How does one measure Avogadro's number?

Question

I mean, how did the early experimentalists count the number of atoms when they were not even sure atoms existed?

Answer 1

As you can see in coolchap_einstein's answer (taken from www.wikipedia.org), the Avogadro number was no initially related with number of atoms just with "particles" of gas, and Kinetic Theory of gases was a standard knowledge in mid XIX century.

Was until recent times that we use Avogadro number as reference to compute the number of atoms, molecules, ions, etc. that is contained in a mole of substance.

There was no problem with the knowledge of this value in those years when existence of atoms were not even proved.

Good luck!

Answer 2

Avogadro's number is named after the early nineteenth century Italian scientist Amedeo Avogadro. It appears that Jean Baptiste Perrin was the first to name it. Perrin called it "Avogadro's constant" and it is still sometimes known by that name. The numerical value was first estimated by Johann Josef Loschmidt in 1865 using the kinetic gas theory. In German-speaking countries, the number may still be referred to as Loschmidt's number. Unfortunately, in a few cases (mainly in the older literature) Loschmidt's number refers to the number of atoms (or molecules) in a cubic centimeter, a usage now disparaged, viz: [1].

In the nineteenth century physicists measured the mass of one atom of hydrogen to be about 1/(6.023x1023) grams in an attempt to measure the number of ideal gas molecules would fit in 1 cubic centimeter [2] at STP ... which is related to Avogadro's number via the ideal gas law. Before 1960, there were conflicting definitions based on 16 grams of oxygen : physicists generally used oxygen-16 while chemists generally used the "naturally occurring" isotope ratio. Switching to 12 grams of carbon-12 ended this dispute and had other advantages [3].


[edit] Application
Avogadro's number can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams. For example, the atomic mass of iron is 55.847 u, so Avogadro's number of iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains Avogadro's number of iron atoms. Thus Avogadro's number NA corresponds to the conversion factor between grams (g) and atomic mass units:



[edit] Chemical significance of Avogadro's number
The definition of Avogadro's number depends on the definition of the kilogram. The latter is based on arbitrary convention, namely the mass of a particular "standard" cylinder of metal in France. This means that the particular value of Avogadro's number is the result of convention; there is no physical reason for it. For this reason, Avogadro's number is not considered a fundamental constant in the strictest sense. However, for practical purposes, Avogadro's number is regarded as a chemical constant.

Avogadro's number can be regarded as a conversion factor between the microscopic mass system (atomic mass units or Daltons) and the kilogram system. The microscopic mass system is based on the mass of carbon-12, while the kilogram system is currently based on the mass of a particular "standard" cylinder of metal in France. So naturally there's no simple conversion factor between the two. However, if a method were developed to count atoms, it would be possible to redefine the kilogram in a way that did not depend on an arbitrary cylinder of metal. The number of atoms picked would presumably be equal or close to the latest accepted value of Avogadro's number. In that case, the kilogram would be redefined as 83.33 x the mass of Avogadro's number of carbon-12 atoms (i.e. 83.33 x 12 g = 1 kg).


[edit] Additional physical relations
Because of its role as a scaling factor, Avogadro's number provides the link between a number of useful physical constants when moving between an atomic mass scale and a kilogram (SI) scale. For example, it provides the relationship between:

the universal gas constant R and the Boltzmann constant kB: R = kB NA
the Faraday constant F and the elementary charge e: F = e NA
In the 19th century physicists measured the mass of one atom of hydrogen to be about 6.02214199×10-23 grams. The gram was originally defined to be the mass of a cubic centimeter of pure water at standard temperature and pressure [4]. As experiments became more accurate, it was found that water was contaminated with variable amounts of heavy water, which made it undesirable to maintain a standard with hydrogen having one atomic mass unit. Carbon was found to have a more constant isotopic composition, and it was also possible to separate pure carbon-12. Therefore, the atomic mass unit was changed to 1⁄12 the mass of an atom of carbon-12. Hence 12 grams of carbon-12 has about 6.0221415×1023 atoms. The recent history and more details can be found in the document, Atomic Weight: The Name, Its History, Definition and Units.


[edit] Numerical value
At present it is not technologically feasible to count the exact number of atoms in 12 g of carbon-12, so the precise value of Avogadro's number is unknown. The 2002 CODATA recommended value for Avogadro's number is

.
A number of methods can be used to measure Avogadro's number. One modern method is to calculate Avogadro's number from the density of a crystal, the relative atomic mass, and the unit cell length determined from x-ray crystallography. Very accurate values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to obtain the value of Avogadro's number.


[edit] Connection to masses of protons and neutrons
A carbon-12 atom consists of 6 protons and 6 neutrons (which have approximately the same mass) and 6 electrons (whose mass is negligible as a first approximation, being about 1⁄1840 of the mass of the proton). One could therefore think that NA is the number of protons or neutrons that have a mass of 1 gram. While this is approximately correct, the mass of a free proton is 1.00727 amu, so a mole of protons would actually have a mass of 1.00727 g. Similarly, a mole of neutrons has a mass of 1.00866 g. Clearly, 6 moles of protons combined with six moles of neutrons would have a mass greater than 12 g. So it would appear that one mole of carbon-12 atoms, which should consist of 6 moles each of protons, neutrons, and electrons would have a mass greater than 12 g. The discrepancy or mass defect (as it is known) is related to the equivalence of matter and energy discovered by Albert Einstein as part of the theory of special relativity. When an atom is formed, the protons and neutrons in the nucleus are bound together by the strong nuclear force. This binding results in the formation of a low energy state and is accompanied by a large release of energy. Since energy is equivalent to mass (which means that all energy has mass), the released energy has mass and carries away the loss in the mass of the nucleus relative to that of the separated protons and neutrons (note that mass is conserved in this process just as energy is). Thus, protons and neutrons in the nucleus have masses that are less (about 0.7 percent less) than those of free protons and neutrons. The precise amount of mass loss is related to the binding energy of the nucleus and varies depending on the type of atom.

One may therefore say that NA is approximately the number of nuclear neutrons or protons (nucleons) that have a mass of 1 gram. This is approximate because the precise mass of a nuclear proton or neutron depends on the composition of the nucleus, as explained above. For example, iron nucleons will have a significantly lower mass than those in hydrogen or plutonium.


[edit] Avogadro's number in life
Avogadro's number may also yield practical reasonings in real life. For example, the fact that a known number of atoms are in a given amount of a substance is one reason for scientific criticism of homeopathy, in which medicinal substances are often diluted to the extent that a single molecule appears in only one dose amongst the hundreds or thousands prepared, as a simple calculation involving Avogadro's number will reveal.

Another common sense application shows that without determining the actual weight of a substance, a good rule of thumb to use is that a cubic centimeter of solid matter contains about 1024 atoms