Estimating Avogadro's Number Using Surface Tension Experiment

[JM92]

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 V_m = 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

V_molecule = V_cube = h³

V_monolayer = V_cylinder = πr²h

h = V_m/(n/A)

# of molecules = V_monolayer/V_molecule

n = (n/A)πr²

N_A = 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:
V_molecule = h³ = (0.459 cm)³ = 0.0964 cm³

and the volume of the monolayer is:
V_monolayer = 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:
N_A = (0.0223 molecules)/(2.349 x 10^-5 mol) = 949 molecules/mol

..which is unbelievably wrong. Any help is appreciated!

 

[Borek]

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.

 

[JM92]

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!

 

[Mishao]

Was this ever solved?