Elements and Atoms: Chapter 8
Combination by Volume: Gay-Lussac

The French scientist Joseph-Louis Gay-Lussac (1778-1850; view portrait at the Edgar Fahs Smith collection) made important contributions concerning the physical and chemical properties of gases. Besides the work described in this selection, he helped establish that the volume of a gas at constant pressure varies simply with its temperature [Gay-Lussac 1802], a result known today as Charles' law. His study of gases was not confined to the laboratory: he ascended several thousand meters in a baloon to make meteorological and magnetic measurements, and to collect samples of gas for chemical analysis (as depicted in this illustration in Chemical Achievers at the Chemical Heritage Foundation). Outside his study of gases, Gay-Lussac was first to isolate the element boron. His work on the acids hydrogen fluoride, hydrogen chloride, hydrogen iodide, and hydrogen cyanide led to the realization that acids need not contain oxygen. He was known as a careful experimenter, particularly in developing analytical techniques involving measurements of volume.

The selection presented here deals with the combining volumes of gases, that is to the ratios by volume in which gases react. The empirical evidence presented by Gay-Lussac of gases combining in simple ratios by volume is remarkably consistent with John Dalton's idea of substances combining atom to atom. (See previous chapter.) The congruence between the ideas of Dalton and the experiments of Gay-Lussac is obvious to modern chemists, but was resisted by both Dalton and Gay-Lussac.

Memoir on the Combination of Gaseous Substances with Each Other

Mémoires de la Société d'Arcueil 2, 207-34 (1809), as translated in Alembic Club Reprint No. 4, (Edinburgh, 1890)

Substances, whether in the solid, liquid, or gaseous state, possess properties which are independent of the force of cohesion; but they also possess others which appear to be modified by this force (so variable in its intensity), and which no longer follow any regular law. The same pressure applied to all solid or liquid substances would produce a diminution of volume differing in each case, while it would be equal for all elastic fluids.[1] Similarly, heat expands all substances; but the dilations of liquids and solids have hitherto presented no regularity, and it is only those of elastic fluids which are equal and independent of the nature of each gas.[2] The attraction of the molecules in solids and liquids is, therefore, the cause which modifies their special properties; and it appears that it is only when the attraction is entirely destroyed, as in gases, that bodies under similar conditions obey simple and regular laws.[3] At least, it is my intention to make known some new properties in gases, the effects of which are regular, by showing that these substances combine amongst themselves in very simple proportions, and that the contraction of volume which they experience on combination also follows a regular law. I hope by this means to give a proof of an idea advanced by several very distinguished chemists--that we are perhaps not far removed from the time when we shall be able to submit the bulk of chemical phenomena to calculation.[4]

It is a very important question in itself, and one much discussed amongst chemists, to ascertain if compounds are formed in all sorts of proportions.[5] M. Proust, who appears first to have fixed his attention on this subject, is of opinion that the metals are susceptible of only two degrees of oxidation, a minimum and a maximum; but led away by this seductive theory, he has seen himself forced to entertain principles contrary to physics in order to reduce to two oxides all those which the same metal sometimes presents. M. Berthollet thinks, on the other hand--reasoning from general considerations and his own experiments--that compounds are always formed in very variable proportions, unless they are determined by special causes, such as crystallisation, insolubility, or elasticity. Lastly, Dalton has advanced the idea that compounds of two bodies are formed in such a way that one atom of the one unites with one, two, three, or more atoms of the other.[6] It would follow from this mode of looking at compounds that they are formed in constant proportions, the existence of intermediate bodies being excluded,[7] and in this respect Dalton's theory would resemble that of M. Proust; but M. Berthollet has already strongly opposed it in the Introduction he has written to Thomson's Chemistry,[8] and we shall see that in reality it is not entirely exact. Such is the state of the question now under discussion; it is still very far from receiving its solution,[9] but I hope that the facts which I now proceed to set forth, facts which have entirely escaped the notice of chemists, will contribute to its elucidation.

Suspecting, from the exact ratio of 100 of oxygen to 200 of hydrogen, which M. Humboldt[10] and I had determined for the proportions of water, that other gases might also combine in simple ratios, I have made the following experiments.[11] I prepared fluoboric, muriatic, and carbonic gases, and made them combine successively with ammonia gas. 100 parts of muriatic gas saturate precisely 100 parts of ammonia gas, and the salt which is formed from them is perfectly neutral, whether one or the other of the gases is in excess.[12] Fluoboric gas, on the contrary, unites in two proportions with ammonia gas. When the acid gas is put first into the graduated tube, and the other gas is then passed in, it is found that equal volumes of the two condense, and that the salt formed is neutral. But if we begin by first putting the ammonia gas into the tube, and then admitting the fluoboric gas in single bubbles, the first gas will then be in excess with regard to the second, and there will result a salt with excess of base, composed of 100 of fluoboric gas and 200 ammonia gas.[13] If carbonic gas is brought into contact with ammonia gas, by passing it sometimes first, sometimes second, into the tube, there is always formed a sub-carbonate composed of 100 parts of carbonic gas and 200 of ammonia gas. It may, however, be proved that neutral carbonate of ammonia would be composed of equal volumes of each of these components. M. Berthollet, who has analysed this salt, obtained by passing carbonic gas into the sub-carbonate, found that it was composed of 73.34 parts by weight of carbonic gas and 26.66 of ammonia gas. Now, if we suppose it to be composed of equal volumes of its components, we find from their known specific gravity, that it contains by weight

71.81of carbonic acid
28.19of ammonia
a proportion differing only slightly from the preceding.[14]

If the neutral carbonate of ammonia could be formed by the mixture of carbonic gas and ammonia gas, as much of one gas as of the other would be absorbed; and since we can only obtain it through the intervention of water, we must conclude that it is the affinity of this liquid which competes with that of the ammonia to overcome the elasticity of the carbonic acid, and that the neutral carbonate of ammonia can only exist through the medium of water.

Thus we may conclude that muriatic, fluoboric, and carbonic acids take exactly their own volume of ammonia gas to form neutral salts, and that the last two take twice as much to form sub-salts. It is very remarkable to see acids so different from one another neutralise a volume of ammonia gas equal to their own; and from this we may suspect that if all acids and all alkalis could be obtained in the gaseous state, neutrality would result from the combination of equal volumes of acid and alkali.[15]

It is not less remarkable that, whether we obtain a neutral salt or a sub-salt, their elements combine in simple ratios which may be considered as limits to their proportions. Accordingly, if we accept the specific gravity of muriatic acid determined by M. Biot and myself, and those of carbonic gas and ammonia given by M. Biot and Arago, we find that dry muriate of ammonia is composed of

Muriatic acid,160.761.65
a proportion very far from that of M. Berthollet--[16]
100 of ammonia
213of acid.
In the same way, we find that sub-carbonate of ammonia contains[17]
Carbonic acid,127.356.02
and the neutral carbonate
Carbonic acid,254.671.81

It is easy from the preceding results to ascertain the ratios of the capacity of fluoboric, muriatic, and carbonic acids; for since these three gases saturate the same volume of ammonia gas, their relative capacities will be inversely as their densities, allowance having been made for the water contained in muriatic acid.

We might even now conclude that gases combine with each other in very simple ratios; but I shall still give some fresh proofs.

According to the experiments of M. Amédée Berthollet[18], ammonia is composed of

100 of nitrogen
300 of hydrogen,
by volume.[19]

I have found (1st vol. of the Société d'Arceuil) that sulphuric acid is composed of

100 of sulphurous gas,
50 of oxygen gas.[20]
When a mixture of 50 parts of oxygen and 100 of carbonic oxide (formed by the distillation of oxide of zinc with strongly calcined charcoal) is inflamed, these two gases are destroyed and their place taken by 100 parts of carbonic acid gas. Consequently carbonic acid may be considered as being composed of
100 of carbonic oxide gas,
50 of oxygen gas.[21]

Davy[22], from the analysis of various compounds of nitrogen with oxygen, has found the following proportions by weight:

Nitrous oxide63.3036.70
Nitrous gas44.0555.95
Nitric acid29.5070.50
Reducing these proportions to volumes we find--

Nitrous oxide10049.5
Nitrous gas100108.9
Nitric acid100204.7

The first and the last of these proportions differ only slightly from 100 to 50 and 100 to 200; it is only the second which diverges somewhat from 100 to 100. The difference, however, is not very great, and is such as we might expect in experiments of this sort; and I have assured myself that it is actually nil.[23] On burning the new combustible substance from potash in 100 parts by volume of nitrous gas, there remained over exactly 50 parts of nitrogen, the weight of which, deducted from that of the nitrous gas (determined with great care by M. Berard at Arcueil), yields as a result that this gas is composed of equal parts by volume of nitrogen and oxygen.

We may then admit the following numbers for the proportions by volume of the compounds of nitrogen with oxygen:

Nitrous oxide10050
Nitrous gas100100
Nitric acid100200

From my experiments, which differ very little from those of M. Chenevix, oxygenated muriatic acid is composed by weight of

Oxygen 22.92
Muriatic acid 77.08[24]

Converting these quantities into volumes, we find that oxygenated muriatic acid is formed of

Muriatic gas300.0
Oxygen gas103.2
a proportion very nearly
Muriatic gas300
Oxygen gas100[25]

Thus it appears evident to me that gases always combine in the simplest proportions when they act on one another; and we have seen in reality in all the preceding examples that the ratio of combination is 1 to 1, 1 to 2, or 1 to 3. It is very important to observe that in considering weights there is no simple and finite relation between the elements of any one compound; it is only when there is a second compound between the same elements that the new proportion of the element that has been added is a multiple of the first quantity. Gases, on the contrary, in whatever proportions they may combine, always give rise to compounds whose elements by volume are multiples of each other.[26]

Not only, however, do gases combine in very simple proportions, as we have just seen, but the apparent contraction of volume which they experience on combination has also a simple relation to the volume of the gases, or at least to that of one of them.[27]

I have said, following M. Berthollet, that 100 parts of carbonic oxide gas, prepared by distilling oxide of zinc and strongly calcined charcoal, produce 100 parts of carbonic gas on combining with 50 of oxygen. It follows from this that the apparent contraction of the two gases is precisely equal to the volume of oxygen gas added. The density of carbonic gas is thus equal to that of carbonic oxide gas plus half the density of oxygen gas; or, conversely, the density of carbonic oxide gas is equal to that of carbonic gas, minus half that of oxygen gas. Accordingly, taking the density of air as unity, we find the density of carbonic oxide gas to be 0.9678, instead of 0.9569 experimentally determined by Cruickshanks. We know, besides, that a given volume of oxygen produces an equal volume of carbonic acid; consequently oxygen gas doubles its volume on forming carbonic oxide gas with carbon, and so does carbonic gas on being passed over red-hot charcoal.[28] Since oxygen produces an equal volume of carbonic gas, and the density of the latter is well known, it is easy to calculate the proportion of its elements. In this way we find that carbonic gas is composed of

27.38 of carbon,
72.62 of oxygen,
and carbonic oxide of
42.99 of carbon,
57.01 of oxygen.[29]

Pursuing a similar course, we find that if sulphur takes 100 parts of oxygen to produce sulphurous acid, it takes 150 parts to produce sulphuric acid. As a matter of fact, we find that sulphuric acid, according to the experiments of MM. Klaproth, Bucholz, and Richter, is composed of 100 parts by weight of sulphur and 138 of oxygen.[30]

On the other hand sulphuric acid is composed of 2 parts by volume of sulphurous gas, and 1 of oxygen gas. Consequently the weight of a certain quantity of sulphuric acid should be the same as that of 2 parts of sulphurous acid and 1 of oxygen gas, i.e., 2x2.265, plus 1.10359-- 5.63359; seeing that, according to Kirwan, sulphurous gas weighs 2.265, the density of air being taken as unity. But from the proportion of 100 of sulphur to 138 of oxygen, this quantity contains 3.26653 of oxygen, and if we subtract from it 1.10359 there will remain 2.16294 for the weight of oxygen in 2 parts of sulphurous acid, or 1.08147 for the weight of oxygen contained in 1 part.

Now as this last quantity only differs by 2 per cent. from 1.10359, which represents the weight of oxygen gas, it must be concluded that oxygen gas, in combining with sulphur to form sulphurous gas, only experiences a diminution of a fiftieth of its volume, and this would probably be nil if the data I have employed were more exact. On this last supposition, using Kirwan's value for the specific gravity of sulphurous gas, we should find that this acid is composed of

100.00 of sulphur,
95.02 of oxygen.
But, if, adopting the preceding proportions for sulphuric acid, we allow, as appears probable, that 100 of sulphurous gas contain 100 of oxygen gas, and that 50 have still to be added to convert it into sulphuric acid, we shall obtain for the proportions in sulphurous acid
100.00 of sulphur
92.0 of oxygen.[31]

Its specific gravity calculated on the same suppositions, and referred to that of air, would be 2.30314, instead of 2.2650 as Kirwan found directly.[32],[33]

Phosphorus is very closely connected with sulphur, seeing that both have nearly the same specific gravity. Consequently phosphorus should take up twice as much oxygen to become phosphorous acid, as to pass from this state into phosphoric acid. Since the latter is composed, according to Rose, of

100.0 of phosphorus,
114.0 of oxygen,
it follows that phosphorous acid should contain

100.0 of phosphorus,
76.0 of oxygen.[34]

We have seen that 100 parts of nitrogen gas take 50 parts of oxygen gas to form nitrous oxide, and 100 of oxygen gas to form nitrous gas.[35] In the first case, the contraction is a little greater than the volume of oxygen added; for the specific gravity of nitrous oxide, calculated on this hypothesis, is 1.52092, while that given by Davy is 1.61414. But it is easy to show, from some of Davy's experiments, that the apparent contraction is precisely equal to the volume of oxygen gas added. On passing the electronic spark through a mixture of 100 parts of hydrogen and 97.5 of nitrous oxide the hydrogen is destroyed, and 102 parts of nitrogen remain, including that quantity which is almost always mixed with the hydrogen, and a little of the latter gas which has escaped combustion. The residue, after making all corrections, would be nearly equal in volume to the nitrous oxide employed. Similarly, on passing the electric spark through a mixture of 100 parts of phosphoretted hydrogen and 250 of nitrous oxide, water and phosphoric acid are formed, and exactly 250 parts of nitrogen remain[36],--another evident proof that the apparent contraction of the elements of nitrous oxide is equal to the whole volume of oxygen added. From this circumstance, its specific gravity referred to that of air should be 1.52092.

The apparent contraction of the elements of nitrous gas appears, on the other hand, to be nil. If we admit, as I have shown, that it is composed of equal parts of oxygen and nitrogen, we find that its density, calculated on the assumption that there is no contraction, is 1.036, while that determined directly is 1.038.[37]

Ammonia gas is composed of three parts by volume of hydrogen and one of nitrogen, and its density compared to air is 0.596. But if we suppose the apparent contraction to be half of the whole volume, we find 0.594 for the density. Thus it is proved, by this almost perfect concordance, that the apparent contraction of its elements is precisely half the total volume or rather double the volume of the nitrogen.

I have already proved that oxygenated muriatic gas is composed of 300 parts of muriatic gas and 100 of oxygen gas. Admitting that the apparent contraction of the two gases is half the whole volume, we find 2.468 for its density, and by experiment 2.470. I have also assured myself by several experiments that the proportions of its elements are such that it forms neutral salts with the metals. For example, if we pass oxygenated muriatic gas over copper, there is formed a slightly acid green muriate, and a little oxide of copper is precipitated, because the salt cannot be obtained perfectly neutral. It follows from this that in all the muriates, as in oxygenated muriatic acid, the acid reduced to volume is thrice the oxygen. It would be the same for carbonates and fluorides, the acids of which have for equal volumes the same saturation capacity as muriatic acid.[38]

We see, then, from these various examples, that the contraction experienced by two gases on combination is in almost exact relation with their volume, or rather with the volume of one of them. Only very slight differences exist between the densities of compounds obtained by calculation and those given by experiment, and it is probable that, on undertaking new researches, we shall see them vanish entirely.

Recalling the great law of chemical affinity, that every combination involves an approximation of the elementary molecules, it is difficult to conceive why carbonic oxide gas should be lighter than oxygen.[39] Indeed, that is the principal reason which has led M. Berthollet to assume the existence of hydrogen in this gas, and thus explain its low density. But it seems to me that the difficulty arises from supposing that the approximation of the elementary molecules is represented in gases by the diminution of volume which they suffer on combination. This supposition is not always true, and we might cite several gaseous combinations, the constituent molecules of which would be brought very close together, although there is not only no diminution of volume, but even a dilation. Such, for example, is nitrous gas, whether we consider it as being formed directly from nitrogen and oxygen, or from nitrous oxide and oxygen. In the first case, there is no diminution of volume; and in the second, there would be dilation, for 100 parts of nitrous oxide and 50 of oxygen would produce 200 of nitrous gas.[40] We know too that carbonic gas represents an exactly equal volume of oxygen, and that the affinity which unites its elements is very powerful. Nevertheless, if we admitted an immediate relation between the condensation of the elements and the condensation of volume, we should conclude, contrary to experiment, that there is no condensation. Otherwise it would be necessary to suppose that if carbon were in the gaseous state it would combine in equal volumes (or in any other proportion) with oxygen, and that the apparent condensation would then be equal to the whole volume of the gaseous carbon. But if we make this supposition for carbonic acid, we may also make it for carbonic oxide, by assuming, for instance, that 100 parts of the gaseous carbon would produce 100 parts of the gas on combining with 50 parts of oxygen. However it may stand with these suppositions, which only serve to make it conceivable that oxygen can produce a compound lighter than itself by combining with a solid substance, we must admit, as a truth founded on a great number of observations, that the condensation of the molecules of two combining substances, in particular of two gases, has no immediate relation to the condensation of volume, since we often see that whilst one is very great the other is very small or even nil.

According to Dalton's ingenious idea, that combinations are formed from atom to atom, the various compounds which two substances can form would be produced by the union of one molecule of the one with one molecule of the other, or with two, or with a greater number, but always without intermediate compounds.[41] Thomson and Wollaston have indeed described experiments which appear to confirm this theory. Thomson has found that super-oxalate of potash contains twice as much acid as is necessary to saturate the alkali; and Wollaston, that the sub-carbonate of potash contains, on the other hand, twice as much alkali as is necessary to saturate the acid.

The numerous results I have brought forward in this Memoir are also very favorable to the theory. But M. Berthollet, who thinks that combinations are made continuously, cites in proof of his opinion the acid sulphates, glass alloys, mixtures of various liquids,--all of which are compounds with very variable proportions, and he insists principally on the identity of the force which produces chemical compounds and solutions.[42]

Each of these two opinions has, therefore, a large number of facts in its favour; although they are apparently utterly opposed, it is easy to reconcile them.

We must first of all admit, with M. Berthollet, that chemical action is exercised indefinitely in a continuous manner between the molecules of substances, whatever their number and ratio may be, and that in general we can obtain compounds with very variable proportions. But then we must admit at the same time that,--apart from insolubility, cohesion, and elasticity, which tend to produce compounds in fixed proportions,--chemical action is exerted more powerfully when the elements are in simple ratios or in multiple proportions among themselves, and that compounds are thus produced which separate out more easily. In this way we reconcile the two opinions, and maintain the great chemical law, that whenever two substances are in presence of each other they act in their sphere of activity according to their masses, and give rise in general to compounds with very variable proportions, unless these proportions are determined by special circumstances.


I have shown in this Memoir that the compounds of gaseous substances with each other are always formed in very simple ratios, so that representing one of the terms by unity, the other is 1, or 2, or at most 3. These ratios by volume are not observed with solid or liquid substances, nor when we consider weights, and they form a new proof that it is only in the gaseous state that substances are in the same circumstances and obey regular laws. It is remarkable to see that ammonia gas neutralizes exactly its own volume of gaseous acids; and it is probable that if all acids and alkalies were in the elastic state, they would all combine in equal volumes to produce neutral salts. The capacity of saturation of acids and alkalies measured by volume would then be the same, and this might perhaps be the true manner of determining it. The apparent contraction of volume suffered by gases on combination is also very simply related to the volume of one of them, and this property likewise is peculiar to gaseous substances.[43]


[1]Gay-Lussac states a consequence of Boyle's law [Boyle 1662]. According to Boyle's law, the volume of a gas at constant temperature is inversely proportional to its pressure: V ∝ 1/p. Furthermore, the proportionality constant was the same for every gas. The result is that a given volume of any gas subjected to a given compression (pressure increase) will result in the same change of volume. This regular behavior of gases is contrasted with that of solids and liquids: compressing them also diminishes their volume, but by a small amount and a different amount for different substances.

[2]Gay-Lussac here states an aspect of Charles' law (named after his contemporary Jacques Charles), a subject on which he also conducted significant research. [Gay-Lussac 1802] The extent to which a gas expands at constant pressure is directly proportional to its temperature, with a proportionality constant the same for all gases. Solids and liquids also expand upon heating, but each to a different extent.

[3]Gay-Lussac offers some insight into the reason behind a well-known fact in the physical sciences: gases are simple while solids and especially liquids are complicated. That is, many properties of gases are regular, and are either the same in different gases or they vary in a fairly simple way with fundamental properties like mass. Properties of solids and liquids tend to be not nearly so regular. After giving some examples of the regular behavior of gases, he correctly speculates that the details of cohesion in solids and liquids differ from substance to substance, and in the absence of that cohesion (i.e., in gases) the behavior is simpler.

[4]The application of mathematics to chemistry was a common goal in chemistry from the late 18th century. The philosopher Immanuel Kant considered chemistry to be incapable of the application of mathematics [Kant 1786]. (Kant also classed chemistry as "nothing more than a systematic art or experimental doctrine, but never science proper.") Jeremias Richter had been a student of Kant, and he pursued the role of mathematics in chemistry. In 1791, Richter formulated law of definite proportions and idea of associating combining masses (equivalents) to reacting substances. [Partington 1948] The collection of quantitative data on combining masses, Dalton's program of compiling specific heats and his program of measuring atomic weights (previous chapter), and Gay-Lussac's work on combining volumes can be seen as efforts to make chemistry a quantitative science.

[5]Are the proportions of elements in a chemical compound variable or definite? That is the question Gay-Lussac poses. At this time, examples were already known of more than one compound being formed from the same two elements in different compositions. For example, there are two distinct compounds of carbon and oxygen, two different gases with different properties. Given the existence of multiple compounds of the same elements, is there a relationship of the compositions (combining proportions) in these compounds?

[6]Gay-Lussac summarizes three opinions on the question of combining proportions: Joseph-Louis Proust (1754-1826; see portrait at the Edgar Fahs Smith collection, University of Pennsylvania) believed that there were only two combining proportions possible for any pair of elements [e.g. Proust 1799]; Claude-Louis Berthollet (1748-1822; see portrait at the Edgar Fahs Smith collection, University of Pennsylvania) believed that combining proportions between two elements was as a rule variable between upper and lower limits; and Dalton [Dalton 1808] believed that there were only a few (though perhaps more than two) discrete combining proportions. (By the way, Proust was not the first to pursue this question; Richter had preceded him (note 4).)

[7]How does the hypothesis of definite proportions follow from the atomic hypothesis? Consider the following example. Suppose (as Dalton did) that carbon and oxygen form two different compounds, one consisting of an oxygen atom bound to a carbon atom and the other consisting of two oxygen atoms bound to a carbon atom; suppose further that the mass of a carbon atom is 12 and that of an oxygen atom 16. Each of these compounds has a definite ratio of oxygen mass to carbon mass, namely 16:12 = 11/3 and 32:12 = 22/3. It only makes sense to speak of whole numbers of atoms, so there is no possibility of intermediate mass ratios--at least in compounds that have only one carbon atom.

[8]Thomas Thomson presented Dalton's atomic hypothesis before Dalton published his A New System of Chemical Philosophy. The third edition of Thomson's System of Chemistry [Thomson 1807] contains a description of Dalton's views. Berthollet included some critical remarks on Dalton's ideas in his introduction to a French edition of Thomson's book.

[9]By the time Gay-Lussac presented this paper, most of the available evidence supported the hypothesis of definite proportions, and much of the evidence for variable proportions could be explained as due to mixtures rather than compounds. Indeed, the results Gay-Lussac presents support the hypothesis of definite proportions and Dalton's atomic hypothesis. Interestingly, though, Gay-Lussac's attitude in this paragraph seems either neutral or inclined to disbelieve Berthollet's opponents. The fact that Gay-Lussac was an associate and protégé of Berthollet perhaps inclined Gay-Lussac to have more confidence in his work than perhaps the evidence merited. [Nash 1957]

[10]The Prussian Baron Alexander von Humboldt (1769-1859; see portrait at Humboldt-Universität, Berlin) was better known as a naturalist and geographer than a chemist. The early 19th century, however, was still a time of generalists rather than specialists in science.

[11]This and the following paragraphs contain the results of many chemical analyses of compounds with unfamiliar names. Notes will explain some of the reactions (in modern notation) and the modern names and formulas of the compounds. What is important, however, is not so much the identity of the compounds involved in these reactions (for indeed, Gay-Lussac did not know the formulas of many of them, and did not report the quantities of product formed), but the fact that in all the reactions the gases combined in simple ratios by volume. That is to say (for example) one liter of one reactant with one, two, or three liters of another. Consideration of combining masses led to ratios not nearly as simple. In the first example given, that of water, Gay-Lussac means (although does not say so explicitly) that water contains 200 parts of hydrogen by volume for every 100 parts of oxygen.

[12]"Muriatic gas" is now known as hydrogen chloride or hydrochloric acid (HCl). The formula for ammonia is NH3. The reaction between these gases produces a solid salt, "muriate of ammonia" in Gay-Lussac's day, now called ammonium chloride:

NH3 + HCl --> NH4Cl .
[13]"Fluoboric gas" (fluoboric acid) is a complex between hydrogen fluoride and boron trifluoride: HF·BF3. If one slowly adds ammonia to HF·BF3, the resulting solid forms according to the reaction:
NH3 + HF·BF3 --> NH4BF4 .
However, if one slowly adds HBF4 to ammonia, the reaction occurs according to:
2 NH3 + HF·BF3 --> NH4F + NH3BF3 .
Thus two distinct reactions take place, one involving equal volumes of ammonia and fluoboric acid, the other requiring twice as much ammonia as fluoboric acid.

[14]"Carbonic gas," also known at this time as "carbonic acid," is now known as carbon dioxide (CO2). The reactions Gay-Lussac reports on only occur between dissolved ammonia and carbon dioxide, as he notes in the next paragraph. When carbon dioxide is dissolved in water, it first forms a compound with formula H2CO3; that substance is what is now called carbonic acid. The available data (Berthollet's) concern masses, not volumes. Gay-Lussac, however, is able to convert masses to volumes, because he knows the density of carbon dioxide and ammonia gases. (Density or specific gravity is mass divided by volume. Knowledge of any two of density, mass, and volume permits calculation of the third.) At any rate, the reactions involving dissolved carbon dioxide are:

NH3 + H2CO3 --> NH4HCO3 ,
2 NH3 + H2CO3 --> (NH4)2CO3 .
The first requires equal volumes of ammonia and carbon dioxide; the second requires twice as much ammonia as carbon dioxide.

[15]After presenting observations on three different acids, Gay-Lussac formulates a hypothesis that generalizes from those observations.

[16]An earlier footnote (9) suggested that Gay-Lussac was perhaps not entirely objective regarding the work of his associate Berthollet. Note here, however, that Gay-Lussac is willing to note an instance where Berthollet's measurement and his own disagree. So he was not afraid to disagree with Berthollet in print. (As a further irony, Berthollet's measurement here is correct!) I think the attitude Gay-Lussac exhibits toward Berthollet and his work is not uncommon in science. Particular measurements or observations seem to be more clear cut than theories or hypotheses; they appear to be more "matters of fact," closer to direct experience. Since their acceptance or rejection requires less judgment, it is easier for one to maintain objectivity about them. In concrete terms, Gay-Lussac has enough objectivity and integrity to disagree openly with Berthollet about the analysis of "muriate of ammonia," even while his respect for Berthollet seems to cloud his judgment concerning definite proportions.

[17]Note that the combining ratios which are very simple in terms of volumes are not at all simple in terms of mass (as in this and the previous paragraph). Yet even from the combining masses, a simple relationship is apparent between the two carbonates of ammonia: the "neutral carbonate" requires twice as much carbonic acid as the "sub-carbonate." This relationship is apparent in the left-hand column of numbers and not in the right; that is, the relationship is clear when combining weights are reported for a given weight of ammonia, but not clear when they are reported as a percentage of the product.

[18]Son of Claude Louis Berthollet.

[19]That is, ammonia can be regarded as a product of a reaction between hydrogen and nitrogen. The reaction is:

3 H2 + N2 --> 2 NH3 .

[20]The reaction is:

2 SO2 + O2 --> 2 SO3 .

[21]The reaction is:

2 CO + O2 --> 2 CO2 .

[22]Humphry Davy (1778-1829; see portrait at National Portrait Gallery, London) was an English chemist best known for isolating several elements in the early 19th century mainly by newly developed electrochemical means. Gay-Lussac in collaboration with Louis Jacques Thénard (1777-1857; see portrait at the Edgar Fahs Smith collection, University of Pennsylvania) used similar electrochemical techniques, often working on similar projects at about the same time.

[23]One may ask how Gay-Lussac convinced himself that the actual ratio was 100:100 by volume. How could one convince oneself? One possible way, of course, is to try to replicate the experiment. One might also use estimates of the error inherent in Davy's data. Quantitative estimates of error and precision were not often found in chemical analyses published at this time; indeed, statistical methods for the quantitative treatment of error were not yet well developed. The question "How close is close enough?" is an important one in experimental science, and one that will be treated in more detail later in a later chapter. Here Gay-Lussac presents some additional evidence for the composition of "nitrous gas."

[24]"Oxygenated muriatic acid" is now known as chlorine, Cl2; it contains no oxygen. Its name until 1810 (oxymuriatic acid), however, reflected the belief that it did. It is difficult to explain completely the analyses Gay-Lussac reports here [Gay-Lussac & Thénard 1809]: how was oxygen reported when there was no oxygen present? It is worth remembering that whatever reagent an analyst used to try to break "oxygenated muriatic acid" into its elements most likely reacted with the already elementary chlorine to form a new compound. Note also that chlorine, like oxygen, is an oxidizer, so a reaction of "oxygenated muriatic acid" could well be confused with a similar reaction of the oxygen it supposedly contains.

We see an example of this in the next footnote (present in Gay-Lussac's original): he infers a quantity of oxygen in "oxygenated muriatic acid" from the amount of hydrogen consumed in a reaction with it. He notes that "oxygenated muriatic acid" can destroy an equal volume of hydrogen, a reaction we now write as

Cl2 + H2 --> 2 HCl ,
from which he infers that oxygen constitutes half its volume.

[25]In the proportion of weight of oxygenated muriatic acid, the muriatic acid is supposed to be free from water, whilst in the proportion by volume it is supposed to be combined with a fourth of its weight of water, which, since the reading of this paper, M. Thénard and I have proved to be absolutely necessary for its existence in the gaseous state. But since the simple ratio of 300 of acid to 100 of oxygen cannot be due to chance, we must conclude that water by combining with dry muriatic acid to form ordinary muriatic acid does not sensibly change its specific gravity. We should be led to the same conclusion from the consideration that the specific gravity of oxygenated muriatic acid, which from our experiments contains no water, is exactly the same as that obtained by adding the density of oxygen gas to three times that of muriatic gas to three times that of muriatic gas, and taking half of this sum. M. Thénard and I have also found that oxygenated muriatic gas contains precisely half its volume of oxygen, and that it can destroy in consequence its own volume of hydrogen. [Gay-Lussac's note]

[26]In sum, there is no simple relationship in the combining weights of compounds, but gases seem to combine in simple ratios by volume. The fact that gases combine in simple ratios by volume is consistent with Dalton's atomic theory if the number of atoms or molecules in a given volume of different gases was equal or was itself a simple ratio. For example, if the number of molecules in a given volume of nitrogen was the same as that in hydrogen, then the volume ratio of three hydrogens to one nitrogen corresponds to a reaction in which every nitrogen atom combines with three hydrogen atoms. (This turns out to be the case, as is argued in the next chapter.) Or it is also plausible, although it turns out not to be true, that a given volume of nitrogen might contain three times as many molecules as the same volume of hydrogen; then the reaction would involve every atom of nitrogen reacting with one atom of hydrogen. Either way, the observation that reactions occur among whole numbers of volumes of gas is consistent with Dalton's idea of reactions taking place among atoms--which by definition come only in whole numbers.

Gay-Lussac mentions in passing that the combining weights of multiple compounds of the same element are simply related (as in carbonic acid and carbonic oxide mentioned above). That is, the weights of one element that can combine with a given amount of another element (in different compounds of those elements) are simple multiples. This is the law of multiple proportions. This law also follows from Dalton's atomic hypothesis. If compounds are formed by combinations of small numbers of atoms, each of which has a definite weight, then the weight of B in the compound ABn is obviously n times that in the compound AB. Atoms come only in whole numbers, so n must be a whole number.

[27]Gay-Lussac now turns his attention to the products as well as the reactants. When the product of a reaction is also gaseous, its volume is also closely related to the volumes of the reactants. Actually, Gay-Lussac focuses not on the volume of the product but on the "contraction of volume," that is the difference in volume between the product and the combined reactants. In the example Gay-Lussac takes up, the volume of CO2 produced in the reaction of CO and O2 is the same as the volume of CO used up, not the combined volume of CO and O2.

[28]The reactions mentioned here are:

O2 + C --> CO2 ,
O2 + 2 C --> 2 CO ,
CO2 + C --> 2 CO .
In each case the carbon or charcoal is a solid, not a gas, so the comparison is between the first reactant and the product (which are both gases).

[29]Gay-Lussac expresses the composition by weight here as a percentage, which disguises the multiple-proportions relationship of these two carbon-oxygen compounds. (See footnote 17.) These reported compositions are equivalent to saying that CO2 has 2.65 grams of oxygen for every gram of carbon and that CO has 1.33 grams of oxygen for every gram of carbon.

[30]Gay-Lussac's exposition from here to the concluding paragraph is not as clear or sharp as it has been to this point. He strays from the focus of the paper so far: from demonstrating the combination of gases in simple ratios by volume to applying the principle that gases combine in simple ratios. These applications amount to testable predictions based on the simplicity of combining volumes. Unfortunately, he does not tell the reader where he is going.

The objects of the calculations here are to compute the change in volume of the reaction between oxygen and sulfur to form "sulphurous gas" (SO2) and to infer the combining weights of sulfur and oxygen in this compound. Among the flaws in exposition, he refers to numbers without stating what they represent. In addition, he expresses his numbers to a far greater number of decimal places than the precision of the experimental data warrant. Still, it is worthwhile reconstructing the calculation concerning sulfur-compounds to show just how susceptible chemistry already was to quantitative treatment.

The formation of "sulphurous gas" from sulfur and oxygen is not a reaction about which Gay-Lussac has direct information, so he uses information from a variety of related reactions. He knows that two volumes of "sulphurous gas" combine with one of oxygen to make two of "sulphuric acid" (SO3), or in modern notation:

2 SO2 + O2 --> 2 SO3 .
The weight of sulphuric acid produced for every volume of oxygen that reacts is 2x2.265 + 1.10359 = 5.634 (for 2.265 is the density of "sulphurous gas" and 1.10359 that of oxygen). How much of this is oxygen? Here Gay-Lussac uses the quoted result that "sulphuric acid" contains 138 parts oxygen for every 100 parts sulfur, so the oxygen in the sample weighs . Now 1.10359 of this came from the oxygen in the reaction, so 2.163 must have been present in the "sulphurous gas." This represents two volumes of "sulphurous gas," so half of it is the weight of oxygen in one volume of the gas. Noticing that this is very close to the weight of oxygen in one volume of oxygen gas, Gay-Lussac concludes that one volume of oxygen reacts with solid sulfur to produce one volume of "sulphurous gas."

[31]Gay-Lussac goes on to compute the mass ratio of oxygen to sulfur in "sulphurous gas." The proportion is (2.265–1.10359):1.10359, a ratio of the part of the density of "sulphurous gas" due to sulfur vs. the density of oxygen in "sulphurous gas." The result is 100:95. The law of multiple proportions and the mass ratio in "sulphuric acid" would require 100:92, for the ratio of oxygen in "sulphuric acid," namely 100:138, must have 1.5 times as much oxygen as in "sulphurous gas."

[32]In order to remove these differences it would be necessary to make new experiments on the density of sulphurous gas, on the direct union of oxygen gas with sulphur to see if there is contraction, and on the union of sulphurous gas with ammonia gas. I have found, it is true, on heating cinnabar in oxygen gas, that 100 parts of this gas only produce 93 of sulphurous gas. It also appeared as if less sulphurous gas than ammonia gas was necessary to form a neutral salt. But these experiments were not made under suitable conditions--especially the last, which could only be made in presence of water, the sulphurous gas decomposing and precipitating sulphur immediately on being mixed with ammonia gas,--I intend to repeat them and determine exactly all the conditions before drawing any conclusion from them. This is all the more necessary, as sulphurous gas can be used to analyze sulphuretted hydrogen gas, if its proportions are well known. [Gay-Lussac's note]

[33]Cinnabar is mercuric sulfide, HgS. Heating cinnabar in the presence of oxygen causes the sulfur to combine with oxygen.

The upshot of Gay-Lussac's footnote is that more careful experiments are needed to determine the density of the sulfur-oxygen compounds. With more accurate densities, calculations like the ones just made can be used to arrive at the composition of other gases that contain sulfur.

[34]This paragraph begins with an erroneous premise, a mistaken analogy between phosphorus and sulfur. The "acids" of phosphorus (i.e., their acid anhydrides--the oxides that become acids when combined with water) are not exactly analogous to those of sulfur.

[35]Without warning, Gay-Lussac switches from combining ratios by mass (in the previous paragraph) to combining ratios by volume. In this paragraph, he suggests a correction to the density of nitrous oxide as reported by Davy. The formation of nitrous oxide from nitrogen and oxygen, Gay-Lussac maintains, involves a contraction by the amount of oxygen added. This is evident when expressed in modern notation,

2 N2 + O2 --> 2 N2O ,
for the volume of N2O formed is equal to that of the original N2, not the combined volume of N2 and O2. Because 2 volumes of N2O contains the mass of 2 volumes of N2 and 1 volume of O2, its density ought to be that of N2 plus half that of O2. This is another prediction (a correct one) based on gases combining in simple ratios by volume.

[36]The combining ratio reported here appears to be incorrect. The most likely reaction, written in modern notation, is:

PH3 + 4 N2O --> H3PO4 + 4 N2 .
The volume ratio of nitrous oxide to phosphine (PH3) is 4 to 1, not 2.5 to 1; however, the volume of nitrogen produced is still equal to the volume of nitrous oxide used up.

[37]The density of "nitrous gas" calculated on the assumption of a simple relationship between reactant and product volumes agrees well with the measured density. This provides additional evidence for the relationship between volumes. In modern notation, we would write the reaction:

N2 + O2 --> 2 NO .
Here the volume of product is the same as that of the reactants, so there is no contraction. Gay-Lussac makes a similar comparison in the next paragraph for the reaction:

N2 + 3 H2 --> 2 NH3 .
Here the volume of the product is twice the original volume of nitrogen, but half the total volume of reactants.

[38]See note 24 above for oxygenated muriatic gas. Here Gay-Lussac assumes a reaction whose volume proportions are:

oxygen + 3 muriatic gas --> 2 oxygenated muriatic gas .
The coefficient on the product comes from the statement that the apparent contraction of the gases is half the volume of the reactants. In modern terms, the proposed reaction is
O2 + 3 HCl --> 2 Cl2.
Of course, this reaction is incorrect. Nonetheless, the implied relationship among densities is (coincidentally) correct. In hindsight, we can see that this is because the mass of the reactants is about the same as that of the products, as can be seen using modern atomic weights.

[39]Gay-Lussac touches on an apparent paradox, subsequently explained by Avogadro (next chapter): how can an "association" (a reaction in which two substances combine to form a single product) lead to a gaseous product less dense than one of its reactants? Carbonic oxide (CO) can be formed from the reaction of oxygen with solid carbon; how can the carbonic oxide gas be lighter than the oxygen from which it was made? Gay-Lussac and his contemporaries pictured oxygen as a simple atom, and were naturally puzzled how CO gas could weigh less than O. We understand that oxygen actually exists as a diatomic molecule, i.e., two oxygen atoms bound together. There is nothing particularly surprising about CO weighing less than O2.

[40]A related apparent paradox has to do with the diminution in volume expected in "association" reactions. In the reaction between nitrogen and oxygen to form "nitrous air," the mental picture was one of N atoms and O atoms widely separated combining to produce NO molecules in which an N and O were close together. Surely the NO ought to take up less space than the combined N and O! But we know that the reaction is not really an association of N and O atoms, but rather a change of bonding partners:

N2 + O2 --> 2 NO .
The reaction does not change the number of molecules in the gas phase, so no change in volume accompanies it. Even more puzzling was the reaction between nitrous oxide and oxygen to produce "nitrous air." This was also thought of as an association, for which a diminution of volume would be expected; however, an increase in volume (dilation) was observed. In modern notation, we have:

2 N2O + O2 --> 4 NO .
[41]That is, Dalton's theory would not admit compounds of intermediate composition. See footnote 7 above. The experiments Gay-Lussac mentions illustrate the law of multiple proportions, suggesting reaction of a molecule of one reagent with one or two molecules of another.

[42]Gay-Lussac realizes that the examples he presents are consistent with definite proportions and with Dalton's theory. Still, he cites what he regards as examples that support Berthollet's hypothesis of variable proportions, even though those examples are not what the paper is concerned with. Today chemistry makes a distinction between mixtures and compounds. Mixtures are not chemically pure substances, do not involve the strong association of a chemical bond, and may be formed in variable proportions. Alloys, solutions, and mixtures of liquids are mixtures, not compounds. Berthollet did not observe such a distinction. Gay-Lussac goes on to attempt to reconcile Berthollet's and Dalton's hypotheses in a way that must strike modern readers as unconvincing and incorrect.

If Gay-Lussac's attitude toward Dalton's work was lukewarm, Dalton's opinion of Gay-Lussac's work was downright skeptical [Dalton 1810]:

"Gay-Lussac's opinion is founded upon an hypothesis that all elastic fluids combine in equal measures, or in measures that have some simple relation one to another, as 1 to 2, 1 to 3, 2 to 3, &c. In fact, his notion of measures is analogous to mine of atoms; and if it could be proved that all elastic fluids have the same number of atoms in the same volume, or numbers that are as 1, 2, 3, &c. the two hypotheses would be the same, except that mine is universal, and his applies only to elastic fluids. Gay Lussac could not but see (page 188, Part I. of this work) that a similar hypothesis had been entertained by me, and abandoned as untenable; however, as he has revived the notion, I shall make a few observations upon it, though I do not doubt but he will soon see its inadequacy. ... The truth is, I believe, that gases do not unite in equal or exact measures in any one instance; when they appear to do so, it is owing to the inaccuracy of our experiments."

There were, to be sure, experimental flaws in Gay-Lussac's work. Most historians of chemistry, however, regard Gay-Lussac as a more skilled experimenter than Dalton.

Regardless of the merits of their respective arguments, this interchange between Dalton and Gay-Lussac illustrates the interaction between scientists and the subjection of their ideas to criticism which is so crucial a part of how science works.

[43]This excellent summary of the principal points of the paper comes at the end. In modern scientific papers, a summary appears at the beginning of the paper to give a potential reader the opportunity to decide if it is likely to contain information of interest. Such a summary is called an abstract.


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