Calculating Oxygen Volume in Hospital Tanks Using Ideal Gas Law

[colton4286]

Oxygen for hospital patients is kept in special tanks, where the oxgen has a pressure of 65.0 atm and a temp. of 288 K. The tanks are stored in a separate room, and the oxygen is pumped to the patient's room, where it is administered at a pressure of 1.00 atm and a temp. of 297 K. What volume does 1.00 m^3 of oxygen in the tanks occupy at the conditions in the patient's room?

What I did was solve for the # of mols (n) given the tank information: n= PV/RT and used this n value to solve for volume: V= nRT/P. But I got 67 m^3 which is a much larger number than I expected. Am I heading in the right direction on this problem? Thanks!

 

[lzkelley]

That sounds exactly right.
Note that you don't actually have to solve for the number of moles, all you need to know is that it stays constant.

n = PV/RT and n is constant, therefore:
(PV/RT)1 = (PV/RT)2 where 1 and 2 correspond to before and after the pumping, i.e. 1 is at 65 atm 288K and 2 is at 1atm 297K.
Also R is constant, so you can cancel that out.

Cheers

 

[Moetasim]

Yes, you are on the right track with using the ideal gas law to solve this problem. However, there may be a mistake in your calculations. It is important to double check your units and make sure they are all consistent. For example, the units for pressure should be in atmospheres, temperature in Kelvin, and volume in cubic meters. It is also important to make sure you are using the correct values for the ideal gas constant (R). Once you have checked your units and calculations, you should get a more reasonable answer for the volume of oxygen in the patient's room. If you are still getting a significantly larger number, it may be helpful to show your work or seek clarification on the problem.