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Estimating Avogadro's Number

  • Thread starter JM92
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  • #1
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Homework Statement



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.

Homework 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

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!
 

Answers and Replies

  • #2
Borek
Mentor
28,357
2,744
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
0.459 cm per molecule already should tell you something is terribly wrong at this stage.
 
  • #3
9
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0.459 cm per molecule already should tell you something is terribly wrong at this stage.
Right, didn't notice that. Do you have any suggestions on how I could properly start this then? Thank you!
 
  • #4
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Was this ever solved?
 

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