Re: Who discovered the law of conservation of mass, and when?

There is no clear-cut answer to this question. The answer that I will 
venture as probably the best, but by no means the only way of looking at 
it, is that it was discovered by Lavoisier, some time in the 1780s.

The biggest problem with trying to look at the law of conservation of mass 
as a scientific discovery, is that that is not necessarily how it arises. 
The law follows from the following two propositions:

(i) The creation or final destruction of matter is the perogative of the 
good Lord alone.

(ii) Mass is, among other things, the marker of matter.

The first of these propositions was universally and unquestioningly 
believed in mediaeval European society, so much so that it became a deep 
and almost instinctive part of the basis of European culture. 

The second was something that most scientists had considered and hedged 
around. It is certainly implicit in Isaac Newton's work, for example. But 
it was not unquestioningly nor even universally believed among scientists. 
In a number of areas of science there were active proposals for matter 
without mass being explored not only in the 18th century, but well into the 
19th. At least one of them, the idea of caloric, or heat, as a massless 
fluid, even arose out of Lavoisier's own work.

It is very clear cut that solid and liquid bodies are matter and have mass. 
Airs, or gases, are a bit more subtle, but it takes only a little 
scientific work to establish that they too are both material and massive. 
But in the late 18th and early 19th centuries there were at least five 
issues where there was controversy and difficulty both about material and 
mass.

Fire   Heat   Light   Electricity    The Aether

To show how important the creation/destruction axiom was, I will refer you 
to an experiment by Count Rumford in the 19th century which was almost 
universally taken as a solid refutation of Lavoisier's caloric as the 
material embodiment of heat. He simply created a clearly endless supply of 
heat by arranging for continuing friction by rotating a cannon-ball in its 
breech. The accepted explanation of this sort of thing had been that the 
caloric was being released from the metal by the frictional action. But if 
that were the case, the supply should be finite, not endless. It is an 
interesting commentary on European thought that the possibility that 
caloric was being continuously created in the experiment (which could 
rescue the caloric idea) was never even seriously entertained!

So the 'discovery' of conservation of mass was really mainly about two 
things. (1) establishing that mass is a necessary accompaniment of matter, 
and (2) verifying that when the products of a process are carefully 
contained, there is no difference between initial mass and final mass. 
Lavoisier and his followers certainly did the latter. One of the British 
pneumatic chemists may have done so earlier (Boyle, Black, Cavendish, 
Priestley, or one of the lesser lights from that scientific approach). 
Prior to that, nobody really took precautions against gaseous materials 
either entering from the environment or being released to the environment, 
so a verification of conservation of mass would have been quite invalid. 

But there was a big issue between the pneumatic chemists and Lavoisier: the 
pneumatic chemists were adherents of the phlogiston theory.

Phlogiston is the stuff that flames are made of. It gives structural 
integrity, plasticity, elasticity, lustrous appearance, and resilience both 
to metals and to living creatures. It can be lost rapidly in a fire (when 
it is actually seen as flame before it disperses and becomes part of the 
air) or slowly in death, rust, rot, and decay, or even (in smaller 
quantities) in exhalation. The products lack structural strength, lustre, 
and resilience -- they are earths, rusts, ashes. They have lost their 
phlogiston.

When it comes to phlogiston and mass, though, there was a big problem. It 
had been well known for many years that when iron rusts, the total bulk of 
rust produced is much greater than that of the original metal, and the 
actual mass of rust is a little greater than that of the metal it formed 
from. The French chemist Guyton de Morveau did some accurate experiments 
and measured the increase in mass for a number of metals. His explanation 
was that phlogiston must have negative mass. Black took up this idea, and 
described phlogiston as (among other things) a 'principle of levity' that 
buoyed up metals and made them lighter than their rusts, calces, or earths.

But Lavoisier could not swallow the idea of a material that weighed less 
than nothing -- he saw it as absurd. Guyton's work was one of the more 
important factors leading him to his rejection of phlogiston, its 
replacement with the oxygen system, and a whole new approach to chemistry.

It was Lavoisier's revolution that placed the stress in chemistry much more 
on masses of reacting materials, and on containing reactions so that one 
was fully aware of gaseous reactants or products. The idea of conservation 
of mass, and accounting in mass during chemical reactions was one of the 
more immediate spin-offs.

I hope that little bit of history/story-telling justifies my claim that it 
is really impossible to credit a 'discoverer' of the law of conservation of 
mass, and that if credit must be given it belongs with Lavoisier as much as 
anyone.