Ideal Gas Law: Calculating Pressure and Moles of Helium Gas

[map7s]

ideal gas law...I think...

Homework Statement

Useful Constants: 1 Torr = 133.32 Pa; R = 8.3145 J/mol·K

You have a thin metal sphere of unknown volume that contains helium gas at low pressure. You put the entire metal sphere into a bath of liquid nitrogen, and a pressure gauge on the sphere indicates a pressure of 286 torr.

a) You now place the metal sphere in a mixture of dry ice and methanol. What is the new pressure?

b) You now place the metal sphere in ice water. What is the new pressure?

c) You now place the metal sphere in a water bath at room temperature (measured to be 26.0 °C). What is the new pressure?

d) You now place the metal sphere in boiling water. What is the new pressure?

e) Given that the volume of the metal sphere, pressure gauge, etc., was 324 mL, how many moles of helium gas would you have?

Homework Equations

PV=nRT
P/T=P/T

The Attempt at a Solution

Since we were dealing with Helium gas, I assumed that it would fall under the conditions of an ideal gas. I got all of the parts to this question correct, except for the very last part. For the other parts I used the second equation listed to find out the new pressure. For the last part, since conversion factors were given in the beginning, I assumed that the conditions were as stated at the very beginning and converted the original pressure to Pa, the volume to m3 (cm^3=mL), the temperature to K (for all parts temperature was given in K), and used the R value that was given. Is there some other catch to this equation that I am missing? Is there some value that I misconverted? Am I using the wrong conditions? I tried this problem several times and could not figure out what I was doing wrong :(

 

[mgb_phys]

Yes, helium is pretty much the idealist gas!

PV= n RT tells you pretty much everything you need to know - since you aren't changing the amount of gas or volume then nR and V are constant so you can just balance P/T for each change.
There is no need to convert to Pa since you are only dealing with relative changes.
You do have to convet to K because you are dividing by temperature (why would adding them not matter ?)
But always working in SI units might reduce the chance of errors later.
And of course in the last step where you need Pa and R.

Sounds like you have the theory perfectly - post you results if you want us to check the numbers.

 

[map7s]

actually, I double checked my work again and found out that I had accidentally miskeyed a number into my calculator...thanks so much though! It helped to talk it out!