and separating the oxides of nitrogen. The water must be taken in a
greater quantity than that required for the formation of the hydrate
H_{2}SO_{4}, because the latter absorbs oxides of nitrogen. With an
excess of water, however, solution does not take place. If, in the above
reaction, only water, sulphurous anhydride, and nitric or nitrous acid
be taken in a definite quantity, then a definite quantity of sulphuric
acid and nitric oxide will be formed, according to the preceding
equation; but there the reaction ends and the excess of sulphurous
anhydride, if there be any, will remain unchanged. But if we add air and
water, then the nitric oxide will unite with the oxygen to form nitrogen
peroxide, and the latter with water to form nitric and nitrous acids,
which again give sulphuric acid from a fresh quantity of sulphurous
anhydride. Nitric oxide is again formed, which is able to start the
oxidation afresh if there be sufficient air. Thus it is possible
with a definite quantity of nitric oxide to convert an indefinitely
large quantity of sulphurous anhydride into sulphuric acid, water and
oxygen only being required.[64] This may be easily demonstrated by an
experiment on a small scale, if a certain quantity of nitric oxide be
first introduced into a flask, and sulphurous anhydride, steam, and
oxygen be then continually passed in. Thus the above-described reaction
may be expressed in the following manner:--
_n_SO_{2} + _n_O + (_n_ + _m_)H_{2}O + NO
= _n_H_{2}SO_{4},_m_H_{2}O + NO
if we consider only the original substances and those finally formed.
In this way a definite quantity of nitric oxide may serve for the
conversion of an indefinite quantity of sulphurous anhydride, oxygen,
and water into sulphuric acid. In reality, however, there is a limit to
this, because air, and not pure oxygen, is employed for the oxidation,
so that it is necessary to remove the nitrogen of the air and to
introduce a fresh quantity of air. A certain quantity of nitric oxide
will pass away with this nitrogen, and will in this way be lost.[65]
[64] The instance of the action of a small quantity of NO in inducing
a definite chemical reaction between large masses (SO_{2} +
O + H_{2}O = H_{2}SO_{4}) is very instructive, because the
particulars relating to it have been studied, and show that
intermediate forms of reaction may be discovered in the so-called
contact or catalytic phenomena. The essence of the matter here is
that A (= SO_{2}) reacts upon B (= O and H_{2}O) in the presence
of C, because it gives BC, a substance which forms AB with A, and
again liberates C. Consequently C is a medium, a transferring
substance, without which the reaction does not proceed. Many
similar phenomena may be found in other departments of life. Thus
the merchant is an indispensable medium between the producer
and the consumer; experiment is a medium between the phenomena
of nature and the cognisant faculties, and language, customs,
and laws are media which are as necessary for the exchanges of
social intercourse as nitric oxide for those between sulphurous
anhydride and oxygen and water.
[65] If the sulphurous anhydride be prepared by roasting iron pyrites,
FeS_{2}, then each equivalent of pyrites (equivalent of iron,
56, of sulphur 32, of pyrites 120) requires six equivalents of
oxygen (that is 96 parts) for the conversion of its sulphur
into sulphuric acid (for forming 2H_{2}SO_{4} with water),
besides 1-1/2 equivalents (24 parts) for converting the iron
into oxide, Fe_{2}O_{3}; hence the combustion of the pyrites for
the formation of sulphuric acid and ferric oxide requires the
introduction of an equal weight of oxygen (120 parts of oxygen to
120 parts of pyrites), or five times its weight of air, whilst
four parts by weight of nitrogen will remain inactive, and in the
removal of the exhausted air will carry off the remaining nitric
oxide. If not all, at least a large portion of the nitric oxide
may be collected by passing the escaping air, still containing
some oxygen, through substances which absorb oxides of nitrogen.
Sulphuric acid itself may be employed for this purpose if it be
used in the form of the hydrate H_{2}SO_{4}, or containing only
a small amount of water, because such sulphuric acid dissolves
the oxides of nitrogen. They may be easily expelled from this
solution by heating or by dilution with water, as they are only
slightly soluble in aqueous sulphuric acid. Besides which,
sulphurous anhydride acts on such sulphuric acid, being oxidised
at the expense of the nitrous anhydride, and forming nitric
oxide from it, which again enters into the cycle of action. For
this reason the sulphuric acid which has absorbed the oxides of
nitrogen escaping from the chambers in the tower K (_see_ fig.
50) is led back into the first chamber, where it comes into
contact with sulphurous anhydride, by which means the oxides of
nitrogen are reintroduced into the reaction which proceeds in
the chambers. This is the use of the towers (Gay-Lussac's and
Glover's) which are erected at either end of the chambers.
The preceding series of changes serve as the basis of the _manufacture
of sulphuric acid_ or so-called _chamber acid_. This acid is prepared
on a very large scale in chemical works because it is the cheapest acid
whose action can be applied in a great number of cases. It is therefore
used in immense quantities.
[Illustration: FIG. 50.--Section of sulphuric acid chambers, the first
and last chambers only being represented. The tower to the left is
called the Glover's tower, and that on the right the Gay-Lussac's tower.
Less than 1/10th of the natural size.]
The process is carried on in a series of chambers (or in one divided
by partitions as in fig. 50, which shows the beginning and end of a
chamber) constructed of sheet lead. These chambers are placed one
against the other, and communicate by tubes or special orifices so
placed that the inlet tubes are in the upper portion of the chamber, and
the outlet in the lower and opposite end. The current of steam and gases
necessary for the preparation of the sulphuric acid passes through these
chambers and tubes. The acid as it is formed falls to the bottom of the
chambers or runs down their walls, and flows from chamber to chamber
(from the last towards the first), to permit of which the partitions
do not reach to the bottom. The floor and walls of the chambers should
therefore be made of a material on which the sulphuric acid will not
act. Among the ordinary metals lead is the only one suitable.[65 bis]
[65 bis] Other metals, iron, copper, zinc, are corroded by it;
glass and china are not acted upon, but they crack from the
variations of temperature taking place in the chambers, and
besides they are more difficult to join properly than lead; wood,
&c., becomes charred.
For the formation of the sulphuric acid it is necessary to introduce
sulphurous anhydride, steam, air, and nitric acid, or some oxide of
nitrogen, into the chambers. The sulphurous anhydride is produced by
burning sulphur or iron pyrites. This is carried on in the furnace with
four hearths to the left of the drawing. Air is led into the chambers
and furnace through orifices in the furnace doors. The current of air
and oxygen is regulated by opening or closing these orifices to a
greater or less extent. The ingoing draught in the chambers is brought
about by the fact that heated gases and vapours pass into the chambers,
whose temperature is further raised by the reaction itself, and also
by the remaining nitrogen being continually withdrawn from the outlet
(above the tower K) by a tall chimney situated near the chambers. Nitric
acid is prepared from a mixture of sulphuric acid and Chili saltpetre,
in the same furnaces in which the sulphurous anhydride is evolved (or in
special furnaces). Not more than 8 parts of nitre are taken to 100 parts
of sulphur burnt. On leaving the furnace the vapours of nitric acid and
oxides of nitrogen mixed with air and sulphurous anhydride first pass
along the horizontal tubes T into the receiver B B, which is partially
cooled by water flowing in on the right-hand side and running out on the
left by _o_, in order to reduce the temperature of the gases entering
the chamber. The gases then pass up a tower filled with coke, and shown
to the left of the drawing. In this tower are placed lumps of coke (the
residue from the dry distillation of coal), over which sulphuric acid
trickles from the reservoir M. This acid has absorbed in the end tower K
the oxides of nitrogen escaping from the chamber. This end tower is also
filled with coke, over which a stream of strong sulphuric acid trickles
from the reservoir M. The acid spreads over the coke, and, owing to the
large surface offered by the latter, absorbs the greater part of the
oxides of nitrogen escaping from the chambers. The sulphuric acid in
passing down the tower becomes saturated with the oxides of nitrogen,
and flows out at _h_ into a special receiver (in the drawing situated
by the side of the furnaces), from which it is forced up the tubes _h´
h´_ by steam pressure into the reservoir M, situated above the first
tower. The gases passing through this tower (hot) from the furnace
on coming into contact with the sulphuric acid take up the oxides of
nitrogen contained in it, and these are thus returned to the chamber and
again participate in the reaction. The sulphuric acid left after their
extraction flows into the chambers. Thus, on leaving the first coke
tower the sulphurous anhydride, air, and vapours of nitric acid and of
the oxides of nitrogen pass through the upper tube _m_ into the chamber.
Here they come into contact with steam introduced by lead tubes into
various parts of the chamber. The reaction takes place in the presence
of water, the sulphuric acid falls to the bottom of the chamber, and the
same process takes place in the following chambers until the whole of
the sulphurous anhydride is consumed. A somewhat greater proportion of
air than is strictly necessary is passed in, in order that no sulphurous
anhydride should be left unaltered for want of sufficient oxygen. The
presence of an excess of oxygen is shown by the colour of the gases
escaping from the last chamber. If they be of a pale colour it indicates
an insufficiency of air (and the presence of sulphurous anhydride), as
otherwise peroxide of nitrogen would be formed. A very dark colour shows
an excess of air, which is also disadvantageous, because it increases
the inevitable loss of nitric oxide by increasing the mass of escaping
gases.[66]
[66] By this means as much as 2,500,000 kilograms of chamber acid,
containing about 60 per cent. of the hydrate H_{2}SO_{4} and
about 40 per cent. of water, may be manufactured per year in one
plant of 5,000 cubic metres capacity (without stoppages). This
process has been brought to such a degree of perfection that
as much as 300 parts of the hydrate H_{2}SO_{4} are obtained
from 100 parts of sulphur, whilst the theoretical amount is
not greater than 306 parts. The acid parts with its excess of
water on heating. For this purpose it is heated in lead vessels.
However, the acid containing about 75 per cent. of the hydrate
(60° Baumé) already begins to act on the lead when heated,
and therefore the further removal of water is conducted by
evaporating in glass or platinum vessels, as will he described
in Chapter XX. The aqueous acid (50° Baumé) obtained in the
chambers is termed chamber acid. The acid concentrated to 60°
Baumé is more generally employed, and sometimes the hydrate (66°
Baumé) termed vitriol acid is also used. In England alone more
than 1,000 million kilograms of chamber acid are produced by
this method. The formation of sulphuric acid by the action of
nitric acid was discovered by Drebbel, and the first lead chamber
was erected by Roebuck, in Scotland, in the middle of the last
century. The essence of the process was only brought to light
at the beginning of this century, when many improvements were
introduced into practice.
_Nitrous oxide_, N_{2}O,[67] is similar to water in its volumetric
composition. Two volumes of nitrous oxide are formed from two volumes
of nitrogen and one volume of oxygen, which may be shown by the
ordinary method for the analysis of the oxides of nitrogen (by passing
them over red-hot copper or sodium). In contradistinction to the other
oxides of nitrogen, it is not directly oxidised by oxygen, but it
may be obtained from the higher oxides of nitrogen by the action of
certain deoxidising substances; thus, for example, a mixture of two
volumes of nitric oxide and one volume of sulphurous anhydride if left
in contact with water and spongy platinum is converted into sulphuric
acid and nitrous oxide, 2NO + SO_{2} + H_{2}O = H_{2}SO_{4} + N_{2}O.
Nitric acid, also, under the action of certain metals--for instance, of
zinc[68]--gives nitrous oxide, although in this case mixed with nitric
oxide. The usual method of preparing nitrous oxide consists in the
decomposition of ammonium nitrate by the aid of heat, because in this
case only water and nitrous oxide are formed, NH_{4}NO_{3} = 2H_{2}O
+ N_{2}O (a mixture of NH_{4}Cl and KNO_{3} is sometimes taken). The
decomposition[69] proceeds very easily in an apparatus like that used
for the preparation of ammonia or oxygen--that is, in a retort or flask
with a gas-conducting tube. The decomposition must, however, be carried
on carefully, as otherwise nitrogen is formed from the decomposition of
the nitrous oxide.[70]
[67] If the hydrate HNO_{3} corresponds to N_{2}O_{4}, the hydrate HNO,
_hyponitrous acid_, corresponds to N_{2}O, and in this
sense N_{2}O is _hyponitrous anhydride_. Hyponitrous acid,
corresponding with nitrous oxide (as its anhydride), is not
known in a pure state, but its salts (Divers) are known. They
are prepared by the reduction of nitrous (and consequently of
nitric) salts by sodium amalgam. If this amalgam he added to a
cold solution of an alkaline nitrite until the evolution of gas
ceases, and the excess of alkali saturated with acetic acid,
an insoluble yellow precipitate of silver hyponitrite, NAgO,
will he obtained on adding a solution of silver nitrate. This
hyponitrite is insoluble in cold acetic acid, and decomposes when
heated, with the evolution of nitrous oxide. If rapidly heated it
decomposes with an explosion. It is dissolved unchanged by weak
mineral acids, whilst the stronger acids (for example, sulphuric
and hydrochloric acids) decompose it, with the evolution of
nitrogen, nitric and nitrous acids remaining in solution. Among
the other salts of hyponitrous acid, HNO, the salts of lead,
copper, and mercury are insoluble in water. Judging by the bond
between hyponitrous acid and the other compounds of nitrogen,
there is reason for thinking that its formula should he doubled,
N_{2}H_{2}O_{2}. For instance, Thoune (1893) on gradually
oxidising hydroxylamine, NH_{2}(OH), into nitrous acid, NO(OH)
(Note 25), by means of an alkaline solution of KMnO_{4}, first
obtained hyponitrous acid, N_{2}H_{2}O_{2}, and then a peculiar
intermediate acid, N_{2}H_{2}O_{3}, which, by further oxidation,
gave nitrous acid. On the other hand, Wislicenus (1893) showed
that in the action of the sulphuric acid salt of hydroxylamine
upon nitrite of sodium, there is formed, besides, nitrous
oxide (according to V. Meyer, NH_{3}O,H_{2}SO_{4} + NaNO_{2} =
NaHSO_{4} + 2H_{2}O + N_{2}O), a small amount of hyponitrous
acid which may be precipitated in the form of the silver salt;
and this reaction is most simply expressed by taking the doubled
formula of hyponitrous acid, NH_{2}(OH) + NO(OH) = H_{2}O +
N_{2}H_{2}O_{2}. The best argument in favour of the doubled
formula is the property possessed by hyponitrous acid of forming
acid salts, HNaN_{2}O_{2} (Zorn).
According to Thoune, the following are the properties of
hyponitrous acid. When liberated from the dry silver salt by
the action of dry sulphuretted hydrogen, hyponitrous acid is
unstable, and easily explodes even at low temperatures. But
when dissolved in water (having been formed by the action of
hydrochloric acid upon the silver salt), it is stable even
when boiled with dilute acids and alkalis. The solution is
colourless and has a strongly acid reaction. In the course of
time, however, the aqueous solution also decomposes into nitrous
oxide and water. The complete oxidation by permanganate of potash
proceeds according to the following equation: 5H_{2}N_{2}O_{2} +
8KMnO_{4} + 12H_{2}SO_{4} = 10HNO_{3} + 4K_{2}SO_{4} + 8MnSO_{4}
+ 12H_{2}O. In an alkaline solution, KMnO_{4} only oxidises
hyponitrous acid into nitrous and not into nitric acid. Nitrous
acid has a decomposing action upon hyponitrous acid, and if
the aqueous solutions of the two acids be mixed together they
immediately give off oxides of nitrogen. Hyponitrous acid does
not liberate CO_{2} from its salts, but on the other hand it is
not displaced by CO_{2}.
[68] It is remarkable that electro-deposited copper powder gives
nitrous oxide with a 10 p.c. solution of nitric acid, whilst
ordinary copper gives nitric oxide. It is here evident that
the physical and mechanical structure of the substance affects
the course of the reaction--that is to say, it is a case of
contact-action.
[69] This decomposition is accompanied by the evolution of about 25,000
calories per molecular quantity, NH_{4}NO_{3}, and therefore
takes place with ease, and sometimes with an explosion.
[70] In order to remove any nitric oxide that might be present, the
gas obtained is passed through a solution of ferrous sulphate. As
nitrous oxide is very soluble in cold water (at 0°, 100 volumes
of water dissolve 130 volumes of N_{2}O; at 20°, 67 volumes),
it must be collected over warm water. The nitrous oxide is much
more soluble than nitric oxide, which is in agreement with the
fact that nitrous oxide is much more easily liquefied than nitric
oxide. Villard obtained a crystallohydrate, N_{2}O,6H_{2}O, which
was tolerably stable at 0°.
[Illustration: FIG. 51.--Natterer's apparatus for the preparation of
liquid nitrous oxide and carbonic anhydride. The gas first passes though
the vessel V, for drying, and then into the pump (a section of the upper
part of the apparatus is given on the left). The piston _t_ of the
force pump is moved by the crank E and fly-wheel turned by hand. The
gas is pumped into the iron chamber A, where it is liquefied. The valve
S allows the gas to enter A, but not to escape from it. The chamber
and pump are cooled by the jacket B, filled with ice. When the gas is
liquefied the vessel A is unscrewed from the pump, and the liquid may be
poured from it by inverting it and unscrewing the valve _v_, when the
liquid runs out of the tube _x_.]
Nitrous oxide is not a permanent gas (absolute boiling point +36°); it
is easily liquefied by the action of cold under a high pressure; at
15° it may be liquefied by a pressure of about 40 atmospheres. This
gas is usually liquefied by means of the force pump[71] shown in fig.
51. As it is liquefied with comparative ease, and as the cold produced
by its vaporisation is very considerable,[72] it (as also liquid
carbonic anhydride) is often employed in investigations requiring a low
temperature. Nitrous oxide forms a very mobile, colourless liquid, which
acts on the skin, and is incapable in a cold state of oxidising either
metallic potassium, phosphorus, or carbon; its specific gravity is
slightly less than that of water (0° = 0·910, 10° = 0·856, 35° = 0·60,
39° = 0·45, Villard, 1894). When evaporated under the receiver of an
air-pump, the temperature falls to -100°, and the liquid solidifies into
a snow-like mass, and partially forms transparent crystals. Both these
substances are solid nitrous oxide. Mercury is immediately solidified in
contact with evaporating liquid nitrous oxide.[73]
[71] Faraday obtained liquid nitrous oxide by the same method as liquid
ammonia, by beating dry ammonium nitrate in a closed bent
tube, one arm of which was immersed in a freezing mixture. In
this case two layers of liquid are obtained at the cooled end,
a lower layer of water and an upper layer of nitrous oxide.
This experiment should be conducted with great care, as the
pressure of the nitrous oxide in a liquid state is considerable,
namely (according to Regnault), at +10° = 45 atmospheres, at
0° = 36 atmospheres, at -10° = 29 atmospheres, and at -20° = 23
atmospheres. It boils at -92°, and the pressure is then therefore
= 1 atmosphere (_see_ Chapter II., Note 27).
[72] Liquid nitrous oxide, in vaporising at the same pressure as liquid
carbonic anhydride, gives rise to almost equal or even slightly
lower temperatures. Thus at a pressure of 25 mm. carbonic
anhydride gives a temperature as low as -115°, and nitrous oxide
of -125° (Dewar). The similarity of these properties and even of
the absolute boiling point (CO_{2} + 32°, N_{2}O +36°) is all
the more remarkable because these gases have the same molecular
weight = 44 (Chapter VII.)
[73] A very characteristic experiment of simultaneous combustion and
intense cold may be performed by means of liquid nitrous oxide;
if liquid nitrous oxide be poured into a test tube containing
some mercury the mercury will solidify, and if a piece of red-hot
charcoal be thrown upon the surface of the nitrous oxide it
will continue to burn very brilliantly, giving rise to a high
temperature.
When introduced into the respiratory organs (and consequently into the
blood also) nitrous oxide produces a peculiar kind of intoxication
accompanied by spasmodic movements, and hence this gas, discovered by
Priestley in 1776, received the name of 'laughing gas.' On a prolonged
respiration it produces a state of insensibility (it is an anæsthetic
like chloroform), and is therefore employed in dental and surgical
operations.
Nitrous oxide is easily decomposed into nitrogen and oxygen by the
action of heat, or a series of electric sparks; and this explains why a
number of substances which cannot burn in nitric oxide do so with great
ease in nitrous oxide. In fact, when nitric oxide gives some oxygen on
decomposition, this oxygen immediately unites with a fresh portion of
the gas to form nitric peroxide, whilst nitrous oxide does not possess
this capacity for further combination with oxygen.[74] A mixture of
nitrous oxide with hydrogen explodes like detonating gas, gaseous
nitrogen being formed, N_{2}O + H_{2} = H_{2}O + N_{2}. The volume
of the remaining nitrogen is equal to the original volume of nitrous
oxide, and is equal to the volume of hydrogen entering into combination
with the oxygen; hence in this reaction equal volumes of nitrogen
and hydrogen replace each other. Nitrous oxide is also very easily
decomposed by red-hot metals; and sulphur, phosphorus, and charcoal
burn in it, although not so brilliantly as in oxygen. A substance in
burning in nitrous oxide evolves more heat than an equal quantity
burning in oxygen; which most clearly shows that in the formation of
nitrous oxide by the combination of nitrogen with oxygen there was not
an evolution but an absorption of heat, there being no other source for
the excess of heat in the combustion of substances in nitrous oxide
(_see_ Note 29). If a given volume of nitrous oxide be decomposed by
a metal--for instance, sodium--then there remains, after cooling and
total decomposition, a volume of nitrogen, exactly equal to that of the
nitrous oxide taken; consequently the oxygen is, so to say, distributed
between the atoms of nitrogen without producing an increase in the
volume of the nitrogen.
[74] In the following chapter we shall consider the volumetric
composition of the oxides of nitrogen. It explains the difference
between nitric and nitrous oxide. Nitrous oxide is formed with
a diminution of volumes (contraction), nitric oxide without
contraction, its volume being equal to the sum of the volumes of
the nitrogen and oxygen of which it is composed. By oxidation, if
it could be directly accomplished, two volumes of nitrous oxide
and one volume of oxygen would not give three but four volumes
of nitric oxide. These facts must be taken into consideration in
comparing the calorific equivalents of formation, the capacity
for supporting combustion, and other properties of nitrous and
nitric oxides, N_{2}O and NO.
CHAPTER VII
MOLECULES AND ATOMS. THE LAWS OF GAY-LUSSAC AND AVOGADRO-GERHARDT
Hydrogen combines with oxygen in the proportion of two volumes to one.
The composition by volume of nitrous oxide is exactly similar--it
is composed of two volumes of nitrogen and one volume of oxygen. By
decomposing ammonia by the action of an electric spark it is easy to
prove that it contains one volume of nitrogen to three volumes of
hydrogen. So, similarly, it is found, whenever a compound is decomposed
and the volumes of the gases proceeding from it are measured, that
the volumes of the gases or vapours entering into combination are in
a very simple proportion to one another. With water, nitrous oxide,
&c., this may be proved by direct observation; but in the majority of
cases, and especially with substances which, although volatile--that is,
capable of passing into a gaseous (or vaporous) state--are liquid at
the ordinary temperature, such a direct method of observation presents
many difficulties. But, then, if the densities of the vapours and gases
be known, the same simplicity in their ratio is shown by calculation.
The volume of a substance is proportional to its weight, and inversely
proportional to its density, and therefore by dividing the amount by
weight of each substance entering into the composition of a compound by
its density in the gaseous or vaporous state we shall obtain factors
which will be in the same proportion as the volumes of the substances
entering into the composition of the compound.[1] So, for example,
water contains eight parts by weight of oxygen to one part by weight
of hydrogen, and their densities are 16 and 1, consequently their
volumes (or the above-mentioned factors) are 1 and 1/2, and therefore
it is seen without direct experiment that water contains two volumes of
hydrogen for every one volume of oxygen. So also, knowing that nitric
oxide contains fourteen parts of nitrogen and sixteen parts of oxygen,
and knowing that the specific gravities of these last two gases are
fourteen and sixteen, we find that the volumes in which nitrogen and
oxygen combine for the formation of nitric oxide are in the proportion
of 1 : 1. We will cite another example. In the last chapter we saw that
the density of NO_{2} only becomes constant and equal to twenty-three
(referred to hydrogen) above 135°, and as a matter of fact a method
of direct observation of the volumetric composition of this substance
would be very difficult at so high a temperature. But it may be easily
calculated. NO_{2}, as is seen from its formula and analysis, contains
thirty-two parts by weight of oxygen to fourteen parts by weight of
nitrogen, forming forty-six parts by weight of NO_{2}, and knowing the
densities of these gases we find that one volume of nitrogen with two
volumes of oxygen gives two volumes of nitrogen peroxide. Therefore,
knowing the amounts by weight of the substances participating in a
reaction or forming a given substance, and knowing the density of the
gas or vapour,[2] the volumetric relations of the substances acting in
a reaction or entering into the composition of a compound, may be also
determined.
[1] If the weight be indicated by P, the density by D, and the volume
by V, then
P/D = _K_V
where _K_ is a coefficient depending on the system of the
expressions P, D, and V. If D be the weight of a cubic measure
of a substance referred to the weight of the same measure of
water--if, as in the metrical system (Chapter I., Note 9), the
cubic measure of one part by weight of water be taken as a unit
of volume--then _K_ = 1. But, whatever it be, it is cancelled in
dealing with the comparison of volumes, because comparative and
not absolute measures of volumes are taken. In this chapter, as
throughout the book, the weight P is given in grams in dealing
with absolute weights; and if comparative, as in the expression
of chemical composition, then the weight of an atom is taken as
unity. The density of gases, D, is also taken in reference to the
density of hydrogen, and the volume V in metrical units (cubic
centimetres), if it be a matter of absolute magnitudes of volumes,
and if it be a matter of chemical transformations--that is, of
relative volumes--then the volume of an atom of hydrogen, or of
one part by weight of hydrogen, is taken as unity, and all volumes
are expressed according to these units.
[2] As the volumetric relations of vapours and gases, next to the
relations of substances by weight, form the most important
province of chemistry, and a most important means for the
attainment of chemical conclusions, and inasmuch as these
volumetric relations are determined by the densities of gases and
vapours, necessarily the methods of determining the densities of
vapours (and also of gases) are important factors in chemical
research. These methods are described in detail in works on
physics and physical and analytical chemistry, and therefore we
here only touch on the general principles of the subject.
If we know the weight _p_ and volume _v_, occupied by the vapour
of a given substance at a temperature _t_ and pressure _h_, then
its density may be directly obtained by dividing _p_ by the weight
of a volume _v_ of hydrogen (if the density be expressed according
to hydrogen, _see_ Chapter II., Note 23) at _t_ and _h_. Hence,
the methods of determining the density of vapours and gases are
based on the determination of _p_, _v_, _t_, and _h_. The two
last data (the temperature _t_ and pressure _h_) are given by the
thermometer and barometer and the heights of mercury or other
liquid confining the gas, and therefore do not require further
explanation. It need only be remarked that: (1) In the case of
easily volatile liquids there is no difficulty in procuring a
bath with a constant temperature, but that it is nevertheless
best (especially considering the inaccuracy of thermometers) to
have a medium of absolutely constant temperature, and therefore
to take either a bath in which some substance is melting--such
as melting ice at 0° or crystals of sodium acetate, melting at
+56°--or, as is more generally practised, to place the vessel
containing the substance to be experimented with in the vapour
of a liquid boiling at a definite temperature, and knowing the
pressure under which it is boiling, to determine the temperature
of the vapour. For this purpose the boiling points of water at
different pressures are given in Chapter I., Note 11, and the
boiling points of certain easily procurable liquids at various
pressures are given in Chapter II., Note 27. (2) With respect to
temperatures above 300° (below which mercurial thermometers may
be conveniently employed), they are most simply obtained constant
(to give time for the weight and volume of a substance being
observed in a given space, and to allow that space to attain the
calculated temperature _t_) by means of substances boiling at a
high temperature. Thus, for instance, at the ordinary atmospheric
pressure the temperature _t_ of the vapour of sulphur is about
445°, of phosphorus pentasulphide 518°, of tin chloride 606°,
of cadmium 770°, of zinc 930° (according to Violle and others),
or 1040° (according to Deville), &c. (3) The indications of the
hydrogen thermometer must be considered as the most exact (but
as hydrogen diffuses through incandescent platinum, nitrogen is
usually employed). (4) The temperature of the vapours used as
the bath should in every case be several degrees higher than the
boiling point of the liquid whose density is to be determined,
in order that no portion should remain in a liquid state. But
even in this case, as is seen from the example of nitric peroxide
(Chapter VI.), the vapour density does not always remain constant
with a change of _t_, as it should were the law of the expansion
of gases and vapours absolutely exact (Chapter II., Note 26). If
variations of a chemical and physical nature similar to that which
we saw in nitric peroxide take place in the vapours, the main
interest is centred in _constant_ densities, which do not vary
with _t_, and therefore the possible effect of _t_ on the density
must always be kept in mind in having recourse to this means
of investigation. (5) Usually, for the sake of convenience of
observation, the vapour density is determined at the atmospheric
pressure which is read on the barometer; but in the case of
substances which are volatilised with difficulty, and also of
substances which decompose, or, in general, vary at temperatures
near their boiling points, it is best or even indispensable to
conduct the determination at low pressures, whilst for substances
which decompose at low pressures the observations have to be
conducted under a more or less considerably increased pressure.
(6) In many cases it is convenient to determine the vapour density
of a substance in admixture with other gases, and consequently
under the partial pressure, which may be calculated from the
volume of the mixture and that of the intermixed gas (_see_
Chapter I., Note 1). This method is especially important for
substances which are easily decomposable, because, as shown by the
phenomena of dissociation, a substance is able to remain unchanged
in the atmosphere of one of its products of decomposition. Thus,
Wurtz determined the density of phosphoric chloride, PCl_{5},
in admixture with the vapour of phosphorous chloride, PCl_{3}.
(7) It is evident, from the example of nitric peroxide, that a
change of pressure may alter the density and aid decomposition,
and therefore identical results are sometimes obtained (if the
density be variable) by raising _t_ and lowering _h_; but if the
density does not vary under these variable conditions (at least,
to an extent appreciably exceeding the limits of experimental
error), then this _constant_ density indicates the _gaseous_
and _invariable_ state of a substance. The laws hereafter laid
down refer only to such vapour densities. But the majority of
volatile substances show such a constant density at a certain
degree above their boiling points up to the starting point of
decomposition. Thus, the density of aqueous vapour does not vary
for _t_ between the ordinary temperature and 1000° (there are no
trustworthy determinations beyond this) and for pressures varying
from fractions of an atmosphere up to several atmospheres. If,
however, the density does vary considerably with a variation of
_h_ and _t_, the fact may serve as a guide for the investigation
of the chemical changes which are undergone by the substance in a
state of vapour, or at least as an indication of a deviation from
the laws of Boyle, Mariotte, and Gay-Lussac (for the expansion of
gases with _t_). In certain cases the separation of one form of
deviation from the other may be explained by special hypotheses.
With respect to the means of determining _p_ and _v_, with a
view to finding the vapour density, we may distinguish three
chief methods: (_a_) by weight, by ascertaining the weight of
a definite volume of vapour; (_b_) by volume, by measuring the
volume occupied by the vapour of a definite weight of a substance;
and (_c_) by displacement. The last-mentioned is essentially
volumetric, because a known weight of a substance is taken, and
the volume of the air displaced by the vapour at a given _t_ and
_h_ is determined.
[Illustration: FIG. 52.--Apparatus for determining the vapour
density by Dumas' method. A small quantity of the liquid whose
vapour density is to be determined is placed in the glass
globe, and heated in a water or oil bath to a temperature above
the boiling point of the liquid. When all the liquid has been
converted into vapour and has displaced all the air from the
globe, the latter is sealed up and weighed. The capacity of the
globe is then measured, and in this manner the volume occupied by
a known weight of vapour at a known temperature is determined.]
[Illustration: FIG. 53.--Deville and Troost's apparatus for
determining the vapour densities, according to Dumas' method, of
substances which boil at high temperatures. A porcelain globe
containing the substance whose vapour density is to be determined
is heated in the vapour of mercury (350°), sulphur (410°), cadmium
(850°), or zinc (1,040°). The globe is sealed up in an oxyhydrogen
flame.]
The method by weight (_a_) is the most trustworthy and
historically important. _Dumas' method_ is typical. An ordinary
spherical glass or porcelain vessel, like those shown respectively
in figs. 52 and 53, is taken, and an excess of the substance to be
experimented upon is introduced into it. The vessel is heated to a
temperature _t_ higher than the boiling point of the liquid: this
gives a vapour which displaces the air, and fills the spherical
space. When the air and vapour cease escaping from the sphere, it
is fused up or closed by some means; and when cool, the weight
of the vapour remaining in the sphere is determined (either by
direct weighing of the vessel with the vapour and introducing the
necessary corrections for the weight of the air and of the vapour
itself, or the weight of the volatilised substance is determined
by chemical methods), and the volume of the vapour at _t_ and the
barometric pressure _h_ are then calculated.
_The volumetric method_ (_b_) originally employed by Gay-Lussac
and then modified by Hofmann and others is based on the principle
that a weighed quantity of the liquid to be experimented with
(placed in a small closed vessel, which is sometimes fused up
before weighing, and, if quite full of the liquid, breaks when
heated in a vacuum) is introduced into a graduated cylinder heated
to _t_, or simply into a Torricellian vacuum, as shown in fig. 54,
and the number of volumes occupied by the vapour noted when the
space holding it is heated to the desired temperature _t_.
[Illustration: FIG. 54.--Hofmann's apparatus for determining
vapour densities. The internal tube, about one metre long, which
is calibrated and graduated, is filled with mercury and inverted
in a mercury bath. A small bottle (depicted in its natural size
on the left) containing a weighed quantity of the liquid whose
vapour density is to be determined, is introduced into the
Torricellian vacuum. Steam, or the vapour of amyl alcohol, &c., is
passed through the outer tube, and heats the internal tube to the
temperature _t_, at which the volume of vapour is measured.]
[Illustration: FIG. 55.--Victor Meyer's apparatus for determining
vapour densities. The tube _b_ is heated in the vapour of a liquid
of constant boiling point. A glass tube, containing the liquid
to be experimented upon, is caused to fall from _d_. The air
displaced is collected in the cylinder _e_, in the trough _f_.]
_The method of displacement_ (_c_) proposed by Victor Meyer
is based on the fact that a space _b_ is heated to a constant
temperature _t_ (by the surrounding vapours of a liquid of
constant boiling point), and the air (or other gas enclosed in
this space) is allowed to attain this temperature, and when it
has done so a glass bulb containing a weighed quantity of the
substance to be experimented with is dropped into the space. The
substance is immediately converted into vapour, and displaces
the air into the graduated cylinder _e_. The amount of this air
is calculated from its volume, and hence the volume at _t_, and
therefore also the volume occupied by the vapour, is found. The
general arrangement of the apparatus is given in fig. 55.
Such an investigation (either direct, or by calculation from the
densities and composition) of every chemical reaction, resulting in the
formation of definite chemical compounds, shows that the volumes of
the reacting substances in a gaseous or vaporous state are either equal
or are in simple multiple proportion.[3] This forms the _first law_
of those discovered by _Gay-Lussac_. It may be formulated as follows:
_The amounts of substances entering into chemical reaction occupy under
similar physical conditions, in a gaseous or vaporous state, equal or
simple multiple volumes._ This law refers not only to elements, but
also to compounds entering into mutual chemical combination; thus, for
example, one volume of ammonia gas combines with one volume of hydrogen
chloride. For in the formation of sal-ammoniac, NH_{4}Cl, there enter
into reaction 17 parts by weight of ammonia, NH_{3}, which is 8·5 times
denser than hydrogen, and 36·5 parts by weight of hydrogen chloride,
whose vapour density is 18·25 times that of hydrogen, as has been
proved by direct experiment. By dividing the weights by the respective
densities we find that the volume of ammonia, NH_{3}, is equal to two,
and so also the volume of hydrogen chloride. Hence the volumes of the
compounds which here combine together are equal to each other. Taking
into consideration that the law of Gay-Lussac holds good, not only for
elements, but also for compounds, it should be expressed as follows:
_Substances interact with one another in commensurable volumes of their
vapours._[4]
[3] Vapours and gases, as already explained in the second chapter, are
subject to the same laws, which are, however, only approximate. It
is evident that for the deduction of the laws which will presently
be enunciated it is only possible to take into consideration
a perfect gaseous state (far removed from the liquid state)
and chemical invariability in which the _vapour density is
constant_--that is, the volume of a given gas or vapour varies
like a volume of hydrogen, air, or other gas, with the pressure
and temperature.
It is necessary to make this statement in order that it may be
clearly seen that the laws of gaseous volumes, which we shall
describe presently, are in the most intimate connection with the
laws of the variations of volumes with pressure and temperature.
And as these latter laws (Chapter II.) are not infallible, but
only approximately exact, the same, therefore, applies to the laws
about to be described. And as it is possible to find more exact
laws (a second approximation) for the variation of _v_ with _p_
and _t_ (for example, van der Waals' formula, Chapter II., Note
33), so also a more exact expression of the relation between the
composition and the density of vapours and gases is also possible.
But to prevent any doubt arising at the very beginning as to the
breadth and general application of the laws of volumes, it will be
sufficient to mention that the density of such gases as oxygen,
nitrogen, and carbonic anhydride is already known to _remain
constant_ (within the limits of experimental error) between the
ordinary temperature and a white heat; whilst, judging from what
is said in my work on the 'Tension of Gases' (vol. i. p. 9),
it may be said that, as regards pressure, the relative density
remains very constant, even when the deviations from Mariotte's
law are very considerable. However, in this respect the number of
data is as yet too small to arrive at an exact conclusion.
[4] We must recollect that this law is only approximate, like Boyle
and Mariotte's law, and that, therefore, like the latter, a more
exact expression may be found for the exceptions.
The law of combining volumes and the law of multiple proportion were
discovered independently of each other--the one in France by Gay-Lussac,
the other in England by Dalton--almost simultaneously. In the language
of the atomic hypothesis it may be said that atomic quantities of
elements occupy equal or multiple volumes.
The first law of Gay-Lussac expresses the relation between the volumes
of the component parts of a compound. Let us now consider the relation
existing between the volumes of the component parts and of the compounds
which proceed from them. This may sometimes be determined by direct
observation. Thus the volume occupied by water, formed by two volumes
of hydrogen and one volume of oxygen, may be determined by the aid of
the apparatus shown in fig. 56. The long glass tube is closed at the
top and open at the bottom, which is immersed in a cylinder containing
mercury. The closed end is furnished with wires like a eudiometer. The
tube is filled with mercury, and then a certain volume of detonating gas
is introduced. This gas is obtained from the decomposition of water,
and therefore in every three volumes contains two volumes of hydrogen
and one volume of oxygen. The tube is surrounded by a second and wider
glass tube, and the vapour of a substance boiling above 100°--that is,
whose boiling point is higher than that of water--is passed through
the annular space between them. Amyl alcohol, whose boiling point is
132°, may be taken for this purpose. The amyl alcohol is boiled in the
vessel to the right hand and its vapour passed between the walls of the
two tubes. In the case of amyl alcohol the outer glass tube should be
connected with a condenser to prevent the escape into the air of the
unpleasant-smelling vapour. The detonating gas is thus heated up to a
temperature of 132°. When its volume becomes constant it is measured,
the height of the column of mercury in the tube above the level of the
mercury in the cylinder being noted. Let this volume equal _v_; it will
therefore contain 1/3 _v_ of oxygen and 2/3 _v_ of hydrogen. The current
of vapour is then stopped, and the gas exploded; water is formed, which
condenses into a liquid. The volume occupied by the vapour of the water
formed has now to be determined. For this purpose the vapour of the amyl
alcohol is again passed between the tubes, and thus the whole of the
water formed is converted into vapour at the same temperature as that at
which the detonating gas was measured; and the cylinder of mercury being
raised until the column of mercury in the tube stands at the same height
above the surface of the mercury in the cylinder as it did before the
explosion, it is found that the volume of the water formed is equal to
2/3 _v_--that is, it is equal to the volume of the hydrogen contained
in it. Consequently the volumetric composition of water is expressed in
the following terms: Two volumes of hydrogen combine with one volume of
oxygen to form two volumes of aqueous vapour. For substances which are
gaseous at the ordinary temperature, this direct method of observation
is sometimes very easily conducted; for instance, with ammonia, nitric
and nitrous oxides. Thus to determine the composition by volume of
nitrous oxide, the above-described apparatus may be employed. Nitrous
oxide is introduced into the tube, and after measuring its volume
electric sparks are passed through the gas; it is then found that two
volumes of nitrous oxide have given three volumes of gases--namely,
two volumes of nitrogen and one volume of oxygen. Consequently the
composition of nitrous oxide is similar to that of water; two volumes of
nitrogen and one volume of oxygen give two volumes of nitrous oxide. By
decomposing ammonia it is found to be composed in such a manner that two
volumes give one volume of nitrogen and three volumes of hydrogen; also
two volumes of nitric oxide are formed by the union of one volume of
oxygen with one volume of nitrogen. The same relations may be proved by
calculation from the vapour densities, as was described above.
[Illustration: FIG. 56.--Apparatus for demonstrating the volume occupied
by the steam formed from the explosion of detonating gas.]
Comparisons of various results made by the aid of direct observations or
calculation, an example of which has just been cited, led Gay-Lussac to
the conclusion that _the volume of a compound in a gaseous or vaporous
state is always in simple multiple proportion to the volume of each of
the component parts of which it is formed_ (and consequently to the
sum of the volumes of the elements of which it is formed). This is the
_second law of Gay-Lussac_; it extends the simplicity of the volumetric
relations to compounds, and is of the same nature as that presented
by the elements entering into mutual combination. Hence not only the
substances forming a given compound, but also the substances formed,
exhibit a simple relation of volume when measured as vapour or gas.[5]
[5] This second law of volumes may be considered as a consequence of the
first law. The first law requires simple ratios between the
volumes of the combining substances _A_ and _B_. A substance _AB_
is produced by their combination. It may, according to the law
of multiple proportion, combine, not only with substances _C_,
_D_, &c., but also with _A_ and with _B_. In this new combination
the volume of _AB_, combining with the volume of _A_, should be
in simple multiple proportion with the volume of _A_; hence the
volume of the compound _AB_ is in simple proportion to the volume
of its component parts. Therefore only one law of volumes need be
accepted. We shall afterwards see that there is a third law of
volumes embracing also the two first laws.
When a compound is formed from two or more components, there may
or may not be a contraction; the volume of the reacting substances
is in this case either equal to or greater than the volume of the
resultant compound. The reverse is naturally observed in the case of
decompositions, when from one substance there are produced several of
simpler nature. Therefore in the future we shall term _combination_ a
reaction in which a contraction is observed--that is, a diminution in
the volume of the component bodies in a state of vapour or gas; and we
shall term _decomposition_ a reaction in which an expansion is produced;
while those reactions in which the volumes in a gaseous or vaporous
state remain constant (the volumes being naturally compared at the same
temperature and pressure) we shall term reactions of _substitution_ or
of double decomposition. Thus the transition of oxygen into ozone is a
reaction of combination, the formation of nitrous oxide from oxygen and
nitrogen will also be a combination, the formation of nitric oxide from
the same will be a reaction of substitution, the action of oxygen on
nitric oxide a combination, and so on.
The degree of contraction produced in the formation of chemical
compounds not unfrequently leads to the possibility of distinguishing
the degree of change which takes place in the chemical character of the
components when combined. In those cases in which a contraction occurs,
the properties of the resultant compound are very different from the
properties of the substances of which it is composed. Thus ammonia bears
no resemblance in its physical or chemical properties to the elements
from which it is derived; a contraction takes place in a state of
vapour, indicating a proximation of the elements--the distance between
the atoms is diminished, and from gaseous substances there is formed a
liquid substance, or at any rate one which is easily liquefied. For this
reason nitrous oxide formed by the condensation of two permanent gases
is a substance which is somewhat easily converted into a liquid; again,
nitric acid, which is formed from elements which are permanent gases,
is a liquid, whilst, on the contrary, nitric oxide, which is formed
without contraction and is decomposed without expansion, remains a gas
which is as difficult to liquefy as nitrogen and oxygen. In order to
obtain a still more complete idea of the dependence of the properties
of a compound on the properties of the component substances, it is
further necessary to know the quantity of heat which is developed in the
formation of the compound. If this quantity be large--as, for example,
in the formation of water--then the amount of energy in the resultant
compound will be considerably less than the energy of the elements
entering into its composition; whilst, on the contrary, if the amount of
heat evolved in the formation of a compound be small, or if there even
be an absorption of heat, as in the formation of nitrous oxide, then the
energy of the elements is not destroyed, or is only altered to a slight
extent; hence, notwithstanding the contraction (compression) involved in
its formation, nitrous oxide supports combustion.
The preceding laws were deduced from purely experimental and empirical
data and as such evoke further consequences, as the law of multiple
proportions gave rise to the atomic theory and the law of equivalents
(Chapter IV.) In view of the atomic conception of the constitution of
substances, the question naturally arises as to what, then, are the
relative volumes proper to those physically indivisible molecules which
chemically react on each other and consist of the atoms of elements.
The simplest possible hypothesis in this respect would be that the
volumes of the molecules of substances are equal; or, what is the same
thing, to suppose that equal volumes of vapours and gases contain an
equal number of molecules. This proposition was first enunciated by the
Italian savant _Avogadro_ in 1810. It was also admitted by the French
physico-mathematician _Ampère_ (1815) for the sake of simplifying all
kinds of physico-mathematical conceptions respecting gases. But Avogadro
and Ampère's propositions were not generally received in science
until Gerhardt in the forties had applied them to the generalisation
of chemical reactions, and had demonstrated, by aid of a series of
phenomena, that the reactions of substances actually take place with
the greatest simplicity, and more especially that such reactions take
place between those quantities of substances which occupy equal volumes,
and until he had stated the hypothesis in an exact manner and deduced
the consequences that necessarily follow from it. Following Gerhardt,
Clausius, in the fifties, placed this hypothesis of the equality of
the number of molecules in equal volumes of gases and vapours on the
basis of the kinetic theory of gases. At the present day the hypothesis
of Avogadro and Gerhardt lies at the basis of contemporary physical,
mechanical, and chemical conceptions; the consequences arising from it
have often been subject to doubt, but in the end have been verified by
the most diverse methods; and now, when all efforts to refute those
consequences have proved fruitless, the hypothesis must be considered
as verified,[6] and the _law of Avogadro-Gerhardt_ must be spoken of as
fundamental, and as of great importance for the comprehension of the
phenomena of nature. The law may now be formulated from two points of
view. In the first place, from a physical aspect: _equal volumes of
gases_ (or vapours) at equal temperatures and pressures _contain the
same number of molecules_--or of particles of matter which are neither
mechanically nor physically divisible--previous to chemical change. In
the second place, from a chemical aspect, the same law may be expressed
thus: _the quantities of substances entering into chemical reactions
occupy, in a state of vapour, equal volumes_. For our purpose the
chemical aspect is the most important, and therefore, before developing
the law and its consequences, we will consider the chemical phenomena
from which the law is deduced or which it serves to explain.
[6] It must not be forgotten that Newton's law of gravity was first a
hypothesis, but it became a trustworthy, perfect theory, and
acquired the qualities of a fundamental law owing to the concord
between its deductions and actual facts. All laws, all theories,
of natural phenomena, are at first hypotheses. Some are rapidly
established by their consequences exactly agreeing with facts;
others only take root by slow degrees; and there are many which
are destined to be refuted owing to their consequences being found
to be at variance with facts.
When two isolated substances interact with each other directly and
easily--as, for instance, an alkali and an acid--then it is found that
the reaction is accomplished between quantities which in a gaseous
state occupy equal volumes. Thus ammonia, NH_{3}, reacts directly with
hydrochloric acid, HCl, forming sal-ammoniac, NH_{4}Cl, and in this
case the 17 parts by weight of ammonia occupy the same volume as the
36·5 parts by weight of hydrochloric acid.[7] Ethylene, C_{2}H_{4},
combines with chlorine, Cl_{2}, in only one proportion, forming
ethylene dichloride, C_{2}H_{4}Cl_{2}, and this combination proceeds
directly and with great facility, the reacting quantities occupying
equal volumes. Chlorine reacts with hydrogen in only one proportion,
forming hydrochloric acid, HCl, and in this case equal volumes interact
with each other. If an equality of volumes is observed in cases of
combination, it should be even more frequently encountered in cases
of decomposition, taking place in substances which split up into two
others. Indeed, acetic acid breaks up into marsh gas, CH_{4}, and
carbonic anhydride, CO_{2}, and in the proportions in which they
are formed from acetic acid they occupy equal volumes. Also from
phthalic acid, C_{8}H_{6}O_{4}, there may be obtained benzoic acid,
C_{7}H_{6}O_{2}, and carbonic anhydride, CO_{2}, and as all the elements
of phthalic acid enter into the composition of these substances, it
follows that, although they cannot re-form it by their direct action
on each other (the reaction is not reversible), still they form the
direct products of its decomposition, and they occupy equal volumes.
But benzoic acid, C_{7}H_{6}O_{2}, is itself composed of benzene,
C_{6}H_{6}, and carbonic anhydride, CO_{2}, which also occupy equal
volumes.[8] There is an immense number of similar examples among those
organic substances to whose study Gerhardt consecrated his whole life
and work, and he did not allow such facts as these to escape his
attention. Still more frequently in the phenomena of substitution,
when two substances react on one another, and two are produced without
a change of volume, it is found that the two substances acting on
each other occupy equal volumes as well as each of the two resultant
substances. Thus, in general, reactions of substitution take place
between volatile acids, HX, and volatile alcohols, R(OH), with the
formation of ethereal salts, RX, and water, H(OH), and the volume of the
vapour of the reacting quantities, HX, R(OH), and RX, is the same as
that of water H(OH), whose weight, corresponding with the formula, 18,
occupies 2 volumes, if 1 part by weight of hydrogen occupy 1 volume and
the density of aqueous vapour referred to hydrogen is 9. Such general
examples, of which there are many,[9] show that the reaction of equal
volumes forms a chemical phenomenon of frequent occurrence, indicating
the necessity for acknowledging the law of Avogadro-Gerhardt.
[7] This is not only seen from the above calculations, but may be proved
by experiment. A glass tube, divided in the middle by a stopcock,
is taken and one portion filled with _dry_ hydrogen chloride
(the dryness of the gases is very necessary, because ammonia
and hydrogen chloride are both very soluble in water, so that a
small trace of water may contain a large amount of these gases in
solution) and the other with dry ammonia, under the atmospheric
pressure. One orifice (for instance, of that portion which
contains the ammonia) is firmly closed, and the other is immersed
under mercury, and the cock is then opened. Solid sal-ammoniac is
formed, but if the volume of one gas be greater than that of the
other, some of the first gas will remain. By immersing the tube in
the mercury in order that the internal pressure shall equal the
atmospheric pressure, it may easily be shown that the volume of
the remaining gas is equal to the difference between the volumes
of the two portions of the tube, and that this remaining gas is
part of that whose volume was the greater.
[8] Let us demonstrate this by figures. From 122 grams of benzoic acid
there are obtained (_a_) 78 grams of benzene, whose density
referred to hydrogen = 39, hence the relative volume = 2; and
(_b_) 44 grams of carbonic anhydride, whose density = 22, and
hence the volume = 2. It is the same in other cases.
[9] A large number of such generalised reactions, showing reaction
by equal volumes, occur in the case of the hydrocarbon
derivatives, because many of these compounds are volatile. The
reactions of alkalis on acids, or anhydrides on water, &c.,
which are so frequent between mineral substances, present but
few such examples, because many of these substances are not
volatile and their vapour densities are unknown. But essentially
the same is seen in these cases also; for instance, sulphuric
acid, H_{2}SO_{4}, breaks up into the anhydride, SO_{3}, and
water, H_{2}O, which exhibit an equality of volumes. Let us take
another example where three substances combine in equal volumes:
carbonic anhydride, CO_{2}, ammonia, NH_{3}, and water, H_{2}O
(the volumes of all are equal to 2), form acid ammonium carbonate,
(NH_{4})HCO_{3}.
But the question arises, What is the relation of volumes if the reaction
of two substances takes place in more than one proportion, according to
the law of multiple proportions? A definite answer can only be given in
cases which have been very thoroughly studied. Thus chlorine, in acting
on marsh gas, CH_{4}, forms four compounds, CH_{3}Cl, CH_{2}Cl_{2},
CHCl_{3}, and CCl_{4}, and it may be established by direct experiment
that the substance CH_{3}Cl (methylic chloride) precedes the remainder,
and that the latter proceed from it by the further action of chlorine.
And this substance, CH_{3}Cl, is formed by the reaction of equal volumes
of marsh gas, CH_{4}, and chlorine, Cl_{2}, according to the equation
CH_{4} + Cl_{2} = CH_{3}Cl + HCl. A great number of similar cases are
met with amongst organic--that is, carbon--compounds. Gerhardt was led
to the discovery of his law by investigating many such reactions, and by
observing that in them the reaction of equal volumes precedes all others.
But if nitrogen or hydrogen give several compounds with oxygen, the
question proposed above cannot be answered with complete clearness,
because the successive formations of the different combinations cannot
be so strictly defined. It may be supposed, but neither definitely
affirmed nor experimentally confirmed, that nitrogen and oxygen
first give nitric oxide, NO, and only subsequently the brown vapours
N_{2}O_{3} and NO_{2}. Such a sequence in the combination of nitrogen
with oxygen can only be supposed on the basis of the fact that NO forms
N_{2}O_{3} and NO_{2} directly with oxygen. If it be admitted that NO
(and not N_{2}O or NO_{2}) be first formed, then this instance would
also confirm the law of Avogadro-Gerhardt, because nitric oxide contains
equal volumes of nitrogen and oxygen. So, also, it may be admitted that,
in the combination of hydrogen with oxygen, hydrogen peroxide is first
formed (equal volumes of hydrogen and oxygen), which is decomposed by
the heat evolved into water and oxygen. This explains the presence of
traces of hydrogen peroxide (Chapter IV.) in almost all cases of the
combustion or oxidation of hydrogenous substances; for it cannot be
supposed that water is first formed and then the peroxide of hydrogen,
because up to now such a reaction has not been observed, whilst the
formation of H_{2}O from H_{2}O_{2} is very easily reproduced.[10]
[10] This opinion which I have always held (since the first editions
of this work), as to the primary origin of hydrogen peroxide
and of the formation of water by means of its decomposition,
has in latter days become more generally accepted, thanks more
especially to the work of Traube. Probably it explains most
simply the necessity for the presence of traces of water in
many reactions, as, for instance, in the explosion of carbonic
oxide with oxygen, and perhaps the theory of the explosion of
detonating gas itself and of the combustion of hydrogen will
gain in clearness and truth if we take into consideration the
preliminary formation of hydrogen peroxide and its decomposition.
We may here point out the fact that Ettingen (at Dorpat, 1888)
observed the existence of currents and waves in the explosion of
detonating gas by taking photographs, which showed the periods of
combustion and the waves of explosion, which should be taken into
consideration in the theory of this subject. As the formation of
H_{2}O_{2} from O_{2} and H_{2} corresponds with a less amount of
heat than the formation of water from H_{2} and O, it may be that
the temperature of the flame of detonating gas depends on the
pre-formation of hydrogen peroxide.
Thus a whole series of phenomena show that the chemical reaction of
substances actually takes place, as a rule, between equal volumes,
but this does not preclude the possibility of the frequent reaction
of unequal volumes, although, in this case, it is often possible to
discover a preceding reaction between equal volumes.[11]
[11] The possibility of reactions between unequal volumes,
notwithstanding the general application of the law of
Avogadro-Gerhardt, may, in addition to what has been said
above, depend on the fact that the participating substances,
at the moment of reaction, undergo a preliminary modification,
decomposition, isomeric (polymeric) transformation, &c. Thus,
if NO_{2}, seems to proceed from N_{2}O_{4}, if O_{2} is formed
from O_{3}, and the converse, then it cannot be denied that
the production of molecules containing only one atom is also
possible--for instance, of oxygen--as also of higher polymeric
forms--as the molecule N from N_{2}, or H_{3} from H_{2}. In
this manner it is obviously possible, by means of a series of
hypotheses, to explain the cases of the formation of ammonia,
NH_{3}, from 3 vols. of hydrogen and 1 vol. of nitrogen. But
it must be observed that perhaps our information in similar
instances is, as yet, far from being complete. If hydrazine or
diamide N_{2}H_{4} (Chapter VI. Note 20 bis) is formed and the
imide N_{2}H_{2} in which 2 vols. of hydrogen are combined with
2 vols. of nitrogen, then the reaction here perhaps first takes
place between equal volumes. If it be shown that diamide gives
nitrogen and ammonia (3N_{2}H_{4} = N_{2} + 4NH_{3}) under the
action of sparks, heat, or the silent discharge, &c., then it
will be possible to admit that it is formed before ammonia. And
perhaps the still less stable imide N_{2}H_{2}, which may also
decompose with the formation of ammonia, is produced before the
amide N_{2}H_{4}.
I mention this to show that the fact of apparent exceptions
existing to the law of reactions between equal volumes does not
prove the impossibility of their being included under the law
on further study of the subject. Having put forward a certain
law or hypothesis, consequences must be deduced from it, and
if by their means clearness and consistency are attained--and
especially, if by their means that which could not otherwise
be known can be predicted--then the consequences verify the
hypothesis. This was the case with the law now under discussion.
The mere simplicity of the deduction of the weights proper to
the atoms of the elements, or the mere fact that having admitted
the law it follows (as will afterwards be shown) that the _vis
viva_ of the molecules of all gases is a constant quantity, is
quite sufficient reason for retaining the hypothesis, if not
for believing in it as a fact beyond doubt. And such is the
whole doctrine of atoms. And since by the acceptance of the law
it became possible to foretell even the properties and atomic
weights of elements which had not yet been discovered, and these
predictions afterwards proved to be in agreement with the actual
facts, it is evident that the law of Avogadro-Gerhardt penetrates
deeply into the nature of the chemical relation of substances.
This being granted, it is possible at the present time to exhibit
and deduce the truth under consideration in many ways, and in
every case, like all that is highest in science (for example,
the laws of the indestructibility of matter, of the conservation
of energy, of gravity, &c.), it proves to be not an empirical
conclusion from direct observation and experiment, not a direct
result of analysis, but a creation, or instinctive penetration,
of the inquiring mind, guided and directed by experiment and
observation--a synthesis of which the exact sciences are
capable equally with the highest forms of art. Without such a
synthetical process of reasoning, science would only be a mass
of disconnected results of arduous labour, and would not be
distinguished by that vitality with which it is really endowed
when once it succeeds in attaining a synthesis, or concordance
of outward form with the inner nature of things, without losing
sight of the diversities of individual parts; in short, when
it discovers by means of outward phenomena, which are apparent
to the sense of touch, to observation, and to the common mind,
the internal signification of things--discovering simplicity in
complexity and uniformity in diversity. And this is the highest
problem of science.
The law of Avogadro-Gerhardt may also be easily expressed in an
algebraical form. If the weight of a molecule, or of that quantity
of a substance which enters into chemical reaction and occupies in a
state of vapour, according to the law, a volume equal to that occupied
by the molecules of other bodies, be indicated by the letters M_{1},
M_{2} ... or, in general, M, and if the letters D_{1}, D_{2}, ... or,
in general, D, stand for the density or weight of a given volume of the
gases or vapours of the corresponding substances under certain definite
conditions of temperature and pressure, then the law requires that
M_{1}/D_{1} = M_{2}/D_{2} ... = M/D = C
where C is a certain constant. This expression shows directly that the
volumes corresponding with the weights M_{1}, M_{2} ... M, are equal to
a certain constant, because the volume is proportional to the weight and
inversely proportional to the density. The magnitude of C is naturally
conditioned by and dependent on the units taken for the expression of
the weights of the molecules and the densities. The weight of a molecule
(equal to the sum of the atomic weights of the elements forming it) is
usually expressed by taking the weight of an atom of hydrogen as unity,
and hydrogen is now also chosen as the unit for the expression of the
densities of gases and vapours; it is therefore only necessary to find
the magnitude of the constant for any one compound, as it will be the
same for all others. Let us take water. Its reacting mass is expressed
(conditionally and relatively) by the formula or molecule H_{2}O,
for which M = 18, if H = 1, as we already know from the composition
of water. Its vapour density, or D, compared to hydrogen = 9, and
consequently for water C = 2, and therefore and in general for the
molecules of all substances M/D = 2.
Consequently the weight of a molecule is equal to twice its vapour
density expressed in relation to hydrogen, and conversely _the density
of a gas is equal to half the molecular weight referred to hydrogen_.
The truth of this may be seen from a very large number of observed
vapour densities by comparing them with the results obtained by
calculation. As an illustration, we may point out that for ammonia,
NH_{3}, the weight of the molecule or quantity of the reacting
substance, as well as the composition and weight corresponding with
the formula, is expressed by the figures 14 + 3 = 17. Consequently M
= 17. Hence, according to the law, D = 8·5. And this result is also
obtained by experiment. The density, according to both formula and
experiment, of nitrous oxide, N_{2}O, is 22, of nitric acid 15, and of
nitric peroxide 23. In the case of nitrous anhydride, N_{2}O_{3}, as a
substance which dissociates into NO + NO_{2}, the density should vary
between 38 (so long as the N_{2}O_{3} remains unchanged) and 19 (when
NO + NO_{2} is obtained). There are no figures of constant density for
H_{2}O_{2}, NHO_{3}, N_{2}O_{4}, and many similar compounds which are
either wholly or partially decomposed in passing into vapour. Salts and
similar substances either have no vapour density because they do not
pass into vapour (for instance, potassium nitrate, KNO_{3}) without
decomposition, or, if they pass into vapour without decomposing,
their vapour density is observed with difficulty only at very high
temperatures. The practical determination of the vapour density at these
high temperatures (for example, for sodium chloride, ferrous chloride,
stannous chloride, &c.) requires special methods which have been worked
out by Sainte-Claire Deville, Crafts, Nilson and Pettersson, Meyer,
Scott, and others. Having overcome the difficulties of experiment, it
is found that the law of Avogadro-Gerhardt holds good for such salts
as potassium iodide, beryllium chloride, aluminium chloride, ferrous
chloride, &c.--that is, the density obtained by experiment proves to
be equal to half the molecular weight--naturally within the limits of
experimental error or of possible deviation from the law.
Gerhardt deduced his law from a great number of examples of volatile
carbon compounds. We shall become acquainted with certain of them in
the following chapters; their entire study, from the complexity of
the subject, and from long-established custom, forms the subject of a
special branch of chemistry termed 'organic' chemistry. With all these
substances the observed and calculated densities are very similar.
When the consequences of a law are verified by a great number of
observations, it should be considered as confirmed by experiment. But
this does not exclude the possibility of _apparent_ deviations. They may
evidently be of two kinds: the fraction M/D may be found to be either
greater or less than 2--that is, the calculated density may be either
greater or less than the observed density. When the difference between
the results of experiment and calculation falls within the possible
errors of experiment (for example, equal to hundredths of the density),
or within a possible error owing to the laws of gases having an only
approximate application (as is seen from the deviations, for instance,
from the law of Boyle and Mariotte), then the fraction M/D proves but
slightly different from 2 (between 1·9 and 2·2), and such cases as these
may be classed among those which ought to be expected from the nature
of the subject. It is a different matter if the quotient of M/D be
several times, and in general a multiple, _greater_ or less than 2. The
application of the law must then be explained or it must be laid aside,
because the laws of nature admit of no exceptions. We will therefore
take two such cases, and first one in which the _quotient_ M/D _is
greater than 2, or the density obtained by experiment is less than is in
accordance with the law_.
It must be admitted, as a consequence of the law of Avogadro-Gerhardt,
that there is a decomposition in those cases where the volume of the
vapour corresponding with the weight of the amount of a substance
entering into reaction is greater than the volume of two parts by
weight of hydrogen. Suppose the density of the vapour of water to be
determined at a temperature above that at which it is decomposed,
then, if not all, at any rate a large proportion of the water will be
decomposed into hydrogen and oxygen. The density of such a mixture of
gases, or of detonating gas, will be less than that of aqueous vapour;
it will be equal to 6 (compared with hydrogen), because 1 volume of
oxygen weighs 16, and 2 volumes of hydrogen 2; and, consequently, 3
volumes of detonating gas weigh 18 and 1 volume 6, while the density
of aqueous vapour = 9. Hence, if the density of aqueous vapour be
determined after its decomposition, the quotient M/D would be found
to be 3 and not 2. This phenomenon might be considered as a deviation
from Gerhardt's law, but this would not be correct, because it may be
shown by means of diffusion through porous substances, as described in
Chapter II., that water is decomposed at such high temperatures. In the
case of water itself there can naturally be no doubt, because its vapour
density agrees with the law at all temperatures at which it has been
determined.[12] But there are many substances which decompose with great
ease directly they are volatilised, and therefore only exist as solids
or liquids, and not in a state of vapour. There are, for example, many
salts of this kind, besides all definite solutions having a constant
boiling point, all the compounds of ammonia for example, all ammonium
salts--&c. Their vapour densities, determined by Bineau, Deville, and
others, show that they do not agree with Gerhardt's law. Thus the
vapour density of sal-ammoniac, NH_{4}Cl, is nearly 14 (compared with
hydrogen), whilst its molecular weight is not less than 53·5, whence the
vapour density should be nearly 27, according to the law. The molecule
of sal-ammoniac cannot be less than NH_{4}Cl, because it is formed from
the molecules NH_{3} and HCl, and contains single atoms of nitrogen
and chlorine, and therefore cannot be divided; it further never enters
into reactions with the molecules of other substances (for instance,
potassium hydroxide, or nitric acid) in quantities of less than 53·5
parts by weight, &c. The calculated density (about 27) is here double
the observed density (about 13·4); hence M/D = 4 and not 2. For this
reason the vapour density of sal-ammoniac for a long time served as an
argument for doubting the truth of the law. But it proved otherwise,
after the matter had been fully investigated. The low density depends
on the decomposition of sal-ammoniac, on volatilising, into ammonia and
hydrogen chloride. The observed density is not that of sal-ammoniac, but
of a mixture of NH_{3} and HCl, which should be nearly 14, because the
density of NH_{3} = 8·5 and of HCl = 18·2, and therefore the density
of their mixture (in equal volumes) should be about 13·4.[13] The
actual decomposition of the vapours of sal-ammoniac was demonstrated
by Pebal and Than by the same method as the decomposition of water,
by passing the vapour of sal-ammoniac through a porous substance. The
experiment demonstrating the decomposition during volatilisation of
sal-ammoniac may be made very easily, and is a very instructive point
in the history of the law of Avogadro-Gerhardt, because without its
aid it would never have been imagined that sal-ammoniac decomposed
in volatilising, as this decomposition bears all the signs of simple
sublimation; consequently the knowledge of the decomposition itself
was forestalled by the law. The whole aim and practical use of the
discovery of the laws of nature consists in, and is shown by, the fact
that they enable the unknown to be foretold, the unobserved to be
foreseen. The arrangement of the experiment is based on the following
reasoning.[14] According to the law and to experiment, the density of
ammonia, NH_{3}, is 8-1/2, and of hydrochloric acid, HCl, 18-1/4, if
the density of hydrogen = 1. Consequently, in a mixture of NH_{3} and
HCl, the ammonia will penetrate much more rapidly through a porous
mass, or a fine orifice, than the heavier hydrochloric acid, just as
in a former experiment the hydrogen penetrated more rapidly than the
oxygen. Therefore, if the vapour of sal-ammoniac comes into contact with
a porous mass, the ammonia will pass through it in greater quantities
than the hydrochloric acid, and this excess of ammonia may be detected
by means of moist red litmus paper, which should be turned blue. If the
vapour of sal-ammoniac were not decomposed, it would pass through the
porous mass as a whole, and the colour of the litmus paper would not
be altered, because sal-ammoniac is a neutral salt. Thus, by testing
with litmus the substances passing through the porous mass, it may be
decided whether the sal-ammoniac is decomposed or not when passing into
vapour. Sal-ammoniac volatilises at so moderate a temperature that the
experiment may be conducted in a glass tube heated by means of a lamp,
an asbestos plug being placed near the centre of the tube.[15] The
asbestos forms a porous mass, which is unaltered at a high temperature.
A piece of dry sal-ammoniac is placed at one side of the asbestos
plug, and is heated by a Bunsen burner. The vapours formed are driven
by a current of air forced from a gasometer or bag through two tubes
containing pieces of moist litmus paper, one blue and one red paper
in each. If the sal-ammoniac be heated, then the ammonia appears on
the opposite side of the asbestos plug, and the litmus there turns
blue. And as an excess of hydrochloric acid remains on the side where
the sal-ammoniac is heated, it turns the litmus at that end red. This
proves that the sal-ammoniac, when converted into vapour, splits up into
ammonia and hydrochloric acid, and at the same time gives an instance of
the possibility of correctly conjecturing a fact on the basis of the law
of Avogadro-Gerhardt.[15 bis]
[12] As the density of aqueous vapour remains constant within the
limits of experimental accuracy, even at 1,000°, when
dissociation has certainly commenced, it would appear that only a
very small amount of water is decomposed at these temperatures.
If even 10 p.c. of water were decomposed, the density would be
8·57 and the quotient M/D = 2·1, but at the high temperatures
here concerned the error of experiment is not greater than the
difference between this quantity and 2. And probably at 1,000°
the dissociation is far from being equal to 10 p.c. _Hence the
variation in the vapour density of water does not give us the
means of ascertaining the amount of its dissociation._
[13] This explanation of the vapour density of sal-ammoniac, sulphuric
acid, and similar substances which decompose in being distilled
was the most natural to resort to as soon as the application of
the law of Avogadro-Gerhardt to chemical relations was begun; it
was, for instance, given in my work on _Specific Volumes_, 1856,
p. 99. The formula, M/D = 2, which was applied later by many
other investigators, had already been made use of in that work.
[14] The beginner must remember that an experiment and the mode in
which it is carried out must be determined by the principle or
fact which it is intended to illustrate, and not _vice versa_,
as some suppose. The idea which determines the necessity of an
experiment is the chief consideration.
[15] It is important that the tubes, asbestos, and sal-ammoniac should
be dry, as otherwise the moisture retains the ammonia and
hydrogen chloride.
[15 bis] Baker (1894) showed that the decomposition of NH_{4}Cl in
the act of volatilising only takes place in the presence of water,
traces of which are amply sufficient, but that in the total
absence of moisture (attained by carefully drying with P_{2}O_{5})
there is no decomposition, and the vapour density of the
sal-ammoniac is found to be normal, _i.e._, nearly 27. It is not
yet quite clear what part the trace of moisture plays here, and it
must be presumed that the phenomenon belongs to the category of
electrical and contact phenomena, which have not yet been fully
explained (_see_ Chapter IX., Note 29).
So also the fact of a decomposition may be proved in the other instances
where M/D proved greater than 2, and hence the apparent deviations
appear in reality as an excellent proof of the general application and
significance of the law of Avogadro-Gerhardt.
In those cases where the _quotient_ M/D proves to be _less_ than 2,
or the observed density _greater_ than that calculated, by a multiple
number of times, the matter is evidently more simple, and the fact
observed only indicates that the weight of the molecule is as many times
greater as that taken as the quotient obtained is less than 2. So, for
instance, in the case of ethylene, whose composition is expressed by
CH_{2}, the density was found by experiment to be 14, and in the case
of amylene, whose composition is also CH_{2}, the density proved to be
35, and consequently the quotient for ethylene = 1, and for amylene =
2/5. If the molecular weight of ethylene be taken, not as 14, as might
be imagined from its composition, but as twice as great--namely, as
28--and for amylene as five times greater--that is as 70--then the
molecular composition of the first will be C_{2}H_{4}, and of the
second C_{5}H_{10}, and for both of them M/D will be equal to 2. This
application of the law, which at first sight may appear perfectly
arbitrary, is nevertheless strictly correct, because the amount of
ethylene which reacts--for example, with sulphuric and other acids--is
not equal to 14, but to 28 parts by weight. Thus with H_{2}SO_{4},
Br_{2}, or HI, &c., ethylene combines in a quantity C_{2}H_{4}, and
amylene in a quantity C_{5}H_{10}, and not CH_{2}. On the other hand,
ethylene is a gas which liquefies with difficulty (absolute boiling
point = +10°), whilst amylene is a liquid boiling at 35° (absolute
boiling point = +192°), and by admitting the greater density of the
molecules of amylene (M = 70) its difference from the lighter molecules
of ethylene (M = 28) becomes clear. Thus, the smaller quotient M/D
is _an indication of polymerisation_, as the larger quotient is of
decomposition. The difference between the densities of oxygen and ozone
is a case in point.
On turning to the elements, it is found in certain cases, especially
with metals--for instance, mercury, zinc, and cadmium--that that weight
of the atoms which must be acknowledged in their compounds (of which
mention will be afterwards made) appears to be also the molecular
weight. Thus, the atomic weight of mercury must be taken as = 200,
but the vapour density = 100, and the quotient = 2. Consequently the
_molecule of mercury contains one atom_, Hg. It is the same with sodium,
cadmium, and zinc. This is the simplest possible molecule, which
necessarily is only possible in the case of elements, as the molecule
of a compound must contain at least two atoms. However, the molecules
of many of the elements prove to be complex--for instance, the weight
of an atom of oxygen = 16, and its density = 16, so that its molecule
must contain two atoms, O_{2}, which might already be concluded by
comparing its density with that of ozone, whose molecule contains O_{3}
(Chapter IV.) So also the molecule of hydrogen equals H_{2}, of chlorine
Cl_{2}, of nitrogen N_{2}, &c. If chlorine react with hydrogen, the
volume remains unaltered after the formation of hydrochloric acid,
H_{2} + Cl_{2} = HCl + HCl. It is a case of substitution between the
one and the other, and therefore the volumes remain constant. There
are elements whose molecules are much more complex--for instance,
sulphur, S_{6}--although, by heating, the density is reduced to a third,
and S_{2} is formed. Judging from the vapour density of phosphorus
(D = 62) the molecule contains four atoms P_{4}. Hence many elements
when polymerised appear in molecules which are more complex than the
simplest possible. In carbon, as we shall afterwards find, a very
complex molecule must be admitted, as otherwise its non-volatility and
other properties cannot be understood. And if compounds are decomposed
by a more or less powerful heat, and if polymeric substances are
depolymerised (that is, the weight of the molecule diminishes) by a rise
of temperature, as N_{2}O_{4} passes into NO_{2}, or ozone, O_{3}, into
ordinary oxygen, O_{2}, then we might expect to find the splitting-up of
the complex molecules of elements into the simplest molecule containing
a single atom only--that is to say, if O_{2} be obtained from O_{3},
then the formation of O might also be looked for. The possibility but
not proof of such a proposition is indicated by the vapour of iodine.
Its normal density = 127 (Dumas, Deville, and others), which corresponds
with the molecule I_{2}. At temperatures above 800° (up to which the
density remains almost constant), this density distinctly decreases, as
is seen from the verified results obtained by Victor Meyer, Crafts, and
Troost. At the ordinary pressure and 1,000° it is about 100, at 1,250°
about 80, at 1,400° about 75, and apparently it strives to reduce itself
to one-half--that is, to 63. Under a reduced pressure this splitting-up,
or depolymerisation, of iodine vapour actually reaches a density[16]
of 66, as Crafts demonstrated by reducing the pressure to 100 mm. and
raising the temperature to 1,500°. From this it may be concluded that
at high temperatures and low pressures the molecule I_{2} gradually
passes into the molecule I containing one atom like mercury, and that
something similar occurs with other elements at a considerable rise of
temperature, which tends to bring about the disunion of compounds and
the decomposition of complex molecules.[17]
[16] Just as we saw (Chapter VI. Note 46) an increase of the
dissociation of N_{2}O_{4} and the formation of a large
proportion of NO_{2}, with a decrease of pressure. The
decomposition of I_{2} into I + I is a similar dissociation.
[17] Although at first there appeared to be a similar phenomenon in the
case of chlorine, it was afterwards proved that if there is
a decrease of density it is only a small one. In the case of
bromine it is not much greater, and is far from being equal to
that for iodine.
As in general we very often involuntarily confuse chemical
processes with physical, it may be that a physical process
of change in the coefficient of expansion with a change of
temperature participates with a change in molecular weight,
and partially, if not wholly, accounts for the decrease of the
density of chlorine, bromine, and iodine. Thus, I have remarked
(Comptes Rendus, 1876) that the coefficient of expansion of
gases increases with their molecular weight, and (Chapter II.,
Note 26) the results of direct experiment show the coefficient
of expansion of hydrobromic acid (M = 81) to be 0·00386 instead
of 0·00367, which is that of hydrogen (M = 2). Hence, in the
case of the vapour of iodine (M = 254) a very large coefficient
of expansion is to be expected, and from this cause alone
the relative density would fall. As the molecule of chlorine
Cl_{2} is lighter (= 71) than that of bromine (= 160), which is
lighter than that of iodine (= 254), we see that the order in
which the decomposability of the vapours of these haloids is
observed corresponds with the expected rise in the coefficient of
expansion. Taking the coefficient of expansion of iodine vapour
as 0·004, then at 1,000° its density would be 116. Therefore
the dissociation of iodine may be only an apparent phenomenon.
However, on the other hand, the heavy vapour of mercury (M = 200,
D = 100) scarcely decreases in density at a temperature of 1,500°
(D = 98, according to Victor Meyer); but it must not be forgotten
that the molecule of mercury contains only one atom, whilst that
of iodine contains two, and this is very important. Questions
of this kind which are difficult to decide by experimental
methods must long remain without a certain explanation, owing to
the difficulty, and sometimes impossibility, of distinguishing
between physical and chemical changes.
Besides these cases of apparent discrepancy from the law of
Avogadro-Gerhardt there is yet a third, which is the last, and is very
instructive. In the investigation of separate substances they have to be
isolated in the purest possible form, and their chemical and physical
properties, and among them the vapour density, then determined. If
it be normal--that is, if D = M/2--it often serves as a proof of the
purity of the substance, _i.e._ of its freedom from all foreign matter.
If it be abnormal--that is, if D be not equal to M/2--then for those
who do not believe in the law it appears as a new argument against it
and nothing more; but to those who have already grasped the important
significance of the law it becomes clear that there is some error in
the observation, or that the density was determined under conditions in
which the vapour does not follow the laws of Boyle or Gay-Lussac, or
else that the substance has not been sufficiently purified, and contains
other substances. The law of Avogadro-Gerhardt in that case furnishes
convincing evidence of the necessity of a fresh and more exact research.
And as yet the causes of error have always been found. There are not a
few examples in point in the recent history of chemistry. We will cite
one instance. In the case of pyrosulphuryl chloride, S_{2}O_{5}Cl_{2},
M = 215, and consequently D should = 107·5, instead of which Ogier and
others obtained 53·8--that is, a density half as great; and further,
Ogier (1882) demonstrated clearly that the substance is not dissociated
by distillation into SO_{3} and SO_{2}Cl_{2}, or any other two products,
and thus the abnormal density of S_{2}O_{5}Cl_{2} remained unexplained
until D. P. Konovaloff (1885) showed that the previous investigators
were working with a mixture (containing SO_{3}HCl), and that
pyrosulphuryl chloride has a normal density of approximately 107. Had
not the law of Avogadro-Gerhardt served as a guide, the impure liquid
would have still passed as pure; the more so since the determination of
the amount of chlorine could not aid in the discovery of the impurity.
Thus, by following a true law of nature we are led to true deductions.
All cases which have been studied confirm the law of Avogadro-Gerhardt,
and as by it a deduction is obtained, from the determination of the
vapour density (a purely physical property), as to the weight of the
molecule or quantity of a substance entering into chemical reaction,
this law links together the two provinces of learning--physics and
chemistry--in the most intimate manner. Besides which, the law of
Avogadro-Gerhardt places the conceptions of _molecules_ and _atoms_ on
a firm foundation, which was previously wanting. Although since the
days of Dalton it had become evident that it was necessary to admit the
existence of the elementary atom (the chemical individual indivisible
by chemical or other forces), and of the groups of atoms (or molecules)
of compounds, indivisible by mechanical and physical forces; still
the relative magnitude of the molecule and atom was not defined with
sufficient clearness. Thus, for instance, the atomic weight of oxygen
might be taken as 8 or 16, or any multiple of these numbers, and nothing
indicated a reason for the acceptation of one rather than another of
these magnitudes;[18] whilst as regards the weights of the molecules of
elements and compounds there was no trustworthy knowledge whatever. With
the establishment of Gerhardt's law the idea of the molecule was fully
defined, as well as the relative magnitude of the elementary atom.
[18] And so it was in the fifties. Some took O = 8, others O = 16.
Water in the first case would be HO and hydrogen peroxide HO_{2},
and in the second case, as is now generally accepted, water
H_{2}O and hydrogen peroxide H_{2}O_{2} or HO. Disagreement
and confusion reigned. In 1860 the chemists of the whole world
met at Carlsruhe for the purpose of arriving at some agreement
and uniformity of opinion. I was present at this Congress, and
well remember how great was the difference of opinion, and how
a compromise was advocated with great acumen by many scientific
men, and with what warmth the followers of Gerhardt, at whose
head stood the Italian professor, Canizzaro, followed up the
consequences of the law of Avogadro. In the spirit of scientific
freedom, without which science would make no progress, and would
remain petrified as in the middle ages, and with the simultaneous
necessity of scientific conservatism, without which the roots
of past study could give no fruit, a compromise was not arrived
at, nor ought it to have been, but instead of it truth, in the
form of the law of Avogadro-Gerhardt, received by means of the
Congress a wider development, and soon afterwards conquered all
minds. Then the new so-called Gerhardt atomic weights established
themselves, and in the seventies they were already in general use.
The chemical particle or _molecule must be considered as the quantity
of a substance which enters into chemical reaction with other molecules,
and occupies in a state of vapour the same volume as two parts by weight
of hydrogen_.
The molecular weight (which has been indicated by M) of a substance is
determined by its composition, transformations, and vapour density.
The molecule is not divisible by the mechanical and physical changes
of substances, but in chemical reaction it is either altered in its
properties, or quantity, or structure, or in the nature of the motion of
its parts.
An agglomeration of molecules, which are alike in all chemical respects,
makes up the masses of homogeneous substances in all states.[19]
[19] A bubble of gas, a drop of liquid, or the smallest crystal,
presents an agglomeration of a number of molecules, in a state of
continual motion (like the stars of the Milky Way), distributing
themselves evenly or forming new systems. If the aggregation of
all kinds of heterogeneous molecules be possible in a gaseous
state, where the molecules are considerably removed from each
other, then in a liquid state, where they are already close
together, such an aggregation becomes possible only in the
sense of the mutual reaction between them which results from
their chemical attraction, and especially in the aptitude of
heterogeneous molecules for combining together. Solutions and
other so-called indefinite chemical compounds should be regarded
in this light. According to the principles developed in this
work we should regard them as containing both the compounds of
the heterogeneous molecules themselves and the products of their
decomposition, as in peroxide of nitrogen, N_{2}O_{4} and NO_{2}.
And we must consider that those molecules A, which at a given
moment are combined with B in AB, will in the following moment
become free in order to again enter into a combined form. The
laws of chemical equilibrium proper to dissociated systems cannot
be regarded in any other light.
Molecules consist of atoms in a certain state of distribution and
motion, just as the solar system[20] is made up of inseparable parts
(the sun, planets, satellites, comets, &c.) The greater the number of
atoms in a molecule, the more complex is the resultant substance. The
equilibrium between the dissimilar atoms may be more or less stable,
and may for this reason give more or less stable substances. Physical
and mechanical transformations alter the velocity of the motion and
the distances between the individual molecules, or of the atoms in the
molecules, or of their sum total, but they do not alter the original
equilibrium of the system; whilst chemical changes, on the other hand,
alter the molecules themselves, that is, the velocity of motion, the
relative distribution, and the quality and quantity of the atoms in the
molecules.
[20] This strengthens the fundamental idea of the unity and harmony of
type of all creation and is one of those ideas which impress
themselves on man in all ages, and give rise to a hope of
arriving in time, by means of a laborious series of discoveries,
observations, experiments, laws, hypotheses, and theories, at
a comprehension of the internal and invisible structure of
concrete substances with that same degree of clearness and
exactitude which has been attained in the visible structure of
the heavenly bodies. It is not many years ago since the law of
Avogadro-Gerhardt took root in science. It is within the memory
of many living scientific men, and of mine amongst others. It is
not surprising, therefore, that as yet little progress has been
made in the province of molecular mechanics; but the theory of
gases alone, which is intimately connected with the conception of
molecules, shows by its success that the time is approaching when
our knowledge of the internal structure of matter will be defined
and established.
_Atoms are the smallest quantities_ or chemically indivisible masses _of
the elements forming the molecules_ of elements and compounds.
Atoms have weight, the sum of their weights forms the weight of the
molecule, and the sum of the weights of the molecules forms the weight
of masses, and is the cause of gravity, and of all the phenomena which
depend on the mass of a substance.
The elements are characterised, not only by their independent existence,
their incapacity of being converted into each other, &c., but also by
the weight of their atoms.
Chemical and physical properties depend on the weight, composition, and
properties of the molecules forming a substance, and on the weight and
properties of the atoms forming the molecules.
This is the substance of those principles of molecular mechanics which
lie at the basis of all contemporary physical and chemical constructions
since the establishment of the law of Avogadro-Gerhardt. The fecundity
of the principles enunciated is seen at every step in all the particular
cases forming the present store of chemical data. We will here cite a
few examples of the application of the law.
As the weight of an atom must be understood as the minimum quantity of
an element entering into the composition of all the molecules formed
by it, therefore, in order to find the weight of an atom of oxygen,
let us take the molecules of those of its compounds which have already
been described, together with the molecules of certain of those carbon
compounds which will be described in the following chapter:
Molecular Amount of Molecular Amount of
Weight Oxygen Weight Oxygen
H_{2}O 18 16 HNO_{3} 63 48
N_{2}O 44 16 CO 28 16
NO 30 16 CO_{2} 44 32
NO_{2} 46 32
The number of substances taken might be considerably increased, but
the result would be the same--that is, the molecules of the compounds
of oxygen would never be found to contain less than 16 parts by weight
of this element, but always _n_16, where _n_ is a whole number. The
molecular weights of the above compounds are found either directly from
the density of their vapour or gas, or from their reactions. Thus, the
vapour density of nitric acid (as a substance which easily decomposes
above its boiling point) cannot be accurately determined, but the
fact of its containing one part by weight of hydrogen, and all its
properties and reactions, indicate the above molecular composition and
no other. In this manner it is very easy to find the atomic weight of
all the elements, knowing the molecular weight and composition of their
compounds. It may, for instance, be easily proved that less than _n_12
parts of carbon never enters into the molecules of carbon compounds,
and therefore C must be taken as 12, and not as 6 which was the number
in use before Gerhardt. In a similar manner the atomic weights now
accepted for the elements oxygen, nitrogen, carbon, chlorine, sulphur,
&c., were found and indubitably established, and they are even now
termed the Gerhardt atomic weights. As regards the metals, many of
which do not give a single volatile compound, we shall afterwards
see that there are also methods by which their atomic weights may be
established, but nevertheless the law of Avogadro-Gerhardt is here
also ultimately resorted to, in order to remove any doubt which may be
encountered. Thus, for instance, although much that was known concerning
the compounds of beryllium necessitated its atomic weight being taken
as Be = 9--that is, the oxide as BeO and the chloride BeCl_{2}--still
certain analogies gave reason for considering its atomic weight to be Be
= 13·5, in which case its oxide would be expressed by the composition
Be_{2}O_{3}, and the chloride by BeCl_{3}.[21] It was then found that
the vapour density of beryllium chloride was approximately 40, when
it became quite clear that its molecular weight was 80, and as this
satisfies the formula BeCl_{2}, but does not suit the formula BeCl_{3},
it therefore became necessary to regard the atomic weight of Be as 9 and
not as 13-1/2.
[21] If Be = 9, and beryllium chloride be BeCl_{2}, then for every 9
parts of beryllium there are 71 parts of chlorine, and the
molecular weight of BeCl_{2} = 80; hence the vapour density
should be 40 or _n_{4}0. If Be = 13·5, and beryllium chloride be
BeCl_{3}, then to 13·5 of beryllium there are 106·5 of chlorine;
hence the molecular weight would be 120, and the vapour density
60 or _n_60. The composition is evidently the same in both cases,
because 9 : 71 :: 13·5 : 106·5. Thus, if the symbol of an element
designate different atomic weights, apparently very different
formulæ may equally well express both the percentage composition
of compounds, and those properties which are required by the laws
of multiple proportions and equivalents. The chemists of former
days accurately expressed the composition of substances, and
accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6,
Si = 14, &c. The Gerhardt equivalents are also satisfied by them,
because O = 16, C = 12, Si = 28, &c., are multiples of them.
The choice of one or the other multiple quantity for the atomic
weight is impossible without a firm and concrete conception of
the molecule and atom, and this is only obtained as a consequence
of the law of Avogadro-Gerhardt, and hence the modern atomic
weights are the results of this law (_see_ Note 28).
With the establishment of a true conception of molecules and atoms,
chemical formulæ became direct expressions, not only of composition,[22]
but also of molecular weight or _vapour density_, and consequently of a
series of fundamental chemical and physical data, inasmuch as a number
of the properties of substances are dependent on their vapour density,
or molecular weight and composition. The vapour density D = M/2. For
instance, the formula of ethyl ether is C_{4}H_{10}O, corresponding
with the molecular weight 74, and the vapour density 37, which is the
fact. Therefore, the density of vapours and gases has ceased to be
an empirical magnitude obtained by experiment only, and has acquired
a rational meaning. It is only necessary to remember that 2 grams
of hydrogen, or the molecular weight of this primary gas in grams,
occupies, at 0° and 760 mm. pressure, a volume of 22·3 litres (or
22,300 cubic centimetres), in order to directly determine the weights
of cubical measures of gases and vapours from their formulæ, because
_the molecular weights in grams of all other vapours at 0° and 760 mm.
occupy the same volume, 22·3 litres_. Thus, for example, in the case
of carbonic anhydride, CO_{2}, the molecular weight M = 44, hence 44
grams of carbonic anhydride at 0° and 760 mm. occupy a volume of 22·3
litres--consequently, a litre weighs 1·97 gram. By combining the laws of
gases--Gay-Lussac's, Mariotte's, and Avogadro-Gerhardt's--we obtain[23]
a general formula for gases
6200_s_(273 + _t_) = M_p_
where _s_ is the weight in grams of a cubic centimetre of a vapour or
gas at a temperature _t_ and pressure _p_ (expressed in centimetres of
mercury) if the molecular weight of the gas = M. Thus, for instance, at
100° and 760 millimetres pressure (_i.e._ at the atmospheric pressure)
the weight of a cubic centimetre of the vapour of ether (M = 74) is _s_
= 0·0024.[24]
[22] The percentage amounts of the elements contained in a given
compound may be calculated from its formula by a simple
proportion. Thus, for example, to find the percentage amount of
hydrogen in hydrochloric acid we reason as follows:--HCl shows
that hydrochloric acid contains 35·5 of chlorine and 1 part of
hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1
part by weight of hydrogen, consequently 100 parts by weight of
hydrochloric acid will contain as many more units of hydrogen as
100 is greater than 36·5; therefore, the proportion is as
follows--_x_ : 1 :: 100 : 36·5 or _x_ = 100/36·5 = 2·739.
Therefore 100 parts of hydrochloric acid contain 2·739 parts of
hydrogen. In general, when it is required to transfer a formula
into its percentage composition, we must replace the symbols by
their corresponding atomic weights and find their sum, and knowing
the amount by weight of a given element in it, it is easy by
proportion to find the amount of this element in 100 or any other
quantity of parts by weight. If, on the contrary, it be required
to find the formula from a given percentage composition, we must
proceed as follows: Divide the percentage amount of each element
entering into the composition of a substance by its atomic weight,
and compare the figures thus obtained--they should be in simple
multiple proportion to each other. Thus, for instance, from the
percentage composition of hydrogen peroxide, 5·88 of hydrogen and
94·12 of oxygen, it is easy to find its formula; it is only
necessary to divide the amount of hydrogen by unity and the amount
of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained,
which are in the ratio 1 : 1, which means that in hydrogen
peroxide there is one atom of hydrogen to one atom of oxygen.
The following is a proof of the practical rule given above _that
to find the ratio of the number of atoms from the percentage
composition, it is necessary to divide the percentage amounts
by the atomic weights of the corresponding substances, and to
find the ratio which these numbers bear to each other_. Let us
suppose that two radicles (simple or compound), whose symbols
and combining weights are A and B, combine together, forming
a compound composed of _x_ atoms of A and _y_ atoms of B. The
formula of the substance will be A_x_B_y_. From this formula we
know that our compound contains _x_A parts by weight of the first
element, and _y_B of the second. In 100 parts of our compound
there will be (by proportion) (100. _x_A)/(_x_A + _y_B) of the
first element, and (100. _y_B)/(_x_A + _y_B) of the second. Let
us divide these quantities, expressing the percentage amounts by
the corresponding combining weights; we then obtain 100_x_/(_x_A
+ _y_B) for the first element and 100_y_/(_x_A + _y_B) for the
second element. And these numbers are in the ratio _x_ : _y_--that
is, in the ratio of the number of atoms of the two substances.
It may be further observed that even the very language or
nomenclature of chemistry acquires a particular clearness and
conciseness by means of the conception of molecules, because then
the names of substances may directly indicate their composition.
Thus the term 'carbon dioxide' tells more about and expresses
CO_{2} better than carbonic acid gas, or even carbonic anhydride.
Such nomenclature is already employed by many. But expressing
the composition without an indication or even hint as to the
properties, would be neglecting the advantageous side of the
present nomenclature. Sulphur dioxide, SO_{2}, expresses the same
as barium dioxide, BaO_{2}, but sulphurous anhydride indicates
the acid properties of SO_{2}. Probably in time one harmonious
chemical language will succeed in embracing both advantages.
[23] This formula (which is given in my work on 'The Tension of
Gases,' and in a somewhat modified form in the 'Comptes Rendus,'
Feb. 1876) is deduced in the following manner. According to the
law of Avogadro-Gerhardt, M = 2D for all gases, where M is the
molecular weight and D the density referred to hydrogen. But it is
equal to the weight _s__{0} of a cubic centimetre of a gas in
grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is
the weight in grams of a cubic centimetre of hydrogen. But the
weight _s_ of a cubic centimetre of a gas at a temperature _t_ and
under a pressure _p_ (in centimetres) is equal to _s__{0}_p_/76(1
+ _at_). Therefore, _s__{0} = _s_.76(1 + _at_)/_p_; hence D =
76._s_(1 + _at_)/0·0000898_p_, whence M = 152_s_(1 +
_at_)/0·0000898_p_, which gives the above expression, because
1/_a_ = 273, and 152 multiplied by 273 and divided by 0·0000898 is
nearly 6200. In place of _s_, _m/v_ may be taken, where _m_ is the
weight and _v_ the volume of a vapour.
[24] The above formula may be directly applied in order to ascertain
the molecular weight from the data; weight of vapour _m_ grms.,
its volume _v_ c.c., pressure _p_ cm., and temperature _t_°; for
_s_ = the weight of vapour _m_, divided by the volume _v_, and
consequently M = 6,200_m_(273 + _t_)/_pv_. Therefore, instead
of the formula (_see_ Chapter II., Note 34), _pv_ = R(273 +
_t_), where R varies with the mass and nature of a gas, we
may apply the formula _pv_ = 6,200(_m_/M)(273 + _t_). These
formulæ simplify the calculations in many cases. For example,
required the volume _v_ occupied by 5 grms. of aqueous vapour
at a temperature _t_ = 127° and under a pressure _p_ = 76 cm.
According to the formula M = 6,200_m_(273 + _t_)/_pv_, we find
that _v_ = 9,064 c.c., as in the case of water M = 18, _m_ in
this instance = 5 grms. (These formulæ, however, like the laws of
gases, are only approximate.)
As the molecules of many elements (hydrogen, oxygen, nitrogen, chlorine,
bromine, sulphur--at least at high temperatures) are of uniform
composition, the formulæ of the compounds formed by them directly
indicate the composition by volume. So, for example, the formula HNO_{3}
directly shows that in the decomposition of nitric acid there is
obtained 1 vol. of hydrogen, 1 vol. of nitrogen, and 3 vols. of oxygen.
And since a great number of mechanical, physical, and chemical
properties are directly dependent on the elementary and volumetric
composition, and on the vapour density, the accepted system of atoms
and molecules gives the possibility of simplifying a number of most
complex relations. For instance, it may be easily demonstrated _that
the vis viva of the molecules of all vapours and gases is alike_. For
it is proved by mechanics that the _vis viva_ of a moving mass = (1/2)
_mv_^2, where _m_ is the mass and _v_ the velocity. For a molecule,
_m_ = M, or the molecular weight, and the velocity of the motion of
gaseous molecules = a constant which we will designate by C, divided
by the square root of the density of the gas[25] = C/[sqrt]D, and as D
= M/2, the _vis viva_ of molecules = C^2--that is, a constant for all
molecules. _Q.E.D._[26] The specific heat of gases (Chapter XIV.), and
many other of their properties, are determined by their density, and
consequently by their molecular weight. Gases and vapours in passing
into a liquid state evolve the so-called _latent heat_, which also
proves to be in connection with the molecular weight. The observed
latent heats of carbon bisulphide, CS_{2} = 90, of ether, C_{4}H_{10}O,
= 94, of benzene, C_{6}H_{6}, = 109, of alcohol, C_{2}H_{6}O, = 200,
of chloroform, CHCl_{3}, = 67, &c., show the amount of heat expended
in converting one part by weight of the above substances into vapour.
A great uniformity is observed if the measure of this heat he referred
to the weight of the molecule. For carbon bisulphide the formula CS_{2}
expresses a weight 76, hence the latent heat of evaporation referred to
the molecular quantity CS_{2} = 76 x 90 = 6,840, for ether = 9,656, for
benzene = 8,502, for alcohol = 9,200, for chloroform = 8,007, for water
= 9,620, &c. That is, for molecular quantities, the latent heat varies
comparatively little, from 7,000 to 10,000 heat units, whilst for equal
parts by weight it is ten times greater for water than for chloroform
and many other substances.[27]
[25] Chapter I., Note 34.
[26] _The velocity of the transmission of sound through gases and
vapours_ closely bears on this. It = [sqrt](_Kpg_)/D(1 +
[Greek: a]_t_), where _K_ is the ratio between the two specific
heats (it is approximately 1·4 for gases containing two atoms in a
molecule), _p_ the pressure of the gas expressed by weight (that
is, the pressure expressed by the height of a column of mercury
multiplied by the density of mercury), _g_ the acceleration of
gravity, D the weight of a cubic measure of the gas, [Greek: a] =
0·00367, and _t_ the temperature. Hence, if _K_ be known, and as D
can he found from the composition of a gas, we can calculate the
velocity of the transmission of sound in that gas. Or if this
velocity be known, we can find _K_. The relative velocities of
sound in two gases can he easily determined (Kundt).
If a horizontal glass tube (about 1 metre long and closed at
both ends) be full of a gas, and be firmly fixed at its middle
point, then it is easy to bring the tube and gas into a state
of vibration, by rubbing it from centre to end with a damp
cloth. The vibration of the gas is easily rendered visible, if
the interior of the tube be dusted with lycopodium (the yellow
powder-dust or spores of the lycopodium plant is often employed
in medicine), before the gas is introduced and the tube fused
up. The fine lycopodium powder arranges itself in patches, whose
number depends on the velocity of sound in the gas. If there
be 10 patches, then the velocity of sound in the gas is ten
times slower than in glass. It is evident that this is an easy
method of comparing the velocity of sound in gases. It has been
demonstrated by experiment that the velocity of sound in oxygen
is four times less than in hydrogen, and the square roots of the
densities and molecular weights of hydrogen and oxygen stand in
this ratio.
[27] If the conception of the molecular weights of substances does not
give an exact law when applied to the latent heat of evaporation,
at all events it brings to light a certain uniformity in
figures, which otherwise only represent the simple result of
observation. Molecular quantities of liquids appear to expend
almost equal amounts of heat in their evaporation. It may be said
that the latent heat of evaporation of molecular quantities is
approximately constant, because the _vis viva_ of the motion of
the molecules is, as we saw above, a constant quantity. According
to thermodynamics the latent heat of evaporation is equal to
((_t_ + 273)/E)(_n_´-_n_)_dp_/_d_T × 13·59, where _t_ is the
boiling point, _n_´ the specific volume (_i.e._ the volume of a
unit of weight) of the vapour, and _n_ the specific volume of
the liquid, _dp_/_d_T the variation of the tension with a rise
of temperature per 1°, and 13·89 the density of the mercury
according to which the pressure is measured. Thus the latent heat
of evaporation increases not only with a decrease in the vapour
density (_i.e._ the molecular weight), but also with an increase
in the boiling point, and therefore depends on different factors.
Generalising from the above, the weight of the molecule determines the
properties of a substance _independently of its composition_--_i.e._ of
the number and quality of the atoms entering into the molecule--whenever
the substance is in a gaseous state (for instance, the density of
gases and vapours, the velocity of sound in them, their specific heat,
&c.), or passes into that state, as we see in the latent heat of
evaporation. This is intelligible from the point of view of the atomic
theory in its present form, for, besides a rapid motion proper to the
molecules of gaseous bodies, it is further necessary to postulate that
these molecules are dispersed in space (filled throughout with the
luminiferous ether) like the heavenly bodies distributed throughout
the universe. Here, as there, it is only the degree of removal (the
distance) and the masses of substances which take effect, while
those peculiarities of a substance which are expressed in chemical
transformations, and only come into action on near approach or on
contact, are in abeyance by reason of the dispersal. Hence it is at once
obvious, in the first place, that in the case of solids and liquids,
in which the molecules are closer together than in gases and vapours,
a greater complexity is to be expected, _i.e._ a dependence of all
the properties not only upon the weight of the molecule but also upon
its composition and quality, or upon the properties of the individual
chemical atoms forming the molecule; and, in the second place, that,
in the case of a small number of molecules of any substance being
disseminated through a mass of another substance--for example, in the
formation of weak (dilute) solutions (although in this case there is
an act of chemical reaction--_i.e._ a combination, decomposition, or
substitution)--the dispersed molecules will alter the properties of
the medium in which they are dissolved, almost in proportion to the
molecular weight and almost independently of their composition. The
greater the number of molecules disseminated--_i.e._ the stronger the
solution--the more clearly defined will those properties become which
depend upon the composition of the dissolved substance and its relation
to the molecules of the solvent, for the distribution of one kind of
molecules in the sphere of attraction of others cannot but be influenced
by their mutual chemical reaction. These general considerations give
a starting point for explaining why, since the appearance of Van't
Hoff's memoir (1886), 'The Laws of Chemical Equilibrium in a Diffused
Gaseous or Liquid State' (_see_ Chapter I., Note 19), it has been found
more and more that _dilute_ (weak) solutions exhibit such variations
of properties as depend wholly upon the weight and number of the
molecules and not upon their composition, and even give the means of
determining the weight of molecules by studying the variations of the
properties of a solvent on the introduction of a small quantity of a
substance passing into solution. Although this subject has been already
partially considered in the first chapter (in speaking of solutions),
and properly belongs to a special (physical) branch of chemistry, we
touch upon it here because the meaning and importance of molecular
weights are seen in it in a new and peculiar light, and because it gives
a method for determining them whenever it is possible to obtain dilute
solutions. Among the numerous properties of dilute solutions which have
been investigated (for instance, the osmotic pressure, vapour tension,
boiling point, internal friction, capillarity, variation with change of
temperature, specific heat, electroconductivity, index of refraction,
&c.) we will select one--the 'depression' or fall of the temperature of
freezing (Raoult's cryoscopic method), not only because this method has
been the most studied, but also because it is the most easily carried
out and most frequently applied for determining the weight of the
molecules of substances in solution, although here, owing to the novelty
of the subject there are also many experimental discrepancies which
cannot as yet be explained by theory.[27 bis]
[27 bis] The osmotic pressure, vapour tension of the solvent, and
several other means applied like the cryoscopic method to dilute
solutions for determining the molecular weight of a substance in
solution, are more difficult to carry out in practice, and only
the method of _determining the rise of the boiling point_ of
dilute solutions can from its facility be placed parallel with the
cryoscopic method, to which it bears a strong resemblance, as in
both the solvent changes its state and is partially separated. In
the boiling point method it passes off in the form of a vapour,
while in cryoscopic determinations it separates out in the form of
a solid body.
Van't Hoff, starting from the second law of thermodynamics, showed
that the dependence of the rise of pressure (_dp_) upon a rise of
temperature (_d_T) is determined by the equation _dp_ =
(_kmp_/2T^2)_d_T, where _k_ is the latent heat of evaporation of
the solvent, _m_ its molecular weight, _p_ the tension of the
saturated vapour of the solvent at T, and T the absolute
temperature (T = 273 + _t_), while Raoult found that the quantity
(_p_-_p´_)/_p_ (Chapter I., Note 50) or the measure of the
relative fall of tension (_p_ the tension of the solvent or water,
and _p´_ of the solution) is found by the ratio of the number of
molecules, _n_ of the substance dissolved, and N of the solvent,
so that (_p_-_p´_)/_p_ = C_n_/(N + _n_) where C is a constant.
With very dilute solutions _p_ _-p´_ may be taken as equal to
_dp_, and the fraction _n_/(N + _n_) as equal to _n_/N (because in
that case the value of N is very much greater than _n_), and then,
judging from experiment, C is nearly unity--hence: _dp/p_ = _n_/N
or _dp_ = _np_/N, and on substituting this in the above equation
we have (_kmp_/2T^2)_d_T = _np_/N. Taking a weight of the solvent
_m_/N = 100, and of the substance dissolved (per 100 of the
solvent) _q_, where _q_ evidently = _n_M, if M be the molecular
weight of the substance dissolved, we find that _n_/N = _qm_/100M,
and hence, according to the preceding equation, we have M =
(0·02T^2/_k_)·(_q_/_d_T), that is, by taking a solution of _q_
grms. of a substance in 100 grms. of a solvent, and determining by
experiment the rise of the boiling point _d_T, we find the
molecular weight M of the substance dissolved, because the
fraction 0·02T^2/_k_ is (for a given pressure and solvent) a
constant; for water at 100° (T = 373°) when _k_ = 534 (Chapter I.,
Note 11), it is nearly 5·2, for ether nearly 21, for bisulphide of
carbon nearly 24, for alcohol nearly 11·5, &c. As an example, we
will cite from the determinations made by Professor Sakurai, of
Japan (1893), that when water was the solvent and the substance
dissolved, corrosive sublimate, HgCl_{2}, was taken in the
quantity _q_ = 8·978 and 4·253 grms., the rise in the boiling
point _d_T was = O°·179 and 0°·084, whence M = 261 and 263, and
when alcohol was the solvent, _q_ = 10·873 and 8·765 and _d_T =
0°·471 and 0°·380, whence M = 266 and 265, whilst the actual
molecular weight of corrosive sublimate = 271, which is very near
to that given by this method. In the same manner for aqueous
solutions of sugar (M = 342), when _q_ varied from 14 to 2·4, and
the rise of the boiling point from 0°·21 to 0°·035, M was found to
vary between 339 and 364. For solutions of iodine I_{2} in ether,
the molecular weight was found by this method to be between 255
and 262, and I_{2} = 254. Sakurai obtained similar results
(between 247 and 262) for solutions of iodine in bisulphide of
carbon.