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Ideal Gas Law: messing with ratios

  1. Dec 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Air is pumped into a bicycle tire. The 43 moles of air initially in the tire have a gauge pressure of 1 atm. How many moles of air must be pumped into the tire in order to raise the gauge pressure to 5 atm? Assume that the volume and temperature of the air inside the tire are approximately constant.

    2. Relevant equations

    Ideal Gas Law:
    PV = nRT


    3. The attempt at a solution

    Since the V and T were constant, as well as R, I set it up as (P1V1)/(n1T1) = (P2V2)/(n2T2) on the condition that R1 = R2.

    V1=V2, T1=T2 So that would leave the equation at P1/n1 = P2/n2.

    I decided to plug in and solve. P1=1 atm, n1=43 moles, P2=5 atm. 1/43 = 5/n2

    When I solved for n2, I came out with 215 moles. My homework said it was wrong. can someone tell me where I went wrong?
     
  2. jcsd
  3. Dec 17, 2013 #2

    SteamKing

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    You are given the pressures in terms of gauge pressures. Are these the correct units to use with the ideal gas law?
     
  4. Dec 17, 2013 #3

    According to my instructor and the lessons/homework, the units should not matter as long as they are uniform throughout the problem and equations.
     
  5. Dec 17, 2013 #4

    ehild

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    Definition: Gauge pressure refers to the pressure of a system above atmospheric pressure.

    Gauge Pressure = Total Pressure - 1 atm.

    [PLAIN]http://chemistry.about.com/o...finition.htm[Í/url][/PLAIN] [Broken] ehild
     
    Last edited by a moderator: May 6, 2017
  6. Dec 17, 2013 #5
    It's not a mater of units. Both absolute and gauge pressure are measured in the same units.
    The gas law in the format you used is "designed" to work for absolute pressure. Same as it only works with temperature in Kelvin but not in Celsius.
     
  7. Dec 17, 2013 #6
    Ok, I see the problem. thank you guys for the help. Much appreciated. ^_^
     
  8. Dec 17, 2013 #7
    Well, I went back and re-did my work and came out with 129 moles. It was still wrong.
     
  9. Dec 17, 2013 #8
    Nevermind, error on my part. I needed the amount of moles that was added, not the amount of moles in the end.
     
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