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Mole fraction concept help

  1. Sep 29, 2011 #1
    It looks like my first post on this did not make it on this forum some how.

    I came across this statement.
    Even though [tex]\frac{N_i}{N}=X_i[/tex], [tex]\frac{dN_i}{N}\neq dX_i[/tex]

    How does this work? The book offered no help as well as searches on the internet.
     
  2. jcsd
  3. Sep 29, 2011 #2

    Borek

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    Staff: Mentor

    My guess is that as N is sum of all Nk, if Ni changes, denominator changes as well.
     
  4. Sep 29, 2011 #3
    I guess that makes sense. Seems logical to me.
     
  5. Sep 29, 2011 #4
    Yep, that's it.

    [itex]dx_i = \frac{{N \cdot dN_i - N_i \cdot dN}}{{N^2 }}[/itex]

    and

    [itex]dN = dN_i[/itex]

    gives

    [itex]dx_i = \frac{{N - N_i }}{{N^2 }} \cdot dN_i[/itex]

    But for small [itex]x_i[/itex]

    [itex]dx_i = \frac{{dN_i }}{N}[/itex]

    is a good approximation.
     
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