7

To my understanding the mole is the unit used to translate between mass on the atomic level and mass in the macro level, defined as the number of atoms in $12$ grams of Carbon-$12$, which apparently turns out to be $\pu{6.0221409e23}$ atoms, and this was defined as Avogadro's Number.

How was this number derived? Is it something I can derive myself? If I had $12$ grams of Carbon-$12$, how would I be able to deduce that it had $\pu{6.0221409e23}$ atoms?

mhchem
  • 3,316
  • 2
  • 16
  • 34
user51819
  • 231
  • 1
  • 4
  • 1
    It would be hard, very hard. I'll point out that there is a gigantic different in stating that $N_A \approx 6.022 \times 10^{23}$ and stating that $N_A = 6.0221409\times 10^{23}$. Determining a value to eight significant figures requires extremely good experimental technique. – MaxW Jul 13 '18 at 03:29
  • @MaxW How did Avogadro do it in his time, to whatever degree of precision that he did? – user51819 Jul 13 '18 at 03:48
  • 4
    This information is readily available on the web in sources such as Wikipedia. https://en.wikipedia.org/wiki/Avogadro_constant, "By dividing the charge on a mole of electrons by the charge on a single electron..." Look up Millikan oild rop experiment for charge of e-, Faraday and electrolysis for atomic mass/charge ratio etc. – DrMoishe Pippik Jul 13 '18 at 04:36
  • @DrMoishePippik What is interesting to me is that apparently the oil drop experiment gave an answer that was technically wrong / inaccurate, but we still used it anyway to derive all these other numbers? – user51819 Jul 13 '18 at 04:43
  • It's been refined over time. As @MaxW states, original values had a very large margin of error. It's like Galileo using a chandelier as a clock... instrumentation has improved since then. – DrMoishe Pippik Jul 13 '18 at 05:09
  • But as those values get refined, is the same done for all other constants that depend on them, and are experiments re-interpreted using new values? – user51819 Jul 13 '18 at 05:23
  • RE: But as those values get refined, is the same done for all other constants that depend on them, and are experiments re-interpreted using new values? // Now you are catching on. Recently there has been an effort to identify the "fundamental" values that are ones necessary to define all the others. So if I have a standard for length, a cube of that standard value has a defined volume rather than needing a separate volume standard too. So all the values have gone through a tortuous path to their current state. – MaxW Jul 13 '18 at 05:31
  • 2
    A fascinatingly simple experiment based on spreading oil over a large water surface and assuming monolayer formation can actually be used to determine Avogadro's number. Not very precisely, of course... – a-cyclohexane-molecule Jul 13 '18 at 18:29
  • The above info is obsolete now, as the latest SI definition is Avogadro number is defined as $\pu{6.02214076E23}$ – Poutnik Jan 04 '23 at 09:10
  • @a-cyclohexane-molecule That link doesn't work, which is a pity as it the experiment is a school-level way to get a crude estimate of Avogadro's number. – matt_black Jan 04 '23 at 10:25
  • The constant enters into the model for the MSD in Brownian motion, so if you're able to make those measurements, you could calculate an estimate. – Zhe Jan 04 '23 at 13:36

2 Answers2

9

To determine Avogadro's number you have to measure the same unit at the atomic and macroscopic scales.

This was first achieved by Millikan who measured the charge of an electron. The charge of one mole of electrons was already known and is a Faraday. Dividing both, you get Avogadro's number.

Before that, Josef Loschmidt was the first one to calculate the number of particles in a cubic meter of gas, using the kinetic theory of gases. This is, of course, also related to Avogadro's number. Avogadro himself did not give any number. He just stated that equal volumes of different gases at the same pressure and temperature have equal amount of particles.

A more modern way of doing it is determining the density of an ultra pure element and then determine the number of atoms and their distances in a unit cell with X-ray diffraction.

So yes, you could, in principle, derive Avogadro's number with pure monocrystalline carbon 12. You will, however, need very good instrumentation.

As per the answer to this question on Chemistry SE it might become the other way round. The Avogadro number will be absolute (defined, with 0 error) and then the kilogram will be redefined as a function of the number of atoms in a monocrystalline perfect $\ce{^{28}Si}$ sphere.

Raoul Kessels
  • 4,372
  • 8
  • 24
3

There is a school-level experiment that can estimate Avogadro's number

Avogadro's number is now defined to be a precise constant. But the question is whether simple experiments can be used to estimate it. The historic experiments designed to estimate it are not always useful as they usually involve techniques or equipment unavailable outside fully-equipped laboratories. Like the indirect method used by Millikan (measuring the charge on a single electron in the famous oil-drop experiment which, via known electrical measurements, can be converted into an estimate of the constant) or the estimates based on x-ray measurements of ultra-pure crystals which estimate density via measuring atomic distances in a known mass).

But a simple experiment can get a good approximate estimate given a small number of assumptions based on an 1890 idea from Lord Rayleigh. The experiment involves spreading a known quantity of a pure surfactant over a water surface and measuring the area it occupies. The assumption is that the surfactant occupies a compact monomolecular layer on the water surface (there are other ways to verify this). If you put in assumptions about the size of the molecule and the thickness of the layer and measurements of the mass of the surfactant that created the layer (easy to measure with some accuracy) then a decent estimate of avogadro's constant can be derived.

The process of doing the calculation is described in this Physics.SE answer (with the caution that assuming a surfactant occupies a cube is wrong).

In the 1980s this was a common school experiment. One description of that experiment is here.

So there are simple experiments that can be used to estimate the Avogadro constant. But more reliable estimates need a lot more equipment.

matt_black
  • 35,967
  • 4
  • 86
  • 173