LETTER OF PROFESSOR STANISLAO CANNIZZARO

TO
PROFESSOR S. DE LUCA:
SKETCH OF A COURSE OF CHEMICAL PHILOSOPHY

Given in the Royal University of Genoa

Il Nuovo Cimento, vol. vii. (1858), pp. 321-366

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Thus the weight 200 mercury, whether as an element or in its compounds, requires to heat it 1° the same quantity of heat as 127 of iodine, 80 of bromine, and almost certainly as 35.5 of chlorine and 1 of hydrogen, if it were possible to compare these two last substances in the same physical state as that in which the specific heats of the above-named substances have been compared.

But the atoms of hydrogen, iodine, and bromine are half their respective molecules: thus is it natural to ask if the weight 200 mercury also corresponds to half a molecule of free mercury. It is sufficient to look at the table of numbers expressing the molecular weights to perceive that if 2 is the molecular weight of hydrogen, the weight of the molecule of mercury is 200, i.e., equal to the weight of the atom. In other words, one volume of vapour, whether of protochloride or protoiodide, whether of bichloride or of biniodide, contains an equal volume of mercury vapour; so that each molecule of these compounds contains an entire molecule of mercury, which, entering as a whole into all the molecules, is the atom of this substance. This is confirmed by observing that the complete molecule of mercury requires for heating it 1°, the same quantity of heat as half a molecule of iodine, or half a molecule of bromine. It appears to me, then, that I can sustain that what enters into chemical actions is the half molecule of hydrogen and the whole molecule of mercury: both of these quantities are indivisible, at least in the sphere of chemical actions actually known. You will perceive that with this last expression I avoid the question if it is possible to divide this quantity further. I do not fail to apprise you that all those who faithfully applied the theory of Avogadro and of Ampère, have arrived at this same result. First Dumas and afterwards Gaudin showed that the molecule of mercury, differing from that of hydrogen, always entered as a whole into compounds. On this account Gaudin called the molecule of mercury monatomic, and that of hydrogen biatomic. However, I wish to avoid the use of these adjectives in this special sense, because to-day they are employed as you know in a very different sense, that is, to indicate the different capacity for saturation of the radicals.

The formulae of the two chlorides of mercury having been demonstrated, I next compare them with that of hydrochloric acid. The atomic formulae indicate that the constitution of the protochloride is similar to that of hydrochloric acid, if we consider the number of atoms existing in the molecules of the two; if, however, we compare the quantities of the components with those which exist in their free molecules, then a difference is perceived. To make this evident I bring the atomic formulae of the various molecules under examination into comparison with the formulae made with the symbols expressing the weights of the entire molecules, placing them in the manner which you see below:-

  Symbols of the molecules of the elements and formulae of their compounds made with these symbols, i.e., symbols and formulae representing the weights of equal volumes in the gaseous state Symbols of the atoms of the elements and formulae of their compounds made with these symbols Numbers expressing the corresponding weights
Atom of Hydrogen H (1/2)H1
Molecule of Hydrogen HH22
Atom of Chlorine Cl (1/2)Cl35.5
Molecule of Chlorine ClCl271
Atom of Bromine Br (1/2)Br80
Molecule of Bromine BrBr2160
Atom of Iodine I (1/2)I127
Molecule of Iodine II2254
Atom of Mercury HgHg200
Molecule of Mercury HgHg200
      "       Hydrochloric Acid H (1/2) Cl (1/2)HCl36.5
      "       Hydrobromic Acid H (1/2) Br (1/2)HBr81
      "       Hydriodic Acid H (1/2) I (1/2)HI128
      "       Mol. of protochloride of Mercury HgCl (1/2)HgCl235.5
      "       protobromide of Mercury HgBr (1/2)HgBr280
      "       protoiodide of Mercury HgI (1/2)HgI327
      "       bichloride of Mercury HgClHgCl2271
      "       bibromide of Mercury HgBrHgBr2360
      "       biniodide of Mercury HgIHgI2454

[Reader's Note: Cannizzaro uses a Gothic font in column two. It is impossible to reproduce in this transcription.]

The comparison of these formulae confirms still more the preference which we must give to the atomic formulae, which indicate also clearly the relations between the gaseous bodies. It is sufficient to recall that whilst the atoms of chlorine, bromine, iodine, and hydrogen are represented by the weight of 1/2 volume, the atom of mercury is represented by the weight of the whole volume.

I then come to the examination of the two chlorides of copper. The analogy with those of mercury forces us to admit that they have a similar atomic constitution, but we cannot verify this directly by determining and comparing the weights and the compositions of the molecules, as we do not know the vapour densities of these two compounds.

The specific heats of free copper and of its compounds confirm the atomic constitution of the two chlorides of copper deduced from the analogy with those of mercury. Indeed the composition of the two chlorides leads us to conclude that if they have the formulae CuCl, CuCl2, the atomic weight of copper indicated by Cu is equal to 63, which may be seen from the following proportions :--

  Ratio between the
components expressed
by numbers whose
sum = 100.
Ratio between the
components
expressed by
atomic weights.
Protochloride of Copper 36.04 : 63.96
Chlorine. Copper.
35.5 : 63
Cl. Cu.
Bichloride of Copper 52.98 : 47.02
Chlorine. Copper.
71 : 63
  Cl. Cu.

Now 63 multiplied by the specific heat of copper gives a product practically equal to that given by the atomic weight of iodine or of mercury into their respective specific heats. Thus :

63  x  0.009515  =  6
Atomic weight
of copper.
  Specific heat
of copper.

The same quantity of heat is required to heat the weight of 63 of copper in its compounds through 1°. Thus :--

Formulae
of the
compounds
of Copper.
Weights of
their
molecules
= p.
Specific
heats of
unit weights
= c.
Specific
heats of the
molecules
= p x c.
Number of
atoms in the
molecules
= n.
Specific
heat of
each atom
= (p x c) / n.
CuCl .98.50.1381713.61959526.809797
CuI .1900.0686914.051127.0255

After this comes the question, whether this quantity of copper which enters as a whole into the compounds, the calorific capacity of the atoms being maintained, is an entire molecule or a sub-multiple of it. The analogy of the compounds of copper with those of mercury would make us inclined to believe that the atom of copper is a complete molecule. But having no other proof to confirm this, I prefer to declare that there is no means of knowing the molecular weight of free copper until the vapour density of this substance can be determined.

I then go on to examine the constitution of the chlorides, bromides, and iodides of potassium, sodium, lithium, and silver. Each of these metals makes with each of the halogens only one well characterised and definite compound ; of none of these compounds is the vapour density known ; we are therefore in want of the direct means of discovering if in their molecules there are one, two, or more atoms of the halogens. But their analogies with the protochloride of mercury, HgCl, and with the protochloride of copper, CuCl, and the specific heats of the free metals and of their compounds make us assume that in the molecules of each of these compounds there is one atom of metal and one of halogen. According to this supposition, the atomic weight of potassium K = 39, that of sodium Na = 23, that of silver Ag = 108. These numbers multiplied by the respective specific heats give the same product as the atomic weights of the substances previously examined.

Name of substance Atomic weight
= p.
Specific heats of
unit weight = c.
Specific heats of
the atoms = p x c.
Solid Bromine .800.084326.74560
Iodine . .1270.054126.87324
Solid Mercury .2000.032416.48200
Copper . .630.095156
Potassium .390.1695566.612684
Sodium . .230.29346.7482
Silver . .1080.057016.15708

Besides this, the specific heats of the chlorides, bromides, and iodides of these metals confirm the view that their molecules contain the same number of atoms of the two components. Thus :--

Formulae and
Names of the
compounds.
Weights
of their
molecules
= p.
Specific
heats of
unit weight
= c.
Specific
heats of the
molecules = p x c.
No. of
atoms
in the
mole-
cules = n
Specific
heat of
each atom
= (p x c) / n.
KCl .
Chl. of Potassium.
74.50.1729512.88477526.442387
NaCl .
Chl. of Sodium.
58.50.2140112.51958526.259792
AgCl .
Chl. of Silver.
143.50.0910913.07141526.535707
KBr .
Brom. of Potassium.
1190.1132113.4731826.73659
NaBr .
Brom. of Sodium.
1030.1384214.2572627.12863
AgBr .
Brom. of Silver.
1880.0739113.8950826.94754
KI .
Iod. of Potassium.
1660.0819113.5970626.79853
NaI .
Iod. of Sodium.
1500.0868413.026026.5130
AgI .
Iod. of Silver.
2350.0615914.4736527.23682

Are the atoms of potassium, sodium, lithium, and silver equal to 1/2 molecule, like that of hydrogen, or equal to a whole molecule, like that of mercury? As the vapour densities of these elements are wanting, we cannot answer the question directly ; I will give you later some reasons which incline me to believe that the molecules of these elements, like that of hydrogen, are composed of two atoms.

Gold makes with each of the halogens two compounds. I show that the first chloride is analogous to calomel, i. e., that it has AuCl as its formula. The atomic weight of gold deduced from the composition of the protochloride to which this formula is given corresponds to the law of specific heats, as may be seen from what follows :

196.32 x 0.03244 = 6.3696208
Au Specific heat
of Gold.

I show in the sequel that the first or only chlorides of the following metals have a constitution similar to the bichloride of mercury and of that of copper, that is, for each atom of metal they contain two atoms of chlorine.

Not knowing the density in the gaseous state of these lower or only chlorides, we cannot show directly the quantity or chlorine existing in their molecules, yet the specific heats of these free metals and of their compounds show what I have said above. I write the quantities of these different elements combined with the weight of two atoms of chlorine in the lower or only chlorides, and confirm in these quantities the properties of the other atoms ; I write the formulae of the lower chlorides, bromides, and iodides all as MCl2, and verify that they correspond to the laws of specific heats of a compound substances.

Names of
Substances.
Symbols and
weights of the
atoms.
Specific heats
of
unit weight.
Specific heats
of the atoms.
Iodine . .I = 1270.054126.87324
Solid Mercury .Hg = 2000.032416.48200
Copper . .Cu = 630.095156
Zinc . .Zn = 660.095556.30630
Lead . .Pb = 2070.03146.4998
Iron . .Fe = 560.113796.37224
Manganese .Mn = 550.11816.04955
Tin . .Sn = 117.60.056236.612648
Platinum .Pt = 1970.032436.38871
Calcium . .Ca = 40
Magnesium .Mg = 24
Barium . .Ba = 137
Formulae
of the
compounds
Weights
of their
molecules
= p.
Specific
heats of
unit weight
= c.
Specific
heats of
the molecules
= p x c.
No. of
atoms in
the
molecules
= n.
Specific
heat of
each atom
= (p x c) / n.
HgCl2 .2710.0688918.6691936.22306
ZnCl2 .1340.1361818.6566636.21888
SnCl2 .188.60.1016119.16364636.387882
MnCl2 .1260.1425517.9613035.98710
PbCl2 .2780.0664118.4619836.15399
MgCl2 .950.194618.487036.1623
CaCl2 .1110.164218.226236.0754
BaCl2 .2080.0895718.6305636.21018
HgI2 .4540.0419719.0543836.35146
PbI2 .4610.0426719.6708736.55695

Some of the metals indicated above make other compounds with chlorine, bromine, and iodine, whose molecular weights may be determined and compositions compared ; in such cases the values found for the atomic weights are confirmed. Thus, for example, a molecule of perchloride of tin weighs 259.6, and contains 117.6 of tin (=Sn) and 142 of chlorine (=Cl4). A molecule of perchloride of iron weighs 325, and contains 112 of iron (=Fe2) and 213 of chlorine (=Cl6).

For zinc there are some volatile compounds which confirm the atomic weights fixed by me. Chemists believing chloride of zinc to be of the same type as hydrochloric acid, made the atom of zinc Zn = 33, that is half of that adopted by me ; having them prepared some compounds of zinc with the alcohol radicals, they were astonished that, expressing the composition by folmulae corresponding to gaseous volumes equal to those of other well-known compounds, it was necessary to express the quantity of zinc contained in the molecule by Zn2 being only a single atom, which is equivalent in its saturation capacity to two atoms of hydrogen. Since in the sequel of my lectures I return to this arguement, you will therefore find it spoken of later in this abstract.

Are the atoms of all these metals equal to their molecules or to a simple sub-multiple of them? I gave you above the reasons which make me think it probable that the molecules of these metals are similar to that of mercury ; but I warn you now that I do not believe my reasons to be of such value as to lead to that certainty which their vapour densities would give us if we only knew them.

Reviewing what I show in the lecture of which I have given an abstract, we find it amounts to the following :--Not all the lower chlorides corresponding to the oxide with one atom of oxygen have the same constitution ; some of them contain a single atom of chlorine, others two, as may be seen in the following list :--

HCl
Hydro-
choric acid.
HgCl
Proto-
chloride
of
mercury.
CuCl
Proto-
chloride
of
copper.
KCl
Chloride
of
potassium.
NaCl
Chloride
of
sodium.
LiCl
Chloride
of
lithium.
AgCl
Chloride
of
silver.
AuCl
Proto-
chloride
of gold.
HgCl2
Bichloride
of
mercury
CuCl2
Bichloride
of
copper.
ZnCl2
Chloride
of
zinc.
PbCl2
Chloride
of
ead.
CaCl2
Chloride
of
calcium.
SnCl2
Proto-
chloride
of tin.
PtCl2
Proto-
chloride of
plantium.
etc. etc.

Regnault, having determined the specific heats of the metals and of many of their compounds, had observed that it was necessary to modify the atomic weights attributed to them, namely, to divide by 2 those of potassium, sodium, and silver, leaving the others unaltered ; or, vice versa, to multiply these latter by 2, leaving unaltered those of potassium, sodium, silver, and hydrogen. From this he drew the conclusion that the chlorides of potassium, sodium, and silver, are analogous to calomel (protochloride of mercury) and to protochloride of copper : on the other hand, that those of zinc, lead, calcium, etc., etc., are analogous to corrosive sublimate and to bichloride of copper ; but he supposed that the molecules of calomel and of the analogous chlorides all contained 2 atoms of metal and 2 of chlorine, whilst the molecules of corrosive sublimate and the other analogous chlorides contained 1 atom of metal and 2 of chlorine. Here follows the list of the formulae proposed by Regnault.

H2Cl2
Hydro-
choric acid.
Hg2Cl2
Proto-
chloride
of
mercury.
Cu2Cl2
Proto-
chloride
of
copper.
K2Cl2
Chloride
of
potassium.
Na2Cl2
Chloride
of
sodium.
Li2Cl2
Chloride
of
lithium.
Ag2Cl2
Chloride
of
silver.
Au2Cl2
Proto-
chloride
of gold.
HgCl2
Bichloride
of
mercury
CuCl2
Bichloride
of
copper.
ZnCl2
Chloride
of
zinc.
PbCl2
Chloride
of
ead.
CaCl2
Chloride
of
calcium.
etc. etc.

In truth, using the data for specific heats alone, it is not possible to decide whether the molecules of the chlorides written in the first horizontal line are MCl or M2Cl2; the only thing that can be said is that they contain the same number of atoms of metal and of chlorine. But knowing the densities in the gaseous state of hydrochloric acid and of the two chlorides of mercury, and thus the weights of their molecules, we can compare their composition and decide the question ; and I have already explained to you how I show to my pupils that the molecules of the two chlorides of mercury contain the same weight of mercury, and that the molecule of one of them contains the same quantity of chlorine as hydrochloric acid, i. e., 1/2 molecule of free chlorine, whilst the molecule of the other chloride contains twice as much. This shows with certainty that the two formulae Hg2Cl2, HgCl2 are inexact, because they indicate that in the molecules of the two chlorides there is the same quantity of chlorine and different quantities of mercury, which is precisely the opposite of what is shown by the vapour densities. The formulae proposed by me harmonize the results funished by the specific heats and by the gaseous densities.

Now I wish to direct your attention to an incosistency of Gerhardt. From the theory of Avogadro, Ampère, and Dumas, that is, from the comparision of the gaseous densities as representing the molecular weights, Gerhardt drew arguements in support of the view that the atoms of hydrogen, of chlorine, and of oxygen are half molecules ; that the molecule of water contains twice as much hydrogen as that of hydrochloric acid ; that in the molecule of ether there is twice as much of the radical ethyl as in that of alcohol ; and that to form one molecule of anhydrous monobasic acid two molecules of hydrated acid must come together : and yet Gerhardt did not extend to the whole of chemistry the theory of Ampère, but arbitrarily, in opposition to its precepts, assumed that the molecules of chloride of potassium, of bichloride of mercury, in fact of all the chlorides corresponding to the protoxides, had the same atomic constitution as hydrochloric acid, and that the atoms of all the metals were, like that of hydrogen, a simple sub-multiple of the molecule.

I have already explained to you the reasons which show the contrary.

After having demonstrated the constitution of the chlorides corresponding to the oxides containing one atom of oxygen, I postpone the study of the other chlorides to another lecture, and now define what I mean by capacity for saturation of the various metallic radicals.

If we compare the constitution of the two kinds of chlorides, we observe that one atom of metal is now combined with one atom of chlorine, now with two ; I express this by saying that in the first case the atom of metal is equivalent to 1 of hydrogen, in the second case to 2. Thus, for example, the atom of mercury, as it is in calomel, is equivalent to 1 of hydrogen, whereas in corrosive sublimate it is equivalent to 2 ; the atoms of potassium, sodium, and silver are equivalent to 1 of hydrogen : the atoms of zinc, lead, magnesium, calcium, etc., to 2. Now it is seen from the study of all chemical actions that the number of atoms of the various substances which combine with one and the same quantity of chlorine combine also with one and the same quantity of oxygen, of sulphur, or of any other substance, and vice versa. Thus, for example, if the same quantity of chlorine which combines with a single atom of zinc, or lead, or calcium combines with 2 atoms of hydrogen, of potassium, or of sodium, then the same quantity of oxygen or of any other substance which combines with a single atom of the first will combine with two of the second. This shows that the property possessed by the first atoms of being equivalent to 2 of the second depends on some cause inherent either in their own nature or in the state in which they are placed before combining. We express this constant equivalence by saying that each atom of the first has a saturation capacity twice that of each of the second. These expressions are not new to science, and we now only extend them from compounds of the second order to those of the first order.

For the same reasons given by chemists when they say that phosphoric acid assumes various saturation capacities without changing in composition, it may also be said that the atom of mercury and that of copper assume different saturation capacities according as they are found in the protochlorides or in the bichlorides. Thus, I express the fact that the atoms of these two metals being equivalent to 1 atom of hydrogen in the protochlorides, tend, in double decompositions, to take the place of a single atom of hydrogen, whilst in the bichlorides they tend to take the place of 2 atoms of hydrogen. For the same reason that we say there are three different modifications of phosphoric acid combined with various bases, we may also say that there are two different modifications of the same radical mercury or copper. I call the radicals of the protochlorides and of the corresponding salts, mercurous and cuprous; those of the bichlorides and of the corresponding salts are called mercuric and cupric radicals.

To express the various saturation capacities of the different radicals, I compare them to that of hydrogen or of the halogens, according as they are electro-positive or electro-negative. An atom of hydrogen is saturated by one of a halogen, and vice versa. I express this by saying that the first is a monatomic electro-positive radical, and the second a monatomic electro-negative radical : thus, potassium, sodium, lithium, silver, and the mercurous and cuprous radicals are monatomic electro-positive radicals. The biatomic radicals are those which, not being divisible, are equivalent to 2 of hydrogen or to 2 of chlorine ; among the electro-positive radicals there are the metallic radicals of the mercuric and cupric salts, of the salts of zinc, lead, magnesium, calcium, etc., and amongst the electro-negative we have oxygen, sulphur, selenium, and tellurium, i. e., the amphidic substances. There are, besides, radicals which are equivalent to three or more atoms of hydrogen or of chlorine, but I postpone the study of these until later.

Before finishing the lecture I take care to make clear that the law of equivalents must be considered as a law distinct from the law of atoms.

The latter in fact only says that the quantities of the same element contained in different molecules must be integral multiples of one and the same quantity, but it does not predict, for example, that an atom of zinc is equivalent to 2 of hydrogen not only in its compounds with chlorine, but in all other compounds in which they may replace each other. These constant relations between the numbers of atoms of various substances which displace one another, whatever may be the nature and the number of the other components, is a law which restricts the number of possible combinations, and sums up with greater definiteness all the cases of double decomposition.

I occupy the whole of the seventh lecture in studying some monatomic and biatomic radicals, namely, cyanogen and the alcohol radicals.

I have already told you the method which I faithfully follow for ascertaining the weights and numbers of the molecules of the various substances whose vapour densities can be determined. This method, applied to all the substances which contain alcohol radicals, permits us, so to speak, to follow the path from one molecule to another. To discover the saturation capacity of a radical, it is expedient to begin with the examination of a molecule in which it is combined with a monatomic radical: thus for electro-negative radicals I begin by examining the compounds with hydrogen or with any other monatomic electro-positive radical ; and conversely, for the electro-positive radicals, I examine their compounds with chlorine, bromine, and iodine. Those electro-negative radicals which form a molecule with a single atom of hydrogen are monatomic; those which combine with 2 of hydrogen are biatomic, and so on. Conversely, the electro-positive radicals are monatomic if they combine with a single atom of halogen, biatomic if they combine with 2.

With these rules I establish --

1° That cyanogen, CN, is a monatomic electro-negative radical, and that the molecule of free cyanogen contains twice the quantity of carbon and nitrogen contained in the molecule of the monocyanides; and that in this way cyanogen, CN, behaves in all respects like an atom of chlorine, Cl ;

2° That cacodyle, C2H6As, methyl, CH3, ethyl, C2H5, and the other homologous and isologous radicals, are, like the atom of hydrogen, monatomic, and like it cannot form a molecule alone, but must associate themselves with another monatomic radical, simple or compound, whether of the same or of a different kind ;

3° That ethylene, C2H4, propylene, C3H6, are biatomic radicals analogous to the radicals of mercuric and cupric salts, and to those of the salts of zinc, lead, calcium, magnesium, etc.; and that these radicals, like the atom of mercury, can form a molecule by themselves.

The analogy between the mercuric salts and those of ethylene and propylene has not been noted, so far as I know, by any other chemist. All that I have expounded previously shows it with such clearness that it appears useless to stop and discuss it with you at length. In fact, just as 1 volume of the vapour of mercury, combining with an equal volume of chlorine, makes 1 volume of vapour of mercury bichloride, so 1 volume of ethylene combined with an equal volume of chlorine makes a single volume of vapour of chloride of ethylene -- (oil of Dutch chemists). If the formula of this last is C2H4Cl2 , that of bichloride of mercury should be HgCl2; and if this is the formula of the bichloride of mercury, the chlorides of zinc, lead, calcium, etc., must also be MCl2 ; that is, the atoms of all these metals are, like ethylene and propylene, biatomic radicals. Observing that all the electro-positive monatomic radicals which can be weighed free in the gaseous state, behave like hydrogen, that is, cannot of themselves form molecules, it appears to me very probable that a capacity of saturation equal to that of hydrogen in atoms, or groups which can act as their substitutes, constantly coincides with the fact of their not being able to exist in the isolated state. This is the reason why, until there is proof to the contrary, I believe that the molecules of potassium, sodium, lithium, and silver in the free state are formed of two atoms, that is, are represented by the formulae K2, Na2, Li2, Ag2.

Conversely, observing that if the atom of mercury (which tends to form a biatomic rather than a monatomic radical) like ethylene and propylene can exist in the free state, forming a distinct molecule by itself, it appears to me probable that the atoms of zinc, lead, and calcium should be endowed also with this property, that is, that the molecules of these metals should consist of a single atom. If this correspondence between the number of atoms contained in the molecule and the capacity of the saturation of the atom, or of the group which takes its place, is verified, we may sum up as follows: the metallic radicals whose molecules enter as a whole into compounds are biatomic, those whose atom is half a molecule are monatomic. You already perceive the importance of this correlation, which forces us to conclude that one molecule of mercury (in mercuric salts), or of zinc, or ethylene, or propylene, etc., is equivalent to a molecule of hydrogen, of potassium, or of silver ; thus the former as well as the latter combines with an entire molecule of chlorine, yet with this important difference that the former, not being capable of division, forms a single molecule with two atoms of chlorine, whilst the latter, being divisible, makes with the two atoms of chlorine two distinct molecules. But before drawing a general conclusion of such importance, it is necessary to demonstrate somewhat better the accuracy of the data on which it is founded.

In the eighth lecture I begin to compare the mode of behaviour in some reactions of monatomic and biatomic radicals. The compound radicals indicated in the preceding lecture, since they form volatile compounds, 'frequently afford the means of explaining by analogy what holds good for metallic compounds, the molecular weights of which cannot often be determined directly, since few of them are volatile. This is the great benefit which the study of organic chemistry has rendered to chemistry in general.

In the use of formulae I adhere to the following rules, which I state before representing by means of equations the various types of reaction

1°. I use the coefficients of the symbols in the position of the exponents only when I wish to express that the number of atoms indicated is contained in one and the same molecule ; in other cases I place the coefficient before the symbols. Thus, when I wish to indicate two atoms of free hydrogen as they are contained in a single molecule, I write H2. If, however, I wish to indicate four atoms as they are contained in two molecules, I do not write H4 but 2H2; for the same reason I indicate n atoms of free mercury by the formula nHg.

2°. Sometimes I repeat in the same formula more than once the same symbol to indicate some difference between one part and another of the same element. Thus I write acetic acid C2H3HO2 , to indicate that one of the four atoms of hydrogen contained in the molecule is in a state different from the other three, it alone being replaceable by metals. Occasionally I write the same symbol several times to indicate several atoms of the same element, only to place better in relief what occurs in some reactions.

3°. For this last reason I often write the various atoms of the same component or the residues of various equal molecules in vertical lines. Thus, for example, I indicate the molecule of bichloride of mercury, HgCl2, as follows ; the molecule of acetate of mercury, C4H6HgO4, as follows to indicate that the two atoms of chlorine or the two residues of acetic acid come from two distinct molecules of hydrochloric acid and of hydrated acetic acid.

4°. I indicate by the symbol any monatomic metallic radical whether simple or compound; and with the symbol any biatomic metallic radical. If in the same formula or in the same equation I wish to indicate in general two or more monatomic radicals, the one different from the other, I add to the symbol the small letters a b c, etc., thus indicates a single molecule formed of two different monatomic radicals ; such are the so-called mixed radicals.

The molecules of the monatomic metallic radicals are represented by the formula ; those of the biatomic radicals by the same symbol as for the radical existing in its compounds, since it is the character of these radicals to have the molecule formed of a single atom or of a single group which takes its place. You understand that in speaking of metallic radicals I include all those which can replace metals in saline compounds.

5°. Since all compounds containing in their molecule a single atom of hydrogen replaceable by metals behave similarly when they act on metals or on their compounds, it is convenient to adopt a general formula, and I shall use the following. In HX, X indicates all that there is in the molecule except metallic hydrogen ; thus, for example, in the case of acetic acid, X = C2H3O2 , these being the components which together with H make up the, molecule of hydrated acetic acid. Since there are compounds, also called acids, whose molecules contain two atoms of hydrogen replaceable by metals, and since owing to this last fact they behave in a similar manner towards molecules containing metals, I adopt for them the general formula H2Y, indicating by Y all that there is in the molecules except the two atoms of hydrogen. I hasten to mention that when I indicate by X and by Y the things which in the molecules of acids are combined with H and H2, I do not intend to affirm that X and H, or Y and H2 , are detached within the molecule as its two immediate components; but without touching the question of the disposition of the atoms within the molecule of acids, I only wish to indicate distinctly the part which is not changed in the transformation of the acid into its corresponding salts.

Before treating and discussing the various reactions I remind my pupils once more that all the formula used by me correspond to equal gaseous volumes, the theory of Avogadro and Ampère being constantly the guiding thread which leads me in the study of chemical reactions.

This done, I now give very rapidly an abstract of what I explain in this lecture concerning some reactions of the monatomic and biatomic radicals. I always write the reaction of the molecule containing a monatomic radical alongside a corresponding one of a molecule containing a biatomic radical, in order that the comparison may be easier.

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