Water Vapour and Liquid Water Interactions

Question

It is known that a certain number of particles in a sample of water have enough kinetic energy to ‘escape’ from their intermolecular bonds and into the gas phase. But what is stopping these water vapour molecules from converting back into a liquid?

Answer 1

There is absolutely nothing stopping them, and in fact water molecules are constantly hopping between the phases to a degree dictated by the temperature of the system. The proper term used to describe the steady and balanced state these molecules reach is called chemical equilibrium. If we think about the process of the liquid water evaporating to form a vapor, the chemical reaction looks like, \begin{gather*} H_2O_{\text{(l)}} \iff H_2O_{\text{(g)}} \end{gather*} Since pure solids and liquids are excluded from equilibrium constants, the equilibrium constant for this process is just the vapor pressure of the vapor phase of water, $K_{eq} = P_{H_2O}$. If we look up some standard molar enthalpy and entropy values, we find that the standard Gibbs free energy of this reaction is $\Delta G^\circ_{rxn} = 8.60$ kJ/mol at a temperature of 298 K. Since the pressure is measured against standard state of 1 atm, this means that the vapor pressure of water at 298 K is $K_{eq} = P_{H_2O} = e^{-\frac{\Delta G^\circ_{rxn}}{RT}} = 0.03$ atm, which is the generally accepted vapor pressure of water. Note that this value is highly temperature dependent. Even assuming the molar enthalpy and entropy values are independent of temperature, we would find that at a temperature of about 97$^\circ$C the vapor pressure of water would reach 1 atm, which is the condition for boiling (the reason the value is off is because these values are not temperature independent, but this is a decent approximation).

As an added note, since we typically consider the atmosphere to be an open system, any water molecules that evaporate off of the surface of liquid water are liable to just float away from the original water source, taking them out of the equilibrium. This is why you will hear people refer to the vapor pressure "above a liquid," as it is consistent with open conditions. To compensate for the fact that these molecules are no longer capable of condensing back to the liquid phase (and thus maintaining the equilibrium), more water must evaporate to maintain the vapor pressure. This process will generally repeat until the water evaporates completely. But if you were to seal a small cup of water inside a sealed vessel, it would never evaporate after reaching equilibrium since none of the water vapor would escape at all and there would be no reason for more water to evaporate!