Re: How did Cannizarro use use Avogardo's Principle to determine atomic mass?

For those not "in the know" some of Cannizarro's writings on this subject can be found here.

To get his contributions in perspective we need to get an historical context: Cannizarro's work is 
dated 1858. Relative atomic masses had been available since Dalton's first work on 
atoms (around 1806). Actual atomic masses (and, as a consequence, a value for 
Avogadro's number) did not become available until about 100 years later, in the very early 
twentieth century.

Dalton's values for relative atomic weight were woefully inaccurate (he was a brilliant and original 
thinker, but rather a poor experimentalist!). They were improved on by Thomas Thomson (between 
1810 and 1820), and greatly improved on by Berzelius between about 1825 and 1840.
But there was always a problem -- there was no method of knowing for sure what the formula of a 
simple substance or compound was (e.g. whether water was HO or H2O). There were good clues, 
and in the first half of the 19th century chemists got most of the formulas right, but in any of the 
atomic weight tables up to the 1850s a few elements (not always the same ones) were assigned 
incorrect atomic weights because of wrong assumptions about the formulas of their compounds.

There were two main ways used to determine relative atomic weights before 1850. 
(1) Comparing the density (mass in a fixed volume) of a simple gaseous substance, or a gaseous 
compound of known formula, against that of hydrogen or oxygen as a standard. This would give an 
approximate value. Because of Avogadro's principle, the densities of gases are in the same ratio as 
what we would now call their molar masses. The value is only approximate because of the 
experimental difficulty of accurately determining the mass of a sample of gas. It has to be weighed in 
a rigid container which weighs much more than the gas it contains.
(2) Measuring the combining ratios of masses of two elements as simple substances when they 
combine to form a compound of known formula. This usually gave much more precise and 
accurate values, but difficulties did arise in some cases.

One of the early results of method (1) was to show that oxygen gas much be O2 rather than O, 
because the density of steam is much lower than that of oxygen gas. It is not possible to have HO 
or H2O weighing less than O. To explain the density of steam relative to oxygen gas, oxygen gas 
must be O2. This had two rather unfortunate effects. The first was to lead chemists to the idea that 
all gaseous simple substances were X2 rather than X. This was a wrong conclusion that affected, 
fortunately, only 2 of the elements then being considered: phosphorus (which should have been 
P4) and mercury (which should have been simply Hg). The other effect was shattering trust in 
Avogadro's principle as a useful device in this area, and it fell into disuse.

Cannizarro's contribution was to show how Avogadro's principle could be reliably used to 
determine relative atomic weights from gas densities. The key was to be a bit flexible, and not to 
have too many pre-conceived ideas about what the formulas of various gaseous substances were.
From my reading of the papers I have directed you to, I see his contribution to rest just as much on 
his careful argument and effective advocacy as on any novelty in his scientific ideas.

Cannizarro's experiments did not provide a value for Avogadro's number. For 100 years 
(~1806-1906), the people who believed in atoms had no real way of knowing how small the atoms 
were.

Absolute atomic weights, and the value of Avogadro's number remained inaccessible throughout 
the 19th century. Moreover, chemists divided into three roughly equal camps: those who believed 
in atoms, those who did not believe in atoms except as a convenient fiction, and those who were 
agnostic, declaring atoms to be beyond the boundaries of science because they were (if they 
existed) too small to be detected and subjected to experiment. (If you want to explore the latter 
two positions, check out what Sir Humphry Davy had to say about atoms in the 1820s when 
presenting the Royal Society medal to Dalton. I have a textbook by Alexander Smith, Chemistry, 
dated 1907 that takes a remarkably similar view.)

To determine Avogadro's number, we need some experiment where we can combine direct 
microscopic information about numbers of atomic-scale particles with large scale information 
about masses. Counting numbers of radioactive decays against loss or gain of mass of a particular 
element as a result of these decays was the first way this became possible. It is not a particularly 
precise way of getting at the result. The first and best really precise way became available just a 
few years later when Millikan, in his oil drop experiment, was able to accurately measure the 
electric charge of a single electron. As soon as this was available, a very precise determination was 
possible by measuring the mass transfer from one electrode to the other in a Cu|Cu(2+)(aq)|Cu 
electrolytic cell, along with the current and flow time.

Here are some articles from the Journal of Chemical Education that talk about the possibility of 
determinations of Avogadro's number from radioactive decay:
abstract 1
abstract 2

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An afterthought: It may not be quite clear how you can know relative molecular masses quite 
accurately without actually knowing the mass of a molecule. Here is an analogy I use which seems to 
make it easier:
A food manufacturing company prepares pre-packaged desserts which each include two cherries and 
a pear. They find that they have to buy in eight 10kg boxes of pears for each 10 kg box of cherries 
they go through. It is easy to deduce that a pear must weigh 16 times as much as a cherry without 
either weighing any fruit, or counting fruit in boxes.