Closed yesterday by Jean-Marie Prival, trond hansen, Erik, Universal_learner, Nemesi. What? You closed your own question? This doesn't happen often :)

I believe that it has to do more with the evaporation of the water from the soil. The advection had moved the clouds away, thus leaving clear sky with before mentioned condensing evaporating water. Also, the weight of clouds has nothing to do here (everything in the form of ordinary matter has some weight, thus this is here unnecessary).

I am voting to reopen this question because I believe this isn't a homework question. He says: "For the sake of simplicity lets assume that the pressure in the room should stay the same as before." If this were a homework question, the teacher clearly wouldn't give that (the problem gets harder, not simpler : )

@TimMenser Imagine a bottle filled with nitrogen and oxygen. If you add the nitrogen, the mass of oxygen stays the same. I imagined that scenario because closed room with possible gas escape doesn't exist. (Closed room = no interchange, oxygen escape = interchange -> contradiction). But yes, with a pressure exhaust we would need lower amount.

@uhoh Thank you, corrected in the text (I replaced liters with cubic meters).

@JeopardyTempest See note in my edit. Your equation is more suitable for this I must admit, but I also found out that I converted $6.5\frac{K}{km}=6.5\frac{K}{m}$, so it actually worked with my equation, too. (But Letitbe had no such data.)