How does volume of water in closed system relate to humidity at 25(C) degrees

Question

If I have a closed system with a volume of 100L, at ~24(C) or ~75(F) degrees, what volume must be filled with water to reach a humidity of 90%?

I imagined if you fill it 100% with water, humidity is 100%? But I also imagine that with anything less than 100% filled with water, temperature becomes a limiting factor, and 90% humidity might not be achievable without raising the temperature.

I checked out a max humidity ratio table to see that at 25(C) the saturation pressure is 3130 pa, with a maximum humidity ratio of 0.019826 -kg(w)/kg(a) and that humidity ratio can be expressed with the partial pressure of water vapor:

x = 0.62198 pw / (pa - pw)  

pw = partial pressure of water vapor in moist air (Pa, psi)

pa = atmospheric pressure of moist air (Pa, psi)

The maximum amount of water vapor in the air is achieved when pw = pws the saturation    pressure of water vapor at the actual temperature.

But this is as far as I got, as my understanding of humidity (relative, specific, etc).. is negligible... any suggestions or just a rough estimate?

Answer 1

as long as there is remaining liquid in the system, the space above it will always be 100% saturated...eventually. the temperature just determines how much (mass) can actually be in vapor form at that level (compare with your chart how much more water air can hold at 50'C compared to 25'C), and how fast the system can reach that state. even ice in a container will have vapor pressure above it.

the only way for space in a container to stay less than saturated after a long period of time is to actually run out of liquid to vaporise. essentially the question is asking how much liquid do you need to place in a 100L container so that all of it turns into water vapor--while that space ends up being only 90% saturated. intuitively this might be hard to accept, that water will disappear even at 25'C, but it is easy once you realise that this is a very very small amount of water.

a saturation pressure of 3130 pa basically refers to the partial pressure of water vapor when a space is saturated with water vapor (and possibly other gases). another way to visualise this is to have a container with absolutely nothing inside (vacuum) but water vapor at saturation levels--the absolute pressure in this container will 3130 pa. if you put this value inside the ideal gas law, you can calculate the number of moles of water you will need to saturate a 100L container at 25'C.

just take 90% of this amount of water--that is the amount you need to cause 90% RH in the container.