Is liquid water in equilibrium with water vapor at room temperature? This question was inspired by Why does liquid water form when we exhale on a mirror?.

This question is different from Why does water evaporate at room temperature? because it asks about whether an equilibrium is established. At room temperature under certain circumstances, water molecules leave the liquid phase and end up in the gas phase, as explained in the answers to the linked question. Whether an equilibrium is established is a related but distinct question.

Consider the reversible process of water moving from the liquid phase to the gas phase:

$$\ce{H2O(l) &lt;=&gt; H2O(g)}$$

At room temperature and atmospheric pressure, for which of the following scenarios does this process reach equilibrium?


A glass filled with water
A bottle of water after you poured half of the water out and recapped it.
A zip lock bag filled with water (no air).
Humid air in a zip-lock bag.


According to Wikipedia, 


  [...]chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal.


I am pretty confident in my answers for 1. and 2., but I am having trouble with 3. and 4.

Scenario 1. is an open system, and unless the air is at 100% humidity, the water will evaporate. This means the forward rate is larger than the reverse rate, and it is not at equilibrium.

Scenario 2. is a closed system, and if the temperature is constant, the water will evaporate until the air is at 100% humidity and the equilibrium is reached.

Scenarios 3. and 4 are not clear to me. Would you say these are at equilibrium because there are no changes over time? Or would you say these are not at equilibrium because either product (3.) or reactant (4.) is absent? What about if there is a tiny air bubble in scenario 3., or the bag is wet on the inside in scenario 4., would that make a difference?
It depends on the circumstances, but mostly not

Under most normal atmospheric circumstances water in an open vessel is not in equilibrium with water vapour in the atmosphere. We know this because water usually evaporates, albeit slowly. 

One way to measure whether water is in equilibrium is to measure the humidity which is a measure of the maximum concentration of water vapour under the prevailing temperature and pressure. Humidity is mostly less than 100% which means that the air could have more water vapour in it before the vapour spontaneously condenses. This isn't always true, which is why we get fog and why some countries are unbearable to live in.

At normal temperatures the equilibrium between water and water vapour is established slowly. Any vessel containing water that is open to the atmosphere will try to establish that equilibrium, but that won't be complete until the air is 100% saturated with vapour (humidity=100%). And you'd have to saturate the entire atmosphere in the room or, if the room is open, the entire planet's atmosphere to achieve equilibrium.

That this doesn't happen quickly is obvious. But it can happen locally (we call that weather). It it obviously not true across the whole planet at the same time or the planet would be called "sauna" and not earth.

The point is that the atmosphere is rarely 100% saturated with water vapour, so nothing open to the atmosphere will normally be in equilibrium with liquid water. A close bottle left long enough might establish equilibrium (with 100% humidity) inside the closed bottle, but any exchange with the surrounding air will lower the humidity and the equilibrium might take some time to re-establish.

The key to understanding this is that the kinetics of establishing the equilibrium are slow and the normal atmosphere is not saturated with water vapour. This means that the air above a glass containing open water will have a slightly higher concentration of vapour than the air surrounding the glass but with not be fully in equilibrium because the room surrounding the glass is big. And the atmosphere around the room is even bigger and clearly isn't in equilibrium (we have weather and wind to demonstrate that). The only systems where equilibrium will be established are closed ones which have been left a reasonably long time. atmospheric exchange causes the first; slow kinetics the second of these constraints.