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Calculating Number Density of Gas Molecules

  1. Apr 3, 2014 #1
    1. The problem statement, all variables and given/known data
    What is the number density, N/V, of gas molecules in the closed vessel in the previous problem?

    (Previous problem: A closed vessel contains an ideal gas at an absolute pressure of 1.5 atm and a termperature of 42 degrees celsius. To what final temperature (in °C) must the gas be heated so its final pressure is 2.0 atm?


    2. Relevant equations

    pV=N[itex]k\ =\ 1.3806503(24)\ \times\ 10^{-23}\ J\ K^{-1}[/itex]T

    3. The attempt at a solution
    From the previous problem I have p=2.0 atm, T=420K and reorganizing the equation I get N/V=p/[itex]k\ =\ 1.3806503(24)\ \times\ 10^{-23}\ J\ K^{-1}[/itex]T

    so N/V=2.0atm/[itex]k\ =\ 1.3806503(24)\ \times\ 10^{-23}\ J\ K^{-1}[/itex](420K) = 3.45x10^20. The answer is supposed to be 3.5x10^25. I cannot figure out why I am getting the wrong answer, can anybody shed some light on this?
     
  2. jcsd
  3. Apr 3, 2014 #2

    SteamKing

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    Have you checked the units of the quantities you have plugged into your formula?
     
  4. Apr 3, 2014 #3
    At the initial conditions, I get a molar density of 0.0581 moles/liter. Multiplying this by avagodro's number, I get 3.5 x 1022 molecules/liter. Per cubic meter, this is 3.5 x 1025 molecules. The same result is obtained at the final conditions.

    Chet
     
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