# Estimating Avogadro's Number Using Surface Tension Experiment

• JM92
In summary: No, the conversation does not provide a complete or accurate solution. It is unclear how to properly start the problem and it seems that the calculations provided are incorrect. Further clarification or assistance is needed in order to solve the problem accurately.
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 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!

JM92 said:
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.

Borek said:
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!

## 1. What is Avogadro's Number?

Avogadro's Number, also known as the Avogadro Constant, is a fundamental physical constant that represents the number of particles (atoms or molecules) in one mole of a substance. It is approximately equal to 6.022 x 10^23.

## 2. Why is it important to estimate Avogadro's Number?

Estimating Avogadro's Number is important because it allows us to understand and quantify the relationship between the microscopic world of atoms and molecules, and the macroscopic world that we can see and interact with. It also helps us to accurately measure quantities in chemistry and physics, such as the number of particles in a given amount of a substance.

## 3. How is Avogadro's Number estimated?

Avogadro's Number is typically estimated through experimental methods, such as using x-ray crystallography or measuring the density of a gas. These methods involve measuring the amount of a substance and using the known relationships between mass, volume, and number of particles to calculate Avogadro's Number.

## 4. What is the significance of Avogadro's Number in the development of the atomic theory?

The concept of Avogadro's Number was first proposed by Italian scientist Amedeo Avogadro in the early 19th century. It played a crucial role in the development of the atomic theory, as it helped scientists understand that matter is made up of small, indivisible particles (atoms) and that the relative masses of these particles can be determined by comparing the masses of different substances.

## 5. Has Avogadro's Number been determined with 100% accuracy?

No, Avogadro's Number has not been determined with 100% accuracy. Due to the difficulties in measuring such a large number of particles, the estimated value of Avogadro's Number has a degree of uncertainty. However, efforts are continuously being made to improve the accuracy of its determination through advancements in technology and experimental techniques.

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