Atoms & Moles: Accounting for the Unobservable



Atomic Weights/Masses
Periodic Table
Molecular Masses
Balancing Equations
Practical Chemistry

There are probably many aspects of our world that are not directly detectable to our senses but must be inferred by intelligently piecing together the evidence.  Two diverse examples are “love” and “atoms.”

While this course is not intended to be about “love,” it might be noted that scientists often have found the strategies used to understand one part of nature are also helpful understanding very different matters.


While atoms were first proposed 2400 years ago by Leucippos and his student, Democritos of Abdera, the idea remained in the backwash because no evidence favored their existence.  But Robert Boyle changed all that in his 1661 The Sceptical Chymist where he proposed to redefine the equally old concept of “element.”  A century later Antoine Lavoisier adopted Boyle’s new definition and presented lots of examples as compelling evidence that the new definition was much more useful than the original.  Almost immediately chemists discovered that elements always combine in set volume and weight ratios.  Sometimes elements also combine in several ratios where one ratio is a multiple of the other.

John Dalton in the first decade of the 19th century proposed that atoms must exist.  Dalton’s atomic theory was quickly and widely accepted because it was apparently the sole explanation for set mass and volume ratios and multiple proportions.  That matter exists in invisibly small units called atoms and in clusters of atoms called molecules is now universally accepted.

Atomic Weights/Masses:

Dalton recognized that atoms need to have different weights depending on the kind of element. He realized that relative weights (say how much heavier a particular atom is than the lightest atom) would be useful for preparing compounds composed of molecules.  But firmly establishing relative weights for atoms proved elusive.

A half century later, August Kekule noted that nearly every chemistry text had a unique table of conflicting relative atomic weights.  In an effort to resolve this and other controversies, the First Chemical Congress met in Karlsruhe in 1860.  But the Congress failed to agree to a reliable way to establish atomic weights.  But a pamphlet distributed at the Congress by Stanislao Cannizzaro suggested a 1811 hypothesis by fellow Italian Amedeo Avogadro.  Avogadro claimed that while gases are easily compressed and rarified, that at equal temperature and pressure, equal numbers of molecules are contained in equal volumes.  Cannizzaro recognized that with the numbers of molecules equal, any differences in the weights of the gases would reliably be due to differences in the molecules’ weights.  Upon reading Cannizzaro’s pamphlet, several chemists, particularly Lothar Meyer from Germany and Dmitri Mendeleev from Russia recognized this was the solution sought for finding reliable atomic weights.

Periodic Table:

Nearly immediately both Meyer and Mendeleev proposed periodic tables organizing the atoms by weight and their chemical reactivity.  Mendeleev used his table to predict the existence of several additional elements and their expected properties.  Discover of new elements matching his predictions confirmed both the correctness of Mendeleev’s periodic table, the underlying atomic weights, and Cannizzaro/Avogadro’s approach.


By 1900 Wilhelm Ostwald of Germany had proposed a unit called a “mole” defined as a convenient measure in grams of materials based on the relative atomic weights.  Chemists in English speaking countries preferred terms such as “gram atomic weight” until the IUPAC and high school curriculum (CHEM Study) reform after the mid-20th Century firmly established the term “mole” as the accepted unit for measuring quantities of substances.  The mole remains firmly based on Dalton’s relative atomic masses1  derived from masses of gases according to procedures of Avogadro and Connizaro.

While the mole’s foundation in gases remains, gases are difficult to work with even in high school laboratories.  Their name “gas” derived from “chaos” because it was the most unknowable compared to solids and liquids.  So for a student beginning a study of chemistry, it may be easier to assume that relative atomic masses have been reliably determined by the methods of Avogadro and Cannizzaro.

All the atomic masses are based on hydrogen, the lightest being arbitrarily set about 1 2.  The mole is then established as the number of atoms in one gram of hydrogen.


Alchemists used symbols for a number of substances.  When Lavoisier proposed a new chemical theory based on the new definition of element, he rejected alchemy symbols because they conjured the old theory he wished to replace.  But Dalton wanted an abbreviated way to describe the new atoms, so he introduced a new set of new symbols with circles with internal designs.  But these turned out to be as hard to remember as those of alchemy.  Since Latin was the most universal language in 1813, Jons Jakob Berzelius proposed using the initials of the Latin names for the elements.  There symbols became a major aid for information exchange.  They were slowly adopted but universally used today.

Molecular Masses:

The masses of molecules are simply the sum of the masses of the constituent atoms:
Since H = 1, C = 12, O = 16, etc.

therefore H2O = 18, H2O2 = 34, CO = 28, CO2 = 44, CH 4 = 16, H2 = 2, O2 = 32. 3

Balancing Equations:

According to Dalton, chemical reactions rearrange but don’t create or destroy atoms.  A kind of chemical algebra requires the starting materials called “reactants” must equal the ending “products.”  So
C + O2 -> CO2
where the “subscript” number indicates when a molecule has more than one atom of a kind.

When more than one molecule is required, large “coefficients” are used:

2 H2 + C -> CH4.

Practical Chemistry:

So far atoms and molecular masses have been little more than an intellectual game.  The practical value comes with the measuring concept of a mole.

To comprehend the concept, first image working for a bakery.  Presume all doughnuts are produced and sold in units of dozens.  Imagine a machine that stamps out a dozen rings of dough and boxes that automatically hold exactly a dozen so no one ever actually counts individual doughnuts.  The entire business can be run (sales, expenses, and profits) in terms of dozens of doughnuts.

Now imagine a business involving much smaller items.  It would be convenient to use a unit larger than a dozen = 12.  But the concept of keeping track of sales, expenses, and profits in terms of this unit becomes even more valuable the smaller the size of the item.  Screws are sold by the gross = 144, and paper is sold in reams = 500.  The concept of using such a unit of measure becomes crucial for atoms too small to see or count individually.  Chemists already had relative weights that Avogadro said contained an equal number of molecules.  It was simply a matter of choosing that number to be the “mole.”

That is, if diatom oxygen has a relative mass of 32, we simply say the number of molecules in 32g of oxygen is one mole!  Then all the chemistry business (purchases, manufacture, and sales) can all be conducted in units of moles.  and the amazing thing is that no one will ever have to count the atoms in a mole!  In fact, we rarely ever have any need to know the number of atoms in a mole.

Since we live in a material universe, a great deal of real business is conducted in terms of moles, or other units based on the mole concept.  Sot it will be valuable to become skilled in measuring the “unobservable.”  (And someday, sharp students might find ways to extend these skills to other “unobservable” matters.)


1 Physicist have insisted that weight is provincial, varying from one planet to another and to a small degree, from one place on earth to another.  They point out that mass is a more reliable measure that at any location is proportional to weight.  But many older chemists still use the original terms of atomic and molecular weights although atomic and molecular masses are acknowledge superior.  As with all such changes, the old will eventually retire or die, and the young will adopt the better terms.

2 This has been adjusted twice to make atomic masses more accurate.  The First Chemical Congress redefined oxygen to be exactly 16 and in 1961 the International Union of Pure and Applied Chemists (IUPAC) defined carbon isotope 12 to be exactly 12.  The first change recognized that oxygen forms compounds with far more elements than hydrogen thus allowing the better accuracy of a single measured ratios instead of requiring an element to be compared to hydrogen via a third element that forms compounds with both.  The second change recognized that oxygen, like most elements, is a mixture of (3) isotopes that may vary causing uncertainty in atomic masses.

3 For reasons not understood in the 19th Century, some elements are required by Avogadro’s hypothesis to exist in pairs called diatomic molecules, namely, hydrogen, nitrogen, oxygen, and the halogens.  This seemed impossible if, as many chemists believed, compounds were held together by opposite electric charges.  This caused nearly all early 19th Century chemists to reject Avogadro’s hypothesis.  But after the value of consistent atomic weights was appreciated, the continuing difficulty explaining diatomic molecules became tolerable, but still annoying.


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