So I assume that you are thinking of trapped air in the water. This is my way to look at this experiment. Hook up a vacuum pump to an insulated container of water and have the vacuum pump outlet connected to an insulated recipient container that can measure the increase in volume caused by the removed air and water vapor from the supply container. Pressure and temperature sensing devices will need to be connected to both containers. Obviously the pressure sensors readings speak for themselves. On the other hand the temperature sensors will indicate by using the Mollier diagram how much water vapor is included on the discharge side of the vacuum pump. Knowing the initial and final mass of the water in the supply container will tell you how much water vapor was removed and added to the recipient container. The volume change of the recipient container will be from the water vapor and from the removed trapped air. Since you have the pressure and temperature readings of the mixture within the recipient container, you can figure out the mass of the trapped air and of the water vapor. Your OP requires a knowledge of the Mollier diagram noted in thermodynamics, ideal gas equations that were introduced in chemistry and in thermodynamics, and mass transfer, a particular topic introduced in heat transfer.
spor water andr, ,samass o