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Into to Ideal Gas Law Problem

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    A vacuum pump on Earth can produce a vacuum with a pressure as low as 1.00*10^-8 torr. How many molecules are present in each mL at a temperature of 27.0 degrees Celsius?

    V = 1mL = 10^-3 L <-- How many sig figs should I use here? Should I make it 1.00*10^-3L or keep it 10^-3L?
    P = 1.315789 atm
    T = 300.15 K
    n = ?
    2. Relevant equations

    Pv = nRT

    3. The attempt at a solution

    PV =nRT

    n = PV / RT

    = (1.315789atm)(1.00*10^-3L) / (0.08206 Latm / Kmol)(300.15K)

    = 5.342156*10^-16mol * 6.022*10^23 molecules

    = 3.22*10^8 molecules / L <--- How do I change my answer back to how many molecules/mL and how many sig figs should my answer reflect? 1 or 3?
     
  2. jcsd
  3. Jan 13, 2012 #2

    jedishrfu

    Staff: Mentor

    isnt a liter = 1000 mL
     
  4. Jan 13, 2012 #3
    Yeah so would I just multiply my answer by 1000?
     
  5. Jan 13, 2012 #4

    jedishrfu

    Staff: Mentor

    okay so think a liter is 1000 times bigger than a mL right? so that means it can hold 1000
    times the # of molecules that an mL would have? so do you multiply or divide?
     
  6. Jan 13, 2012 #5
    my mistake, yeah I'd definitely divide my answer by 1000. Also for sig figs, since the question says "one milliliter" how many digits should I interpret that as? Should I let the volume = 1mL, which would give me one sig fig in my answer or should I just make it 1.00mL and include 3 sig figs in my answer?
     
  7. Jan 13, 2012 #6

    jedishrfu

    Staff: Mentor

  8. Jan 13, 2012 #7

    Borek

    User Avatar

    Staff: Mentor

    Your answer was already correct - you used 10-3L as a volume, so you calculated number of moles in 1 mL. You added L at the very end of the calculation out of nothing, confusing yourself.

    Question says "in each mL" which probably means "exactly mL" - so there is as many significant digits as you want. Sure, it doesn't make sense to report all digits your calculator displays - I would go with three.
     
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