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.
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!