How Can We Use Oil to Estimate Avogadro's Number?

  • Thread starter fluidistic
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In summary, Rayleigh put a milligram of oil which density is 0.9g/cm^3 on a water surface and found out that the oil covered an area of 0.9 m^2. The height of the oil film is of the same order as a molecule of oil, which lead us to suppose that the oil film is one molecule thin. If the molar mass of oil is 282.5g/mol, estimate Avogadro's number through the comparison of molecular volume and molar volume.
  • #1
fluidistic
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Hi PF,
I'm getting an headache on this problem.

Homework Statement


Rayleigh put a milligram of oil which density is [tex]0.9g/cm^3[/tex] on a water surface and found out that the oil covered an area of [tex]0.9 m^2[/tex].
1)What is the height of the oil film?
2)The height of the oil film is of the same order as a molecule of oil, which lead us to suppose that the oil film is one molecule thin.
Suppose that the three dimensions of the oil molecule are the same, find the molecular volume of oil.
3)If the molar mass of oil is [tex]282.5g/mol[/tex], estimate Avogadro's number through the comparison of molecular volume and molar volume.

Homework Equations

Avogadro's number is about [tex]6.02 \times 10^{23}[/tex].

The Attempt at a Solution


1)Density [tex]\rho[/tex] is worth [tex]\frac{m}{V}=0.9[/tex] so [tex]V=\frac{0.001}{0.9}=0.00111111...cm^3[/tex] where [tex]V[/tex] is the volume of the oil drop.
Now [tex]V=base \cdot h[/tex] hence [tex]h=0.00001234567889cm[/tex].
2)Calculating the volume of a molecule lead me nowhere. Instead in order to find Avogadro's number I think it's more effective to follow this : as the dimensions of the molecule are the same and that the diameter or height or length of it is worth [tex]0.00001234567889cm[/tex], each molecule cover a surface of [tex](0.00001234567889cm)^2[/tex]. Now I can find how many molecules are in the drop. Because it has a surface of [tex]0.9m^2[/tex] or [tex]90cm^2[/tex]. [tex]\frac{90}{(0.00001234567889cm)^2}=5.904900127\times 10^{11}[/tex].
Now for part 3), we know that the oil drop was [tex]0.001g[/tex] and that a mole of oil is [tex]282.5g[/tex]. So that I must multiply by [tex]282500[/tex] the number of molecules in the drop to find the number of molecule in a mole, that is Avogadro's number. But doing so I find [tex]1.661320857 \times 10^{17}[/tex]...

P.S.: I also tried via the way they suggested, but found something like [tex]3.5\times 10 ^{17}[/tex] and I had to suppose that the form of the molecules was spherical.
Of course I made errors and I'm missing something. If you could help me that would be kind! Thank you.
 
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  • #2
Hi,

You're not converting 0.9 m2 into cm2 correctly.
 
  • #3
Redbelly98 said:
Hi,

You're not converting 0.9 m2 into cm2 correctly.

Thank you SO much. I'll do the algebra tomorrow when I wake up. (too late for now).
 
  • #4
[tex]0.9m^2=8100cm^2[/tex].
My final result becomes [tex]1.50\times 10^{19}[/tex]. I'm getting closer but I'm still very far from what I should get.
 
  • #5
I'm getting much closer to Avogadro's number.

What do you get now for h and also for the number of molecules in the oil drop?
 
  • #6
Redbelly98 said:
I'm getting much closer to Avogadro's number.

What do you get now for h and also for the number of molecules in the oil drop?

I forgot to change the volume! Now I got the right result : [tex]1.216069868 \times 10^{23}[/tex]. If you still mind I got a number of [tex]4.3046721 \times 10^{17}[/tex] for the number of molecules in the drop and h is worth [tex]\frac{0.00111...}{8100}cm[/tex].
Thanks for your help and time.
 
  • #7
Cool, glad it worked out.
 

What is Avogadro's number and why is it important?

Avogadro's number, also known as the Avogadro constant, is a fundamental constant in chemistry and physics. It represents the number of particles (usually atoms or molecules) in one mole of a substance. This number is important because it allows scientists to accurately measure and compare the amount of substances in chemical reactions and other processes.

How is Avogadro's number estimated?

Avogadro's number is estimated by measuring the mass of one mole of a substance and dividing it by the mass of one particle of that substance. This is typically done using a special instrument called a mass spectrometer, which can accurately measure the mass of individual particles.

What is the value of Avogadro's number?

The current accepted value for Avogadro's number is 6.022 x 10^23 particles per mole. However, this value is constantly being refined and updated as new experimental techniques and data become available.

Why is it difficult to measure Avogadro's number accurately?

One of the main challenges in accurately measuring Avogadro's number is that it is an extremely large number. This means that even very small errors in measurement can lead to significant variations in the final value. Additionally, different substances may have slightly different values for Avogadro's number due to variations in their atomic or molecular structures.

How does knowing Avogadro's number benefit scientific research?

Knowing Avogadro's number allows scientists to accurately measure and predict the behavior of different substances in chemical reactions and other processes. It also helps in fields such as material science and nanotechnology, where precise measurements of atoms and molecules are crucial. Additionally, Avogadro's number is used in calculations and formulas in many scientific disciplines, making it an essential constant for researchers.

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