Background Information
John Dalton (1766-1844) was so taken with the notion of atomism that he never quite grasped the
distinction between an atom and a molecule of an element. The most stable form of many elements, such as
oxygen, hydrogen, and the halogens, is not a single atom but a diatomic molecule. Because Dalton believed
that the smallest unit of an element must be an atom, he had a hard time accepting Gay-Lussac's data about
the combining volumes of gases.
The reconciliation between Dalton's theory and Gay-Lussac's data was brought about by Amedeo Carlo
Avogadro (1776-1856). He accomplished this by making the distinction between an atom and a molecule
of an element and by making the hypothesis that equal volumes of gases contain equal numbers of
molecules. For example, if you believe that hydrogen and chlorine are monoatomic and that equal volumes
of gases (at the same temperature and pressure) contain equal numbers of atoms, then one volume of
hydrogen should react with one volume of chlorine to form one volume of HCl:
H(g) + Cl(g) ---> HCl(g)
But when you do the experiment you will find that two volumes of HCl are produced. Avogadro
interpreted this result by assuming that the smallest unit of hydrogen and chlorine is a diatomic molecule,
not an atom, and by writing the equation as follows:
H2(g) + Cl2(g) ---> 2HCl(g)
Many subsequent experiments have proved that Avogadro's explanation was correct.
The hypothesis published in1811, was perhaps ahead of its time and went virtually unnoticed. More than
half a century passed before Cannizzaro demonstrated the general applicability of the hypothesis in an
article published in 1858. When he distributed it in pamphlet so clearly and completely discussed atoms,
molecules, atomic weights, and molecular weights that chemists were convinced of his views, and quietly
incorporated them into chemical thinking. Fifty years of pondering Dalton's atomic theory had created the
right moment for the acceptance of Avogadro's hypothesis. Cannizzaro gave credit to Avogadro as well as
to Ampere and Dumas, and no doubt it was Cannizzaro who saved Avogadro's hypothesis from oblivion.
As a result, today we call the number of particles (atoms or molecles) in a mole Avogadro's number.
How many particles are there in a mole? Avogadro did not invent or use the concept of a mole and never
knew the number of particles in a mole. In 1865, a few years after Avogadro's death, the German chemist
Joseph Loschmidt published an article estimating the size of a molecule and although Loschmidt didn't
present the calculation in his paper, it is possible from the calculations he did present to estimate the
number of molecules in a cubic centimeter of gas. This is only one simple step away from determining the
number of molecules in a mole. For this reason, Germany chemists often called the constant Loschmidt's
number rather than Avogadro's number, and the International Union of Pure and Applied Chemistry
(IUPAC) allows the use of either the symbol NA or L for Avogadro's number, to honor the contributions of
both men.
A French scientist, Jean Perrin, is often given credit for determining the first value of Avogadro's number
in 1908. Perrin measured the vertical distribution in the earth's gravitational field of gambode (a natural
resin) particles suspended in water and obtained values in the range 5.4 X 10 23.
After the American physicist Robert Millikan determined the charge of an electron around 1915, a more
accurate value was obtained by dividing the charge of a mole of electrons (the Farraday constant) by the
charge of a single electron. More refined values have been obtained by accurate measurements of crystals
of silicon by X-ray diffraction: dividing the volume of a silicon atom yields Avogadro's number.
All of the refined measurements require sophisticated and expensive equipment and great care in
experimental technique and treatment of data. The payoff is the most accurate value of Avogadro's number,
NA, that we have to date: NA = 6.02214 X 1023 particles/mol. This is one of the numbers you will
encounter in introductory chemistry that is worth remembering.
The mole is a fundamental unit in the International System (SI) of units. A mole of carbon is precisely
12.000000 g of carbon-12, and Avogadro's number is defined as the number of atoms in a mole of carbon12.
In this experiment you will make an approximate (order of magnitude) estimate of Avogadro's number by
determining the amount of stearic acid that it takes to form a single layer (called a monolayer) on the
surface of water. By making simple assumptions about the way the stearic acid molecules pack together to
form the monolayer, we can determine its thickness, and from that thickness we can estimate the size of a
carbon atom. Knowing the size of a carbon atom, we can compute its volume; and if we know the volume
occupied by a mole of carbon (in the form of a diamond), we can divide the volume of a mole of carbon by
the volume of an atom of carbon to get an estimate of Avogadro's number. The number won't be accurate to
within 10 percent, or even a factor of 2, but it will enable you to estimate to within about a power of 20 the
number of particles in a mole. That's better than chemists could do only 100 years ago.