# Calculating Avogadro's number from scratch

1. Jan 10, 2005

### jetset

Hello there,

Not that I actually want to do this but theoretically I would like to know how I could prove to myself avogardro's number using only the most primative knowledge of math, physics and chemistry as possible.

It all makes sense in whatever text you are reading, but it never gets explained how to do it yourself from start to finish in a simple way, there is always alllutions to other technology that I do not fully understand.

2. Jan 11, 2005

### dextercioby

Think about a Natrium (Na) molecule.It's monoatomic,okay??
It's kilomolar mass is 23.Which means 23Kg per each kilomol of atoms.

Do u agree with this equality:
$$M=N_{A} m_{Na}$$
,where M is the kilomolar mass (unit:Kg/Kmol),N_{A} is the Avogadro's number (unit:molecules/kilomol) and m_{Na} is the mass of a molecule (in this case,atom) of Na.

Form the equality above,the result is immediate...

Daniel.

3. Jan 11, 2005

### jetset

Your equation of course makes a lot of sense. Using your analogy my gap in knowledge lies not in the logic of this formula, but rather how would I go about proving/figuring out that Natruim is monoatomic.

Forgetting fictional elements, how could I do a working example with C12? When scientists back then were working with chemicals, how was the "12" part first proved? You can of couse get this if you have Avg. # and the kilomolar mass, to get the last remaining variable, giving you a solution.
But if you didn't yet know what Avg. # was, 2 out of 3 of the variables are unknown for that formula. I'm assuming an experiement was done to solve the problem...???

Let me rephrase my first question: I am transported back in time to 1700 and wish to show people that a certain substance has a certain molar mass that would lie the foundations for all sorts of chemical experiments. My question is how would I logically prove this to people? (and get a paper published)

Last edited: Jan 11, 2005
4. Jan 11, 2005

### dextercioby

Yes,you're right,that formula contains 3 possible unknowns:kilomolar mass of an element,the element's atom mass and # of Avogadro.
You'll have to agree with me thatever since 1775 and the wonderful work of of Antoine Laurent Lavoisier,for the common known (at that time) elements the kilomolar mass was known.
So that eliminates one unknown,for most elements this is due to the work of Jakob Berzelius and other chemists,the most famous being Mendeleev.
Then came the 20-th century and the use of mass spectrometry (invented by Sir James Joseph Thomson in 1898 and carried on magnificiently by Sir William Aston) which determined the mass (in Kg) for the atoms.
Therefore,the Avogadro's number was found combining results from chemistry (kilomolar mass) and physics (mass of an atom/molecule).
Later on,physics showed the connection between kilomolar mass,atom mass and nucleus mass,so that everything was determined by physics.

Daniel.

5. Jan 11, 2005

### NateTG

Don't you need to throw in Millikan's oil drop experiment to determine the electron charge?

It's possible to experimentally determine the charge of a single electron (Millikan's oil drop experiment). Once the charge of an electron has been determined, the charge of ionized atoms can also be calculated. By observing the deflection of charged atoms (or molecules) in a known electric or magnetic field, the mass of those atoms (or molecules) can be very precisely inferred.

Dealing with the Proton/Neutron/Electron mass issues is also not very difficult at that point, since you can create a chart of various atom masses for isotopes and whatnot.

In practice, I don't think the value avogadro's number is all that important since people generally will not make the transition from particle count to moles, but it would be sufficient to call it A and leave it unspecified.

I believe that what Avogadro did was to use equal volumes of gasses to attempt to determine relative molecular masses (http://scienceworld.wolfram.com/physics/AvogadrosHypothesis.html).

6. Jan 11, 2005

### Gokul43201

Staff Emeritus
I found this site when I was looking around, the last time someone asked a question like this. It does a great job. Give it a look.

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7. Jan 11, 2005

### jetset

interesting stuff, thanks for the replys. ive never heard of the oil drop experiment til now.

So to summarize so far:

IF i get thrown back in time to 1700, in order to prove the Avag. #, I would first have to discover the "kilomolar" mass of a substance (How could I do this using the tools of the time?) Then I must wait for electronic stuff to evolve (or make it happen myself) so that I know enough about electric fields to do the oil drop experiment. Then thridly I could combine those two previous things to come up with Avag. # (which I would call the jetset number:P)

Is that right? Also, is there more than one way of doing my first step of finding the molar mass of a substance?

8. Jan 12, 2005

### Gokul43201

Staff Emeritus
In my opinion, you didn't have to have done the oil drop experiment at all. The concept of charge (quantization) is not essential to the concept of a mole of atoms/molecules. Moreover, there's no way you will completely (z'th ionization energy is required) ionize an atom, so I'm not sure I understand how this is relevant.

Having modern experimental probes make this all a piece of cake, but most of the ideas were well-developed by about the mid-1800s thanks to work by Dalton, Gay-Lussac, Avogadro, and Cannizzaro.

9. Jan 12, 2005

### jetset

So in point form, what do i have to do in order rather than not do?

10. Jan 12, 2005

### Integral

Staff Emeritus
If indeed you found yourself in the late 17th or early 18th century you would have to do exactly what the natural philosophers of that day were doing. Careful observation of reactions to learn how much of various material combine to form the end product. You would have to observe things like, when water breaks down it forms 2 different materials in a 2:1 ratio.

Look at the material covered in a beginning chemistry class that is the essence of what the old timers learned, it would have to be recreated from scratch.

Isn't this how we got to where we are today? Observation and careful measurements that is what it was all about.

11. Jan 12, 2005

### dextercioby

U couldn't...Not in 1700.The balance (is that the word?? ) was introduced in chemistry laboratories around 1750 by the Scottish chemist William Black.Before,noone ever thought of weighing the reaction products.
Let's move it after Lavoisier lost his head (literally) in 1794.The molar/kilomolar masses of some elements were known by then.

U'd have to find the atoms' mass.Kilomolar mass would not be enough.So u'd have to wait unitll 1920 and the experiments by Sir William Aston.It's simple.

Daniel.

12. Jan 12, 2005

### Gokul43201

Staff Emeritus
NateTG was right in that Millikan's oil drop experiment played an important role. It did.

By 1865, Johann Loschmidt had made the first calculation of Avogadro's Number (~5*10^23) building upon work done by Clausius and Maxwell, on the kinetic theory (particularly, viscosity) of gases.

Over the next five decades, the number's accuracy was improved upon, by measurements of blackbody radiation (Planck, 1900), diffusion (Einstein, 1906 - but he made a calculation error which was discovered only much later), and sedimentation equilibria in colloidal systems(Perrin, 1908 - first to determine the multiplier's value at ~6.0, and generally considered the first accurate determination).

Only after the Oil-drop experiment was the accuracy of the number improved (~6.02 ....). Now, with X-ray Diffraction, I think the number is known to at least 7 or 8 significant places, maybe much more.

A great description of Loschmidt's (in Germany, Ausrtia, Denmark and a few other countries, Avogadro's Number is actually refered to as Loschmidt's Number) method for finding the size of molecules, can be found here :
http://www.physicstoday.org/pt/vol-54/iss-3/p45.html [Broken]

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13. Jan 12, 2005

### jetset

So the accuracy basically increased the better we could actually measure the mass of the molecules?

We are gettin to more to the heart of my question now... Basically I've done all sorts of university chemistry several years ago, but I never had time to question things deeply, now it' truely zooming out time.

So it has been established that if I go back to 1700 I could not prove anything to do with Avg. # because of lack of technology.

How bout this then: after the balance has been invented, say I get transported back to 1800. How can I prove the theory of the mole using carbon 12? (is that what was used to actually prove the theory?) Please dont just state some general rule or say a general statement and its easy from there. I dont need a long explaination either, just a short and exact "the following setup is needed, you will need to use the following 3 impirical observations and you need the following elements. Do "bla", and that is the long in short of how the mole was discovered. :D

ps: the forum is pretty cool, kudos to all of yall who devote so much time here!

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14. Jan 13, 2005

### Gokul43201

Staff Emeritus
State specifically, what you mean by "the theory of the mole".

Provide a conjecture, and we can figure out how to go about proving this or determining some desired number.

15. Jan 13, 2005

### jetset

When the word "mole" first came into the scientific community; the proof of that paper that showed what this "mole" was, that is what i am looking for.

16. Jan 13, 2005

### NateTG

I haven't the foggiest about 'mole' but if you start with Avogadro's hypothesis, you can get to some analagus notion fairily quickly. (If you used ounces instead of grams, you would want a different 'Avogadro's number', for example, and, of course, grams were not in common usage at that time.)

Once you've got people convinced that the whole proportional thing works (and, for 1800 this involves explaining covalent bonding among other things.) you can start looking at experiments like spectrometry combined with Milikan's oil drop experiment to determine particles per mole.

I'm not a chemist, or a chem buff, but I don't think that the numerical value of Avogadro's number is all that important compared to the proportionality hypothesis, and moreover, there is a natural order since the proportionality hypothesis makes sense without Avogadro's number, while the converse is false.