Ideal gas equation qusetion?

Question

The question is:
How many molecules of N2(g) remain in an ultra high vacuum chamber of 3.45 m^3 (cube) volume when the pressure is reduced to 6.67 * 10^-7 Pascals at 25 degrees celsius?

Book says 5.59 x 10^14 moles of N2.
I got something a lot smaller. Something to like
X*10^-8

Can anyone please help?

Answer 1

First convert the pressure to atm, the volume to liters, and the temperature to kelvin.

(6.67*10^-7 Pa)(1KPa/1000Pa)(1 atm/ 101.325 KPa)= 6.58 x10^-12 atm

(3.45 m^3)((100cm)^3/1m^3)(1 mL/1cm^3)(1 L/1000 mL)= 3,450 L

25 C + 273 = 298 K

Then use these values in the ideal gas equation, PV=nRT.

n=PV/RT=[(6.58x10^-12atm)(3450 L)]/[(0.08206 L*atm/mol*K)(298K)]= 9.28 x 10^-10 moles N2

Then convert to molecules
(9.28 x 10^-10 moles)(6.022 x 10^23 molecules/ 1 mole N2)=5.59 x 10^14 molecules

Hopefully, this helps you figure out where you went wrong. :)

Answer 2

I'm guessing that your answer is in units of moles, while the question asks about molecules. Just multiply your answer by Avogadro's number, and I'll bet you get the same thing.

Answer 3

okay, they want molecules, not moles. So you will have to use avogadro's number. Furthermore, you should use the gas constant of 8.314. I was able to agree with the book.