## 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!

Borek
Mentor
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.

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!