt before there is significant sublimation, some sublime noticeably before melting, particularly at low pressure. Some well known examples are "dry ice" ($$\ce{CO2}$$), iodine, camphor, carbon or tungsten incandescent lamp filaments blackening the bulb, and ordinary water ice crystals growing from repeated sublimation and condensation.

Second, consider that if all three phases of water at the triple point are in contact, they must be in equilibrium, or at least one of the phases would disappear at the expanse of others. At the molecular level, there is constant interchange, with some fast-moving molecules in the solid becoming liquid or subliming to gas, while some less energetic molecules in the gas are condensing to liquid or solid. At a macroscopic level, one can observe a piece of ice slowly change shape as parts melt and refreeze elsewhere. However, in a closed system, the total amount in each phase should stay the same.

[Trivia: gallium is useful in high-temp thermometers because very little sublimes or evaporates. Ga has the widest range between melting point and boiling point, and a low vapor pressure until quite hot.]

There is vapor pressure above liquids and there is vapor pressure above solids. If their values would not be the same, the respective solid and liquid could be in equilibrium. As the phase with higher pressure would manifest net evaporation and the other net condensation.

It would be like if you put an open jar with water and another with sulfuric acid to a closed container. The volume of liquid water would decrease with time and the volume of sulfuric acid would increase. As water vapor pressure above water is greater than above sulfuric acid.

If you look at phase diagrams, you can see the direct solid–gas transition is common.

• Is it because of Maxwell-Boltzmann distribution that the solid has vapor pressure? Can sublimation of ice happen at $0$ celcius? Jun 14, 2023 at 15:39
• Look at the diagram in the link. What do you see? Conclusions you make yourself have bigger value in several aspects, compared to if you are told so. Jun 14, 2023 at 15:45
• I know it's better but I also know my conclusions might not be correct. Jun 14, 2023 at 15:51
• The biggest mistake is being afraid of making mistakes. One learns from mistakes more than from successes. Jun 14, 2023 at 15:52
• My conclusion is that because 0C is the triple point of water, then all three phases coexist, so that is where the vapor pressure comes from. Jun 14, 2023 at 16:02

At the same temperature solid and/or liquid and vapor, at equilibrium have the same Average Kinetic Energies but they do not have the same velocities because of the added forces of intermolecular attraction and, on Earth etc., of gravity. The differences manifest in the latent heats of melting and vaporization. [It seems that the place to study this is in microgravity, freefall, in a vacuum; or at the critical point.] In a pure water system [A one component system]: ice, water and vapor coexist only at the triple point. At the triple point all 3 phases have the SAME CHEMICAL POTENTIAL. That means the solid and liquid have the same vapor pressure. If temperature change and head space remains either vapor and liquid, or vapor and solid are present [subject to physical constraints]. No head space results in liquid-solid equilibrium or a single phase.

If the headspace is an inert gas such as air, water becomes a 2-component system. You will have to read about the Gibbs Phase Rule in a PChem text for the consequences. Each inert gas pressure changes the vapor pressure of both liquid and vapor differently depending on their molar volumes. This means that the melting point changes and that the melting point at each pressure is a triple point where all three phases are in equilibrium, ie. the liquid and solid have the same vapor pressure. If the temperate changes from the triple [aka freezing] point either the solid or liquid phase vanishes. Each pressure of inert gas has a distinct triple point and set of equilibrium curves. I like to think of it as the 4th dimension in a 3phase brane.