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Density and r.m.s of an ideal gas

  1. Sep 10, 2014 #1
    1. The problem statement, all variables and given/known data

    A can which is sealed of a volume 0.035m3 contains an ideal gas with a pressure of 150kPa, at a temperature of 350K.
    Calculate the gas density and the root mean squared speed of the gas molecules
    (P.S. the molecular mass is stated as 28)

    2. Relevant equations

    r.m.s=sqrt(3kT/m) density=molar massxP/RxT

    3. The attempt at a solution

    So before this I calculated the number of moles: (150x103)*(0.035)/(8.31*350)= 1.81 moles (3.s.f)
    The number of molecules: N=n*Na=(1.80....)*(6.023x1023)=1.09x1024 molecules (3.s.f)
    The mass of the gas (the molecular mass is stated as 28) mass=n*M=(1.80...)(28)=50.5g (3.s.f)

    For r.m.s, do I simply just have to put the mass I just calculated into the equation? For the density, do I just put the molar mass as 28?

    Thanks for any help in advance!
     
    Last edited: Sep 10, 2014
  2. jcsd
  3. Sep 10, 2014 #2

    SteamKing

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    It seems like the following should have been put into the Problem Statement:

     
  4. Sep 10, 2014 #3
    Sorry I have added it now.
     
  5. Sep 10, 2014 #4

    ehild

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    In the formula for the rms speed, m is the mass of one molecule.

    As for the density, you calculated the mass of the gas already: it is 50.5 g. The volume of the gas is given. And you certainly know how the density is defined with mass and volume ?

    ehild
     
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