AMEDEO AVOGADRO

Lorenzo Romano Amedeo Carlo Avogadro (to give him his full name), an Italian scientist, was born in Turin on June 9^th, 1776, and he died in the same city on July 9^th, 1856. He spent most of his life in Turin. There was a legal tradition in his family and Avogadro studied law, following in the family tradition.

His serious study of physics began in 1800, and he became Professor of Physics at Vercelli in 1809. This is where he produced his famous hypothesis on the volumes of perfect gases. Between the years of 1820 and 1850, he occupied the Chair of Physics at the University of Turin, and here he conducted much research into the electrical properties of substances, as well as making investigations into specific heat and thermal expansion.

So, despite being famous as a chemist, Avogadro was actually a very good physicist, mathematician, chemist and he had a doctorate in law!

He was noted to be one of the founders of physical chemistry. In actual fact, he was a physics professor, but he experimented in both physics and chemistry, while using mathematics to base most of his findings.

Mention “Avogadro” to most chemists, and the thing that will instantly spring to mind is the Avogadro constant, its value being 6.02252x10²³. This is what Avogadro is most famous for – his hypothesis called Avogadro’s Law. His law states that:

“Equal volumes of all gases measured under the same conditions of temperature and pressure, contain the same number of molecules”.

The use of the mole is a way of scaling up easily from relative atomic masses and relative molecular masses of substances, into grams. The mole is a unit, just as the gram is a unit; its symbol is “mol”. A mole is defined in terms of carbon-12:

“1 mole is the amount of substance which contains as many particles as there are atoms in exactly 12g of carbon-12.”

The obvious question which arises from this is “how many atoms are there in 12g of carbon-12?” The answer is again the Avogadro constant of 6.02252x10²³.

One mole of any substance always contains 6.02252x10²³ particles. Articles, however, are not always atoms – they may be molecules, ions, electrons or atoms, but the number is always the same.

The specific number of molecules in one gram-mole of a substance, defined as the molecular weight in grams, is 6.02252x10²³. For example, the the molecular weight of oxygen, O₂, is 32.00, so one gram-mole of oxygen has a mass of 32.00 grams, and contains 6.02252x10²³ molecules.

Mass = moles x Relative molecular mass (RMM), and we can see that this is true, as 32 (grams of oxygen molecules) = 1 (mole) x 32 (RMM).

The volumes occupied by one gram-mole of gas is about 0.791 cubic feet at standard temperature and pressure (i.e. 0^oC and 1 atmosphere). It is the same for all gases, according to Avogadro’s law.

The first person to have calculated the number of moles in any mass of substance was Josef Loschmidt, (1821-1895), an Austrian academic. In 1865, he used the new Kinetic Molecular Theory and calculated the number of molecules in one cubic centimetre of gaseous substance under ordinary conditions of temperature and pressure, to be around 2.6x10¹⁹ molecules. This value is called Loschmidt’s constant, and he was not too far out with his initial prediction, as the value is now officially deemed to be 2.6867775x10²⁵.

Yet, indisputably, it was Avogadro who was responsible for a lot of the work on this subject, and indeed it was he who drew up the hypothesis that “equal volumes of gases under the same conditions of temperature and pressure, contain the same number of molecules.” This hypothesis was published in the French “Journal de Physique”. It was published soon after a scientist named Gay-Lussac discovered that the volumes of combining gases bear a simple ratio to each other and to the volume of the new compound.

Avogadro’s hypothesis, in conjunction with Gay-Lussac’s law should have allowed the molecular formulae and atomic weight of gases to be determined experimentally, but Avogadro’s paper on this subject attracted very little attention, since it was supported by so little experimental evidence. It was, and still is, very difficult to experiment on very small masses of a substance.

The vindication of Avogadro’s hypothesis came after his death, when, in 1860, an Italian chemist named Stanislao Cannizzaro presented a system of atomic weights determined using Avogadro’s work. Since then, his hypothesis has been accepted without question, and his ideas on the molecular nature of the simple gases have also proved to be correct.

The Avogadro constant is a huge number, and one may ask, “how was it ever derived?” It can be determined from X-Ray diffraction studies. Using this method, the Avogadro constant, L, can be found to an accuracy of one in 10,000.

2. Knowing the distance between atoms (or ions) in the crystal, it is then possible to find the volume occupied by one atom.

4. Finally, the volume of one mole is divided by the volume of one atom to obtain the Avogadro constant.

Consider the following example. The diagram below shows a unit cell of sodium metal, which has a body-shaped cubic structure.

The unit cell is the simplest arrangement of atoms which, when repeated, will reproduce the same structure. The central atom is totally inside the unit cell. The eight atoms at the corners are equally shared between eight unit cells. Hence, the unit cell contains a total of 1 + 8 x 1/8 (=2) atoms. X-ray diffraction methods show that the width of the unit cell is 0.429nm, or 0.429x10^-7cm.

Thus, the volume of the unit cell (i.e. two atoms) = (0.429x10^-7)³ cm³, = 0.0790x10^-21cm³.

The relative atomic mass of sodium = 22.99, and the density of sodium is 0.97g/cm³.

Using the equation volume = mass/density, the volume of one mole (L atoms) of sodium = 22.99/0.97 = 23.70cm³.

It follows that the Avogadro constant, L

= ^23.70 / 0.0395x10^-²¹=

****** 6x10²³ ***