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Homework Help: Atomic density of argon in liquid and gas form

  1. Apr 28, 2012 #1
    The problem statement, all variables and given/known data

    Argon (atomic weight 40) exists as a monatomic gas at room temperature and
    pressure. The density of liquid argon is 1784 kg m−3.

    (a) Calculate the atomic density (atoms m−3) in liquid argon.

    (b) Calculate the atomic density (atoms m−3) in gaseous argon at a pressure of 1 atm and a temperature of 300K.

    The attempt at a solution


    PV = NkT
    P = 1.01 x 105
    k = 1.38 x 10-23
    T = 300

    N/V = P/kT = 2.44 x 1025 atoms m−3


    I have no idea. I know there should be a difference but I don't know what to do.

    I think perhaps my answer to (a) is in fact the answer to (b) in which case, how do I answer (a)?
  2. jcsd
  3. Apr 28, 2012 #2

    I like Serena

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    Hi EmmaLemming! :smile:

    Yep. Your answer to (a) is the answer to (b).

    That leaves you with 2 quantities that you have not used yet: atomic mass of argon and its density.

    Do you know what that number 40 for the atomic mass represents and how to use it in a formula?
    And what is density (as a formula)?

    Btw, the formula PV = NkT only applies to ideal gasses.
    Luckily gaseous argon does behave like an ideal gas.
  4. Apr 28, 2012 #3
    Hello :)

    Thanks for you're help

    So for part (a) could I just divide the atomic density by the mass?
    I've seen before that atomic mass, 40, can be written as 0.04kg however I thought,

    mass = M/avagadro = 6.64 x 10^-23kg

    Which mass do I use? :s
  5. Apr 28, 2012 #4

    I like Serena

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    Yes, you can divide the mass density by the mass of 1 atom, to get the atomic density.

    The atomic mass number 40 means that 1 mol of argon has a mass of 40 grams.

    And 1 mol of argon is a number of atoms that is equal to the number of avogadro.

    I'm not sure which masses you calculated with just now, however.
    Last edited: Apr 28, 2012
  6. Apr 28, 2012 #5
    I did,

    40/(6.02 x 1023) = 6.64 x 10-23 kg,

    to get the mass of one argon atom. Now that I think about it though should it be,

    0.04/(6.02 x 1023) = 6.64 x 10-26 kg.
  7. Apr 28, 2012 #6

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    Ah okay.
    That looks better. :)
  8. Apr 28, 2012 #7
    Yaaay :) Thanks very much for your help.
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