I Water bath and water vapor + air mixture in a closed system

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In a vacuum chamber with a water bath and a mixture of air and water vapor, the system reaches equilibrium at room temperature, resulting in 100% relative humidity. At this point, the partial pressure of water vapor matches the saturation pressure dictated by the temperature, as per the Buck equation. The amount of air in the chamber does not affect the water vapor amount, as it is solely dependent on temperature. If the air initially has 0% relative humidity, the pressure will increase to the sum of the air pressure and the water vapor pressure once equilibrium is restored. This highlights the counterintuitive nature of the relationship between air pressure and water vapor in such a closed system.
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Hello,

At my work I came up with the following question:

Say we have a vacuum chamber. Inside the vacuum chamber we have at the bottom a water bath. The rest of the chamber is filled with a air and water vapor mixture. The whole system is placed in a room, is at room temperature and is in equilibrium.

Since the system is in equilibrium the relative humidity should be 100% (is this correct?). Therefore the partial water vapor pressure should be the same as the water vapor pressure at room temperature (for example given by the Buck equation). This water vapor pressure is only a function of the temperature.

Does this mean that the amount of air (raising the pressure in the vacuum chamber) has no effect on the amount of water vapor inside the vacuum chamber?

Does this mean that if at the start the air has 0% relative humidity (the whole system is still at room temperature) in which case the air pressure is pair will increase to pair + pvapor when the system in back in equilibrium?

I feel like I am missing something.
 
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Yes to all your questions.
 
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Its a bit counter intuitive, I would expect the air pressure to play a role here. Thank you for your reply.
 
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