Will room-temperature water in a sealed flask evaporate?
Even at room temperature, some of the water molecules in the liquid will have sufficient energy to 'escape' and become vapour. Because the flask is sealed however, some of the water vapour molecules will return to the liquid phase.

Eventually, an equilibrium will be reached when the rate at which water molecules which escape the liquid is equal to the rate at which water molecules in the vapour enter the liquid. At this point, the pressure reached by the water vapour is known as the vapour pressure of water (at the given temperature).

The 'reaction' is not completely reversible since some heat is lost to the surrounding environment through the wall of the flask.