1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Borek

    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Estimating Avogadro's Number
  1. Avogadro's Theory (Replies: 3)

Loading...