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Molar Ratio Problem

  1. Dec 8, 2011 #1
    1. The problem statement, all variables and given/known data

    Unknown amounts of methane and ethane are mixed at STP. The resulting mixture has a density of 1.18 g/L. Find the ratio of ethane to ethane.

    3. The attempt at a solution

    Since it's a ratio, we can convert it to 1 mol methane : X mol ethane

    1 L methane at STP = [itex]\frac{RT}{P}[/itex] = [itex]\frac{.08206 * 273}{1}[/itex] = 22.402 mol

    X L ethane at STP = 22.402X mol

    d = [itex]\frac{m}{V}[/itex]
    1.18 = [itex]\frac{1.18(22.402 + 22.402*X)}{2*22.402}[/itex]
    1 = X

    So it's a 1:1 ratio.

    I was talking to someone who's better at chemistry than I am, and he said it got a 1:4 ratio. Plus, this method doesn't seem right since I didn't use the masses of CH4 or C2H6 (which would mean that there would always be a 1:1 ratio, regardless of the compounds). How do I do this?
     
    Last edited: Dec 8, 2011
  2. jcsd
  3. Dec 8, 2011 #2

    Borek

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    Staff: Mentor

    You are wrong from the start - V is not RT/P, 1L is not 22.4 moles. Quite the opposite - 1 mole is 22.4 liters.

    Hint: for ideal gas there is a simple dependence between molar mass and density. And "molar mass" in the case of a gas mixture can be expressed as a weighted (by molar fractions) average of molar masses of components.
     
  4. Dec 8, 2011 #3
    So...

    n = PV/RT, setting V = 1 gets .044 mol of CH4 and .044*X mol C2H6.

    1.18 = (.044*16+.044*X*30)/(2)

    X = 1.22...so it's 1:1.22 which is about 4:5?

    My teacher gave me this question btw, the choices for the answer were:

    A) 1:2
    B) 1:4
    C) 1:1
    D) 4:1
    E) none of the above
     
  5. Dec 8, 2011 #4
    I know that d = PM/RT, where M is the molar mass.

    I solved for it and got M = 26.434 g/L, but don't know where to go from there.
     
  6. Dec 9, 2011 #5

    Borek

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    Staff: Mentor

    Imagine you have 1 mole of mixture. Assume molar fraction of one gas is x. That means you have x moles of one gas and 1-x of another, and total mass is x*molar mass of the first gas + (1-x)* molar mass of the second gas. Total mass of one mole is just a molar mass. Can you calculate amounts of both gases in the mixture?
     
  7. Dec 9, 2011 #6
    x mol CH4
    1-x mol C2H6

    16*x + 30*(1-x) = 26.434
    -14*x = -3.566
    x ~ .25

    So it's a 1:4 ratio.
     
  8. Dec 9, 2011 #7
    Why is the way I did it in my second post incorrect though?

    Edit: Nevermind
     
  9. Dec 9, 2011 #8

    Borek

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    Staff: Mentor

    If x is 0.25, it is 1:3, or 1 in 4, but not 1:4. For 1:4 you would need x=0.2.

    Yeah, I know - there is 1:3 answer. But that's not my fault.
     
  10. Dec 9, 2011 #9
    Eh...I'm not a fan of my chem professor.

    Thanks for walking me through this.
     
  11. Dec 9, 2011 #10

    Borek

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    Staff: Mentor

    Oops, I meant "there is no 1:3 answer". But you probably got it.
     
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