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Let's say I spill liquid on some fabric or on a impermeable material like a countertop. Eventually, the liquid stops being a liquid and we say it has "dried", but what happened to the molecules? Did they change phase? How were the conditions for phase change met? Assume we are at room temperature and the liquid is something that doesn't naturally boil or freeze at that temperature or pressure (like water).

EDIT: I'm aware this is called evaporation, but what happens to the molecular structure during this process? What causes molecules to leave the liquid?

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    $\begingroup$ Evaporation.... $\endgroup$ – Mithoron Jan 23 '17 at 3:39
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The molecules don't change their structure during evaporation. It is only that they spread further apart. This is associated with the 2nd law of thermodyamics: entropy (basically) always increases. Entropy is the measure of disorder or possible arrangements of a system of particles.

Molecular changes are reactions. Phase changes, e.g. evaporation etc. are merely changes in the "nearest-neighbor" distance between particles.

There may be a very slight change in average bond angles etc. (e.g. when water freezes into a meta-stable state) but all bonds remain intact for a phase change.

Coffee and wine are mixtures of tons of different chemicals but the primary substance is water, so they follow the phase-transition of water very closely, i.e. same $T$ and $p$.

To give you some perspective, gases (e.g. water vapor) are generally 1,000 times less dense than liquids/solids (e.g. water/ice).

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There is no change in molecular structure. A phase change is a physical, not chemical process. To understand why evaporation occurs, you need to realize that every substance has a vapor pressure. This is the pressure exerted by that substance's vapors when it is in thermodynamic equilibrium with its condensed form in a closed system. Substances with high vapor pressures, also called volatile substances, evaporate more quickly than those with low vapor pressures. Consider the illustration below:

This illustration shows a liquid coming into thermodynamic equilibrium with its vapor, only made possible by the stopper in the flask. Remove it, and it is no longer a closed system. As vapor leaves the flask, more liquid will vaporize in order to maintain equilibrium, but as the process continues there is eventually no liquid left to replace the vapor as it leaves.

This is why it's important to put the caps back on your gasoline canisters after you're done using them, and how you're able to dry your clothes on a clothes line.

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Suppose that there are some molecules dissolved in the solvent, say a dye from coffee dissolved in water. These dye molecules usually have a far higher boiling point than water does and so have a lower vapour pressure, often effectively zero, at room temperature. Thus water evaporates at a far greater rate than they do and so the solution 'dries' leaving the dye behind. The dye is chemically unchanged by not being dissolved in a solvent. If the solution was, say, alcohol & water then as both have a large vapour pressure at room temperature both will evaporate and nothing will be left.

The water (solvent) evaporates due to the difference in vapour pressure at the liquid surface and the average value in a room. The liquid will evaporate trying to establish equilibrium, at which point the rate of evaporation will equal the rate of condensation of water vapour in the air entering the liquid. Usually equilibrium is never met and so all the liquid evaporates. However, on hot very humid days you may have noticed that it often takes far longer for a puddle to evaporate than on less humid days.

Not all the molecules in a liquid have the same energy, they follow a (Boltzmann) distribution of energies, many have low energy and fewer higher energy than the average. (Only the average energy is constant at constant temperature). Of these higher energy molecules (achieved by random jostling of molecules in solution) some of them are close to the surface and randomly are on the right trajectory to escape into the gas phase. As some of the most energetic molecules leave the liquid this will cool. (It will therefore receive heat from the surface it is sitting on and from molecules in the air (including water molecules), but if these processes are slow the liquid will be measurably cooled). You can feel the cooling effect of evaporation after stepping out of a hot shower.

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Water (or any liquid in general) consists of particles. Electrostatic forces hold the particles together, but they can still move and slide over each other - which is what makes it a liquid.

Their energy depends on the temperature. The higher the temperature, the more vigorously they move and collide and slide over each other. Through collision, they can gain or lose energy, as well as change direction.

Eventually, by random chance, some particles on the surface has enough speed in the correct direction to leave the surface, overcoming the electrostatic forces that used to hold the particle to the water.

This particle has escaped, and we say that it has evaporated.

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