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   Essay on a Manner of Determining the Relative Masses of the Elementary
   Molecules of Bodies, and the Proportions in Which They Enter Into These

                    Lorenzo Romano Amadeo Carlo Avogadro
                   Journal de physique, 73: 58-76 (1811)

translation from Alembic Club Reprints, No. 4, "Foundations of the Molecular
     Theory: Comprising Papers and Extracts by John Dalton, Joseph Louis
                Gay-Lussac, and Amadeo Avogadro, (1808-1811)"


Reader note: The words "atom" and "molecule" did not yet have their modern
meaning. By "integral molecule" Avogadro meant one molecule of a compound;
by "constituent molecule" a molecule of a gaseous element; and by
"elementary molecule" (or "half molecule") an atom.

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M. Gay-Lussac has shown in an interesting Memoir that gases always unite in
a very simple proportion by volume, and that when the result of the union is
a gas, its volume also is very simply related to those of its components.
But the quantitative proportions of substances in compounds seem only to
depend on the relative number of molecules which combine, and on the number
of composite molecules which result. It must then be admitted that very
simple relations also exist between the volumes of gaseous substances and
the numbers of simple or compound molecules which form them. The first
hypothesis to present itself in this connection, and apparently even the
only admissible one, is the supposition that the number of integral
molecules in any gases is always the same for equal volumes, or always
proportional to the volumes. Indeed, if we were to suppose that the number
of molecules contained in a given volume were different for different gases,
it would scarcely be possible to conceive that the law regulating the
distance of molecules could give in all cases relations so simple as those
which the facts just detailed compel us to acknowledge between the volume
and the number of molecules. On the other hand, it is very well conceivable
that the molecules of gases being at such a distance that their mutual
attraction cannot be exercised, their varying attraction for caloric may be
limited to condensing a greater or smaller quantity around them, without the
atmosphere formed by this fluid having any greater extent in the one case
than in the other, and, consequently, without the distance between the
molecules varying; or, in other words, without the number of molecules
contained in a given volume being different. Dalton, it is true, has
proposed a hypothesis directly opposed to this, namely, that the quantity of
caloric is always the same for the molecules of all bodies whatsoever in the
gaseous state, and that the greater or less attraction for caloric only
results in producing a greater or less condensation of this quantity around
the molecules, and thus varying the distance between the molecules
themselves. But in our present ignorance of the manner in which this
attraction for the molecules for caloric is exerted, there is nothing to
decide us a priori in favour of the one of these hypotheses rather than the
other; and we should rather be inclined to adopt a neutral hypothesis, which
would make the distance between the molecules and the quantities of caloric
vary according to unknown laws, were it not that the hypothesis we have just
proposed is based on that simplicity of relation between the volumes of
gases on combination, which would appear to be otherwise inexplicable.

Setting out from this hypothesis, it is apparent that we have the means of
determining very easily the relative masses of the molecules of substances
obtainable in the gaseous state, and the relative number of these molecules
in compounds; for the ratios of the masses of the molecules are then the
same as those of the densities of the different gases at equal temperature
and pressure, and the relative number of molecules in a compound is given at
once by the ratio of the volumes of the gases that form it. For example,
since the numbers 1.10359 and 0.07321 express the densities of the two gases
oxygen and hydrogen compared to that of atmospheric air as unity, and the
ratio of the two numbers consequently represents the ratio between the
masses of equal volumes of these two gases, it will also represent on our
hypothesis the ratio of the masses of their molecules. Thus the mass of the
molecule of oxygen will be about 15 times that of the molecule of hydrogen,
or more exactly, as 15.074 to 1. In the same way the mass of the molecule of
nitrogen will be to that of hydrogen as 0.96913 to 0.07321, that is, as 13,
or more exactly 13.238, to 1. On the other hand, since we know that the
ratio of the volumes of hydrogen and oxygen in the formation of water is 2
to 1, it follows that water results from the union of each molecule of
oxygen with two molecules of hydrogen. Similarly, according to the
proportions by volume established by M. Gay-Lussac for the elements of
ammonia, nitrous oxide, nitrous gas, and nitric acid, ammonia will result
from the union of one molecule of nitrogen with three of hydrogen, nitrous
oxide from one molecule of oxygen with two of nitrogen, nitrous gas from one
molecule of nitrogen with one of oxygen, and nitric acid from one of
nitrogen with two of oxygen.


There is a consideration which appears at first sight to be opposed to the
admission of our hypothesis with respect to compound substances. It seems
that a molecule composed of two or more elementary molecules should have its
mass equal to the sum of the masses of those molecules; and that in
particular, if in a compound one molecule of one substance unites with two
or more molecules of another substance, the number of compound molecules
should remain the same as the number of molecules of the first substance.
Accordingly, on our hypothesis when a gas combines with two or more times
its volume of another gas, the resulting compound, if gaseous, must have a
volume equal to that of the first of these gases. Now, in general, this is
not actually the case. For instance, the volume of water in the gaseous
state is, as M. Gay-Lussac has shown, twice as great as the volume of oxygen
which enters into it, or, what comes to the same thing, equal to that of the
hydrogen instead of being equal to that of the oxygen. But a means of
explaining facts of this type in conformity with our hypothesis presents
itself naturally enough: we suppose, namely, that the constituent molecules
of any simple gas whatever (i.e., the molecules which are at such a distance
from each other that they cannot exercise their mutual action) are not
formed of a solitary elementary molecule, but are made up of a certain
number of these molecules united by attraction to form a single one; and
further, that when molecules of another substance unite with the former to
form a compound molecule, the integral molecule which should result splits
up into two or more parts (or integral molecules) composed of half, quarter,
&c., the number of elementary molecules going to form the constituent
molecule of the first substance, combined with half, quarter, &c., the
number of constituent molecules of the second substance that ought to enter
into combination with one constituent molecule of the first substance (or,
what comes to the same thing, combined with a number equal to this last of
half-molecules, quarter-molecules, &c., of the second substance); so that
the number of integral molecules of the compound becomes double, quadruple,
&c., what it would have been if there had been no splitting-up, and exactly
what is necessary to satisfy the volume of the resulting gas.* [Thus, for
example, the integral molecule of water will be composed of a half molecule
of oxygen with one molecule, or, what is the same thing, two half-molecules
of hydrogen.]

On reviewing the various compound gases most generally known, I only find
examples of duplication of the volume relatively to the volume of that one
of the constituents which combines with one or more volumes of the other. We
have already seen this for water. In the same way, we know that the volume
of ammonia gas is twice that of the nitrogen which enters into it. M.
Gay-Lussac has also shown that the volume of nitrous oxide is equal to that
of the nitrogen which forms part of it, and consequently is twice that of
the oxygen. Finally, nitrous gas, which contains equal volumes of nitrogen
and oxygen, has a volume equal to the sum of the two constituent gases, that
is to say, double that of each of them. Thus in all these cases there must
be a division of the molecule into two; but it is possible that in other
cases the division might be into four, eight, &c. The possibility of this
division of compound molecules might have been conjectured a priori; for
otherwise the integral molecules of bodies composed of several substances
with a relatively large number of molecules, would come to have a mass
excessive in comparison with the molecules of simple substances. We might
therefore imagine that nature had some means of bringing them back to the
order of the latter, and the facts have pointed out to us the existence of
such means. Besides, there is another consideration which would seem to make
us admit in some cases the division in question; for how could one otherwise
conceive a real combination between two gaseous substances uniting in equal
volumes without condensation, such as takes place in the formation of
nitrous gas? Supposing the molecules to remain at such a distance that the
mutual attraction of those of each gas could not be exercised, we cannot
imagine that a new attraction could take place between the molecules of one
gas and those of the other. But on the hypothesis of division of the
molecule, it is easy to see that the combination really reduces two
different molecules to one, and that there would be contraction by the whole
volume of one of the gases if each compound molecule did not split up into
two molecules of the same nature. M. Gay-Lussac clearly saw that, according
to the facts, the diminution of volume on the combination of gases cannot
represent the approximation of their elementary molecules. The division of
molecules on combination explains to us how these two things may be made
independent of each other.


Dalton, on arbitrary suppositions as to the most likely relative number of
molecules in compounds, has endeavoured to fix ratios between the masses of
the molecules of simple substances. Our hypothesis, supposing it
well-founded, puts us in a position to confirm or rectify his results from
precise data, and, above all, to assign the magnitude of compound molecules
according to the volumes of the gaseous compounds, which depend partly on
the division of molecules entirely unsuspected by this physicist.

Thus Dalton supposes [In what follows I shall make use of the exposition of
Dalton's ideas given in Thomson's "System of Chemistry."] that water is
formed by the union of hydrogen and oxygen, molecule to molecule. From this,
and from the ratio by weight of the two components, it would follow that the
mass of the molecule of oxygen would be to that of hydrogen as 7 1/2 to 1
nearly, or, according to Dalton's evaluation, as 6 to 1. This ratio on our
hypothesis is, as we saw, twice as great, namely, as 15 to 1. As for the
molecule of water, its mass ought to be roughly expressed by 15 + 2 = 17
(taking for unity that of hydrogen), if there were no division of the
molecule into two; but on account of this division it is reduced to half, 8
1/2, or more exactly 8.537, as may also be found directly by dividing the
density of aqueous vapour 0.625 (Gay-Lussac) by the density of hydrogen
0.0732. This mass only differs from 7, that assigned to it by Dalton, by the
difference in the values for the composition of water; so that in this
respect Dalton's result is approximately correct from the combination of two
compensating errors,-the error in the mass of the molecule of oxygen, and
his neglect of the division of the molecule.

Dalton supposes that in nitrous gas the combination of nitrogen and oxygen
is molecule to molecule; we have seen on our hypothesis that this is
actually the case. Thus Dalton would have found the same molecular mass for
nitrogen as we have, always supposing that of hydrogen to be unity, if he
had not set out from a different value for that of oxygen, and if he had
taken precisely the same value for the quantities of the elements in nitrous
gas by weight. But by supposing the molecule of oxygen to be less than half
what we find, he has been obliged to make that of nitrogen also equal to
less than half the value we have assigned to it, viz., 5 instead of 13. As
regards the molecule of nitrous gas itself, his neglect of the division of
the molecule again makes his result approach ours; he has made it 6 + 5 =
11, whilst according to us it is about (15 + 13) / 2 = 14, or more exactly
(15.074 + 13.238) / 2 = 14.156, as we also find by dividing 1.03636, the
density of nitrous gas according to Gay-Lussac, by 0.07321. Dalton has
likewise fixed in the same manner as the facts have given us, the relative
number of molecules in nitrous oxide and in nitric acid, and in the first
case the same circumstance has rectified his result for the magnitude of the
molecule. He makes it 6 + 2 x 5 = 16, whilst according to our method it
should be (15.074 + 2 x 13.238) / 2 = 20.775, a number which is also
obtained by dividing 1.52092, Gay-Lussac's value for the density of nitrous
oxide, by the density of hydrogen.

In the case of ammonia, Dalton's supposition as to the relative number of
molecules in its composition is on our hypothesis entirely at fault. He
supposes nitrogen and hydrogen to be united in it molecule to molecule,
whereas we have seen that one molecule of nitrogen unites with three
molecules of hydrogen. According to him the molecule of ammonia would be 5 +
1 = 6: according to us it should be (13 + 3) / 2 = 8, or more exactly 8.119,
as may also be deduced directly from the density of ammonia gas. The
division of the molecule, which does not enter into Dalton's calculations,
partly corrects in this case also the error which would result from his
other suppositions.

All the compounds we have just discussed are produced by the union of one
molecule of one of the components with one or more molecules of the other.
In nitrous acid we have another compound of two of the substances already
spoken of, in which the terms of the ratio between the number of molecules
both differ from unity. From Gay-Lussac's experiments, it appears that this
acid is formed from 1 part by volume of oxygen and 3 of nitrous gas, or,
what comes to the same thing, of 3 parts of nitrogen and 5 of oxygen; whence
it would follow, on our hypothesis, that its molecules should be composed of
3 molecules of nitrogen and 5 of oxygen, leaving the possibility of division
out of account. But this mode of combination can be referred to the
preceding simpler forms by considering it as the result of the union of 1
molecule of oxygen with 3 of nitrous gas, i.e. with 3 molecules, each
composed of a half-molecule of oxygen and a half-molecule of nitrogen, which
thus already includes the division of some of the molecules of oxygen which
enter into that of nitrous acid. Supposing there to be no other division,
the mass of this last molecule would 57.542, that of hydrogen being taken as
unity, and the density of nitrous acid gas would be 4.21267, the density of
air being taken as unity. But it is probable that there is at least another
division into two, and consequently a reduction of the density to half: we
must wait until this density has been determined by experiment. . . .


It will have been in general remarked on reading this Memoir that there are
many points of agreement between our special results and those of Dalton,
although we set out from a general principle, and Dalton has only been
guided by considerations of detail. This agreement is an argument in favour
of our hypothesis, which is at bottom merely Dalton's system furnished with
a new means of precision from the connection we have found between it and
the general fact established by M. Gay-Lussac. Dalton's system supposes that
compounds are made in general in fixed proportions, and this is what
experiment shows with regard to the more stable compounds and those most
interesting to the chemist. It would appear that it is only combinations of
this sort that can take place amongst gases, on account of the enormous size
of the molecules which would result from ratios expressed by larger numbers,
in spite of the division of the molecules, which is in all probability
confined within narrow limits. We perceive that the close packing of the
molecules in solids and in liquids, which only leaves between the integral
molecules distances of the same order as those between the elementary
molecules, can give rise to more complicated ratios, and even to
combinations in all proportions; but these compounds will be so to speak of
a different type from those with which we have been concerned, and this
distinction may serve to reconcile M. Berthollet's ideas as to compounds
with the theory of fixed proportions.