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Ideal gas law problem: part 2

  1. Jan 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Calculate the mass of a mole of dry air, which is mixture of N2(78 percent by volume, O2 (21 percent) and argon (1 percent).

    Use the ideal gas law to write the density of air in terms of pressure, temperature , and the average mass of the air molecules. Show , then, that the pressure obeys the differential equation

    dP/dz=-mgP/kT
    2. Relevant equations

    PV=nkT

    3. The attempt at a solution

    m(total)=.78(28 grams)+.21(16 grams)+.01(40 grams)= 29 grams

    rho=m/V , from Ideal gas law, V=nKT/P ==> rho=m*P/nkT


    I am having difficulties with show that dP/dz=-mgP/kT. I know other thread on the ideal gas law problem concerning the same problem I said that dP/dz=-rho*g. and I know that rho=mP/nkT, therefore I guess dP/dz=rho*g=mgP/nkT. The only problem is how would I get rid of n? Should I assume that they are talking about one mole of air and therefore n=1?
     
  2. jcsd
  3. Jan 15, 2009 #2

    turin

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    Homework Helper

    you just need to be careful about your definition of m and n.
     
  4. Jan 15, 2009 #3
    what do you mean?
     
  5. Jan 16, 2009 #4

    turin

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    Homework Helper

    There is a number of moles and there is a number of molecules. There is a molar mass and a molecular mass. In your equations, which ones are you using? You don't have to choose a particular number of moles in order to get the answer. You need to write the ideal gas law entirely in terms intensive variables and constants.
     
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