Hi everybody. Hope everyones doing well. Let's take a look at this question. Many of the students have responded correctly, but I'd like to add a bit explanation to their correct answer for those confused.
A) The volume is independent of the pressure of the gas
PV = nRT; and the volume cannot be independent of the pressure. It would be best to think of real life examples, as it will make it easier to understand the question. If you have ever tried to fill a balloon, one knows that the pressure and volume are related to one another. One time I tried to fill those air beds by mouth, and since the volume of the bed is big, a lot of gas molecules have to be blown into it to increase the pressure; thus they are related to each other (not to mention I was about to faint afterwards).
B) The pressure is inversely proportional to the number of moles of gas
Inversely...wow. This would mean that if you put more air molecules into a tire, the tire would go flat. Makes no sense. They are directly related, if you put more moles (hence more molecules) of a given gas, the pressure would increase. This is why we have tired, and balloons.
C) The volume is directly proportional to the pressure of the gas
Boyles Law: They are indirectly related. The formula is P1V1 = P2V2, and P1V1 = Constant; Therefore, in order to obtain the same constant each time, when one increases the other factor would have to decrease. Real life analogy: You increase the volume of the thoracic cavity, the pressure drops and air rushes into your lungs.
D) The volume is inversely proportional to the pressure of the gas
Please see "C"
E) The pressure is independent of the number of moles of gas
This is a funny one. For those of you who have had a balloon blow up in your face, you very well know that the more you fill it, the larger the pressure, until the elastic walls give way.
Your answer is D.
My suggestion would be to think of these types of questions in a more realistic fashion. Once you can do this, then the concepts are easy to understand, and the formulas...well, they are just ways to complicate simple concepts.