How was the mole determined?

First, the "international ampere" was an early realization of the ampere, defined as the current that would deposit0.001118000 gramsof silver per second from asilver nitratesolution. Later, more accurate measurements revealed that this current is0.99985 A.  Why does this matter?  In early scientific work with electricity, scientists learned that lightning could be produced by taking wire and putting it in a spool and turning a magnet inside the spool.  Spinning a magnet inside a spool of copper wire is how the common electric motor generates electricity.  However at this time, scientists did not know that the electron was a part of the structure of the atom.  Joseph John Thompson used a cathode ray tube to show that the electrons generated by the motor were the same as those found in a magnet.  The magnet is independent of the electrons being generated, so the field of electrons found in the magnet must have a role in the atomic structure of the atom.   

Experiments demonstrate that Silver ions can gain electrons when a current is applied to a solution of silver nitrate and this led to the Faraday constant.  How is the faraday constant different from the ampere?  The faraday constant resulted from the development of the periodic table.   

Although theatomic theoryof matter, in its various forms, existed a good two thousand years before the time of John Dalton, he was the first to propose, in his 1808 bookA New System of Chemical Philosophy, that atoms had weight. Atoms, as Dalton defined them, were hard, solid, indivisible particles with no inner spaces, rather than something that could not be seen, touched, or tasted. They were indestructible and preserved their identities in allchemical reactions. Furthermore, each kind of element had its own specific kind of atom different from the atoms of other elements. These assumptions led him to propose that atoms were tangible matter and therefore had weight. 

Because atoms were much too small to be seen or measured by any common methods, absolute weights of atoms could not be determined. Rather, these first measurements were made by comparing weights of various atoms tohydrogen. Hydrogen was chosen as the unit of comparison because it was the lightest substance known and the weights of the other elements would be very close to whole numbers. 

The weight of oxygen could then be calculated because of earlier work by Humboldt and Gay-Lussac, who found thatwaterconsisted of only two elements, hydrogen and oxygen, and that there were eight parts of oxygen for every one part of hydrogen. Lacking any knowledge about how many atoms of hydrogen and oxygen combine in amoleculeof water, Dalton again had to make some assumptions. He assumed that nature is basically very simple and, therefore, one atom of hydrogen combines with only one atom of oxygen. Using this hypothesis and the fact that hydrogen was assigned a weight of one unit, it follows that oxygen, which is eight times heavier than hydrogen, would have a weight of eight units. Of course, if theratiobetween hydrogen and oxygen in water were not one to one, but some other ratio, the weight of oxygen would have to be adjusted accordingly. Dalton used experimental results and similar reasoning to prepare the very first Table of Atomic Weights, but because of the lack of knowledge about the real formulas for substances, many of the weights were incorrect and had to be modified later. 
Read more:Atomic Weight - History - Hydrogen, Oxygen, Weights, and Atoms - JRank Articles  

It is important to understand that water is not easily separated and a current of electricity applied to a metal typically platinum result in the breaking of the hydrogen to oxygen polar covalent bond.  What was the faulty reasoning that led to inaccurate relative atomic masses (atomic weights)? There were two main faults. First chemists were not distinguishing between the weights of atoms and of molecules. Seven common elements exist as diatomic molecules (molecules containing two atoms, such as oxygen, O2), of special importance being hydrogen, the original standard for atomic weights. If amoleculeof H2is given a relative mass of 1 instead of 2, then when other elements are compared with it, their relative atomic masses are halved. 

Second, at the time chemists used a term called equivalent, or combining weight. This was the number of grams of an element that combined with 8 g of oxygen (They used this because 8 g of oxygen combine with 1 g hydrogen so 8 g of oxygen wasequivalentto 1 g hydrogen.) Chemists used this because it is in general easier practically to measure the weight of an element that combines with oxygen than the weight that combines with hydrogen. Atomic weights were then found from the equivalent weight using the relationship: 

Equivalent weight x valency = atomic weight 

where valency is the combining power of an element (the number of atoms of hydrogen that would combine with an atom of the element). 

For example the equivalent weight of carbon is 3 g, because 3 g of carbon combine with 8 g oxygen. The valency of carbon is 4 because it forms the compound methane, CH4. So the relative atomic mass of carbon is 3 x 4 = 12. 

Even when the equivalent weight was accurately determined, if the valency was wrong then a simple fraction of the correct atomic weight was obtained. (In the above example, if the valency of carbon was thought to be two, the value for carbon’s atomic weight would be 6.) The combining (or equivalent) weights were generally accurate but sometimes an element was given the wrong valency. Thus beryllium, combining weight 4.6, was given the valency 3 because it was chemically similar to aluminium. This gave an atomic weight of 13.8, placing it between carbon and nitrogen where there was no space. 

It is still important to note that the mass of Silver was predicted to be 108 using this method.  The mass of the element is the amount that determines the end point for the faraday constant.  For example, if an electrical current is applied to a solution of Silver Nitrate until 108grams of silver are produced, then a faraday constant (the amount of energy needed to produce that mass) would be required.  The ampere was the unit used to measure the current needed to produce a faraday constant.  Once the total amount of energy was known to produce the atomic mass of an element, then the charge of an electron would provide the number of atoms in the weight of 108grams of Silver. 

The American scientist Robert A. Millikan (1868-1953) carried out experiments that allowed him to find the quantity of charge carried by an electron.  He determined the charge of an electron to be 1.60 x 10^-19 coulombs. 


The Mole =    Faraday’s Constant / Charge of an electron 

The Mole =   9.648 70 x 10^4, coulombs/faraday (C mol-1)  / 1.60x10^-19 coulombs    

The Mole =   6.022x10^23 things 

The Mole is a Trinity or three in one: Periodic Table Atomic Mass, 22.4 Liters at STP,  and Avogadro’s  number.