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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

**V**, estimate Avogadro's number.

_{m}= 91.5 cm^{3}⋅mol^{-1}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}= h

^{3}

V

_{monolayer}= V

_{cylinder}= πr

^{2}h

h = V

_{m}/(n/A)

# of molecules = V

_{monolayer}/V

_{molecule}

n = (n/A)πr

^{2}

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 = 91.5cm

^{3}⋅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}= h

^{3}= (0.459 cm)

^{3}=

**0.0964 cm**

^{3}and the volume of the monolayer is:

V

_{monolayer}= π(0.0386273 cm)

^{2}(0.459 cm) =

**2.15 x 10**

^{-3}cm^{3}(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}cm

^{3})/(0.0964 cm

^{3}) =

**0.0223 molecules**

The number of moles is:

n = (5.012 x 10

^{-3}mol⋅cm

^{-2})(0.0386273 cm)

^{2}π =

**2.349 x 10**

^{-5}molThen 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!