Quote (Underneath @ Apr 20 2013 03:01pm)
So PV = nRT. I would assume that if pressure increased, then volume decreases.If the volume decreases, then the number of moles of the gas should decrease as well,making pressure and number moles inversely proportional. However, apparently the book says that P and n are directly proportional. Can anyone explain this? Thanks!
You are forgetting that the temperature may have changed as well.
Think of the following situation: You have 1 mol of a gas at STP in a closed container (V = 22.4 L, P = 1 1atm, T = 25C) with a piston on the top.
You lower the piston causing the pressure to increase from 1 atm to 2 atm. This means that V must now = 11.2 L (P1V1 = P2V2).
I think where you are becoming confused is that you are now thinking, well if 1 mol = 22.4L then if the volume is only 11.2 L then we can only have .5 mol. But this isn't true, as 1 mol = 22.4L is only true at STP, which we are no longer at.
Since this is a closed container we know that the number of mols is constant (No gas can escape and gas isn't just going to be created out of thin air), which means it must be the temperature that has changed in order to keep PV= nRT true.
The temperature has increased because with the increased pressure/decreased volume we are now having more atomic collisions. You can calculate the new temperature using P1V1/T1 = P2V2/T2.
Pressure is only directly proportional to the number of moles if Volume and Temperature are held constant.
This post was edited by RzChaos on Apr 20 2013 05:38pm