Way to ruin the funSorry to interrupt your guys's chain of questions but I can finally answer one! Since we are dealing with an ideal gas, we can use the ideal gas law which states PV = nRT. Volume and R stay constant, so we can ignore those. The initial ratio of P/nT must equal the final ratio of P/nT. Lets assume we start with a pressure of 1 to keep the math simple. This gives us an equation 1/(46*(273+22)) = .5/(n*(273+22-13)). Solving for n gives us a final mass of 24 kg for the air. The question asks for how much is removed, so subtracting 24.1 from 46 gives us 22 kg of air pumped out of the room.

Jk haha, that's the right answer. Go ahead with the next question!