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Homework Help: Estimating Avogadro's Number

  1. Jan 18, 2015 #1
    1. The problem statement, all variables and given/known data

    I did a surface tension experiment with n-butanol in water using the capillary rise method. Using my data and the Gibb's adsorption equation, I found the number of moles adsorbed at the surface per unit area to be
    n/A = 5.012 x 10-3 mol⋅cm-2.

    I also calculated the radius of the capillary to be r = 0.0386273 cm.

    Given that the density of n-butanol is assumed to be the same as water ρ = 0.9970 g⋅cm-3
    and the molar volume of n-butanol is Vm = 91.5 cm3⋅mol-1, estimate Avogadro's number.

    Also assume the surface is a monolayer of n-butanol molecules, and that an n-butanol molecule is a cube.

    2. Relevant equations

    Vmolecule = Vcube = h3

    Vmonolayer = Vcylinder = πr2h

    h = Vm/(n/A)

    # of molecules = Vmonolayer/Vmolecule

    n = (n/A)πr2

    NA = Avogadro's number = # of molecules/n

    3. The attempt at a solution

    Since the surface is a monolayer, I think the length of a molecule is the height of the monolayer.
    h = 91.5cm3⋅mol-1/5.012 x 10-3 mol⋅cm-2 = 0.459 cm

    Now I can calculate the volume of a single cubic molecule to be:
    Vmolecule = h3 = (0.459 cm)3 = 0.0964 cm3

    and the volume of the monolayer is:
    Vmonolayer = π(0.0386273 cm)2(0.459 cm) = 2.15 x 10-3 cm3

    (This must already be incorrect since the volume of a single molecule can't be larger than that of the whole monolayer of molecules).

    The number of molecules would incorrectly be:
    # of molecules = (2.15 x 10-3 cm3)/(0.0964 cm3) = 0.0223 molecules

    The number of moles is:
    n = (5.012 x 10-3 mol⋅cm-2)(0.0386273 cm)2π = 2.349 x 10-5 mol

    Then Avogadro's number is calculated as:
    NA = (0.0223 molecules)/(2.349 x 10-5 mol) = 949 molecules/mol

    ..which is unbelievably wrong. Any help is appreciated!
  2. jcsd
  3. Jan 18, 2015 #2


    User Avatar

    Staff: Mentor

    0.459 cm per molecule already should tell you something is terribly wrong at this stage.
  4. Jan 18, 2015 #3
    Right, didn't notice that. Do you have any suggestions on how I could properly start this then? Thank you!
  5. Oct 4, 2016 #4
    Was this ever solved?
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