Chapter I: On Water and Its Compounds (4)

According to the law of partial pressures, whatever gas be dissolved in water will be expelled from the solution in an atmosphere of another gas. This depends on the fact that gases dissolved in water escape from it in a vacuum, because the pressure is nil. An atmosphere of another gas acts like a vacuum on a gas dissolved in water. Separation then proceeds, because the molecules of the dissolved gas no longer impinge upon the liquid, are not dissolved in it, and those previously held in solution leave the liquid in virtue of their elasticity.[36] For the same reason a gas may be entirely expelled from a gaseous solution by boiling--at least, in many cases when it does not form particularly stable compounds with water. In fact the surface of the boiling liquid will be occupied by aqueous vapour, and therefore all the pressure acting on the gas will be due to the aqueous vapour. On this account, the partial pressure of the dissolved gas will be very inconsiderable, and this is the sole reason why _a gas separates from a solution on boiling the liquid containing it_. At the boiling point of water the solubility of gases in water is still sufficiently great for a considerable quantity of a gas to remain in solution. The gas dissolved in the liquid is carried away, together with the aqueous vapour; if boiling be continued for a long time, all the gas will finally be separated.[37]

[36] Here two cases occur; either the atmosphere surrounding the
solution may be limited, or it may be proportionally so vast
as to be unlimited, like the earth's atmosphere. If a gaseous
solution be brought into an atmosphere of another gas which is
limited--for instance, as in a closed vessel--then a portion of
the gas held in solution will be expelled, and thus pass over
into the atmosphere surrounding the solution, and will produce
its partial pressure. Let us imagine that water saturated with
carbonic anhydride at 0° and under the ordinary pressure is
brought into an atmosphere of a gas which is not absorbed by
water; for instance, that 10 c.c. of an aqueous solution of
carbonic anhydride is introduced into a vessel holding 10 c.c.
of such a gas. The solution will contain 18 c.c. of carbonic
anhydride. The expulsion of this gas proceeds until a state
of equilibrium is arrived at. The liquid will then contain a
certain amount of carbonic anhydride, which is retained under the
partial pressure of that gas which has been expelled. Now, how
much gas will remain in the liquid and how much will pass over
into the surrounding atmosphere? In order to solve this problem,
let us suppose that _x_ cubic centimetres of carbonic anhydride
are retained in the solution. It is evident that the amount
of carbonic anhydride which passed over into the surrounding
atmosphere will be 18-_x_, and the total volume of gas will be
10 + 18-_x_ or 28-_x_ cubic centimetres. The partial pressure
under which the carbonic anhydride is then dissolved will be
(supposing that the common pressure remains constant the whole
time) equal to (18-_x_)/(28-_x_), hence there is not in solution
18 c.c. of carbonic anhydride (as would be the case were the
partial pressure equal to the atmospheric pressure), but only
18(18-_x_)/(28-_x_), which is equal to _x_, and we therefore
obtain the equation 18(18-_x_)/(28-_x_) = _x_, hence _x_ = 8·69.
Again, where the atmosphere into which the gaseous solution is
introduced is not only that of another gas but also unlimited,
then the gas dissolved will, on passing over from the solution,
diffuse into this atmosphere, and produce an infinitely small
pressure in the unlimited atmosphere. Consequently, no gas can
be retained in solution under this infinitely small pressure,
and it will be entirely expelled from the solution. For this
reason water saturated with a gas which is not contained in air,
will be entirely deprived of the dissolved gas if left exposed
to the air. Water also passes off from a solution into the
atmosphere, and it is evident that there might be such a case as
a constant proportion between the quantity of water vaporised and
the quantity of a gas expelled from a solution, so that not the
gas alone, but the entire gaseous solution, would pass off. A
similar case is exhibited in solutions which are not decomposed
by heat (such as those of hydrogen chloride and iodide), as will
afterwards be considered.

[37] However, in those cases when the variation of the co-efficient of
solubility with the temperature is not sufficiently great, and
when a known quantity of aqueous vapour and of the gas passes
off from a solution at the boiling point, an atmosphere may be
obtained having the same composition as the liquid itself. In
this case the amount of gas passing over into such an atmosphere
will not be greater than that held by the liquid, and therefore
such a gaseous solution will distil over unchanged. The solution
will then represent, like a solution of hydriodic acid in water,
a liquid which is not altered by distillation, while the pressure
under which this distillation takes place remains constant. Thus
in all its aspects solution presents gradations from the most
feeble affinities to examples of intimate chemical combination.
The _amount of heat_ evolved in the solution of equal volumes of
different gases is in distinct relation with these variations of
stability and solubility of different gases. 22·3 litres of the
following gases (at 760 mm. pressure) evolve the following number
of (gram) units of heat in dissolving in a large mass of water;
carbonic anhydride 5,600, sulphurous anhydride 7,700, ammonia
8,800, hydrochloric acid 17,400, and hydriodic acid 19,400. The
two last-named gases, which are not expelled from their solution
by boiling, evolve approximately twice as much heat as gases like
ammonia, which are separated from their solutions by boiling,
whilst gases which are only slightly soluble evolve very much
less heat.

It is evident that the conception of the partial pressures of gases should be applied not only to the formations of solutions, but also to all cases of chemical action of gases. Especially numerous are its applications to the physiology of respiration, for in these cases it is only the oxygen of the atmosphere that acts.[38]

[38] Among the numerous researches concerning this subject, certain
results obtained by Paul Bert are cited in Chapter III., and we
will here point out that Prof. Sechenoff, in his researches on
the absorption of gases by liquids, very fully investigated the
phenomena of the solution of carbonic anhydride in solutions
of various salts, and arrived at many important results, which
showed that, on the one hand, in the solution of carbonic
anhydride in solutions of salts on which it is capable of acting
chemically (for example, sodium carbonate, borax, ordinary sodium
phosphate), there is not only an increase of solubility, but also
a distinct deviation from the law of Henry and Dalton; whilst, on
the other hand, that solutions of salts which are not acted on
by carbonic anhydride (for example, the chlorides, nitrates, and
sulphates) absorb less of it, owing to the 'competition' of the
salt already dissolved, and follow the law of Henry and Dalton,
but at the same time show undoubted signs of a chemical action
between the salt, water, and carbonic anhydride. Sulphuric acid
(whose co-efficient of absorption is 92 vols. per 100), when
diluted with water, absorbs less and less carbonic anhydride,
until the hydrate H_{2}SO_{4},H_{2}O (co-eff. of absorption then
equals 66 vols.) is formed; then on further addition of water the
solubility again rises until a solution of 100 p.c. of water is
obtained.

The solution of _solids_, whilst depending only in a small measure on the pressure under which solution takes place (because solids and liquids are almost incompressible), is very clearly dependent on the temperature. In the great majority of cases the solubility of solids in water increases with the temperature; and further, the rapidity of solution increases also. The latter is determined by the rapidity of diffusion of the solution formed into the remainder of the water. The solution of a solid in water, although it is as with gases, a physical passage into a liquid state, is determined, however, by its chemical affinity for water; this is clearly shown from the fact that in solution there occurs a diminution in volume, a change in the boiling point of water, a change in the tension of its vapour, in the freezing point, and in many similar properties. If solution were a physical, and not a chemical, phenomenon, it would naturally be accompanied by an increase and not by a diminution of volume, because generally in melting a solid increases in volume (its density diminishes). _Contraction_ is the usual phenomenon accompanying solution and takes place even in the addition of solutions to water,[39] and in the solution of liquids in water,[40] just as happens in the combination of substances when evidently new substances are produced.[41] The contraction which takes place in solution is, however, very small, a fact which depends on the small compressibility of solids and liquids, and on the insignificance of the compressing force acting in solution.[42] The change of volume which takes place in the solution of solids and liquids, or the alteration in specific gravity[43] corresponding with it, depends on peculiarities of the dissolving substances, and of water, and, in the majority of cases, is not proportional to the quantity of the substance dissolved,[44] showing the existence of a chemical force between the solvent and the substance dissolved which is of the same nature as in all other forms of chemical reaction.[45]

[39] Kremers made this observation in the following simple form:--He
took a narrow-necked flask, with a mark on the narrow part (like
that on a litre flask which is used for accurately measuring
liquids), poured water into it, and then inserted a funnel,
having a fine tube which reached to the bottom of the flask.
Through this funnel he carefully poured a solution of any salt,
and (having removed the funnel) allowed the liquid to attain a
definite temperature (in a water bath); he then filled the flask
up to the mark with water. In this manner two layers of liquid
were obtained, the heavy saline solution below and water above.
The flask was then shaken in order to accelerate diffusion, and
it was observed that the volume became less if the temperature
remained constant. This can be proved by calculation, if the
specific gravity of the solutions and water be known. Thus at 15°
one c.c. of a 20 p.c. solution of common salt weighs 1·1500 gram,
hence 100 grams occupy a volume of 86·96 c.c. As the sp. gr.
of water at 15° = 0·99916, therefore 100 grams of water occupy
a volume of 100·08 c.c. The sum of the volumes is 187·04 c.c.
After mixing, 200 grams of a 10 p.c. solution are obtained. Its
specific gravity is 1·0725 (at 15° and referred to water at its
maximum density), hence the 200 grams will occupy a volume of
186·48 c.c. The contraction is consequently equal to 0·56 c.c.

[40] The contractions produced in the case of the solution of sulphuric
acid in water are shown in the diagram Fig. 17 (page 77). Their
maximum is 10·1 c.c. per 100 c.c. of the solution formed. A
maximum contraction of 4·15 at 0°, 3·78 at 15°, and 3·50 at 30°,
takes place in the solution of 46 parts by weight of anhydrous
alcohol in 54 parts of water. This signifies that if, at 0°, 46
parts by weight of alcohol be taken per 54 parts by weight of
water, then the sum of their separate volumes will he 104·15, and
after mixing their total volume will be 100.

[41] This subject will be considered later in this work, and we shall
then see that the contraction produced in reactions of
combination (of solids or liquids) is very variable in its
amount, and that there are, although rarely, reactions of
combination in which contraction does not take place, or when an
increase of volume is produced.

[42] The compressibility of solutions of common salt is less, according
to Grassi, than that of water. At 18° the compression of water
per million volumes = 48 vols. for a pressure of one atmosphere;
for a 15 p.c. solution of common salt it is 32, and for a 24
p.c. solution 26 vols. Similar determinations were made by Brown
(1887) for saturated solutions of sal ammoniac (38 vols.), alum
(46 vols.), common salt (27 vols.), and sodium sulphate at +1°,
when the compressibility of water = 47 per million volumes.
This investigator also showed that substances which dissolve
with an evolution of heat and with an increase in volume (as,
for instance, sal ammoniac) are partially separated from their
saturated solutions by an increase of pressure (this experiment
was particularly conclusive in the case of sal ammoniac), whilst
the solubility of substances which dissolve with an absorption
of heat or diminution in volume increases, although very
slightly, _with an increase of pressure_. Sorby observed the same
phenomenon with common salt (1863).

[43] The most trustworthy data relating to the variation of the
specific gravity of solutions with a change of their composition
and temperature, are collected and discussed in my work cited
in footnote 19. The practical (for the amount of a substance in
solution is determined by the aid of the specific gravities of
solutions, both in works and in laboratory practice) and the
theoretical (for specific gravity can be more accurately observed
than other properties, and because a variation in specific
gravity governs the variation of many other properties) interest
of this subject, besides the strict rules and laws to which it
is liable, make one wish that this province of data concerning
solutions may soon be enriched by further observations of as
accurate a nature as possible. Their collection does not present
any great difficulty, although requiring much time and attention.
Pickering in London and Tourbaba in Kharkoff must be ranked first
among those who have pursued problems of this nature during
recent years.

[44] Inasmuch as the degree of change exhibited in many properties on
the formation of solutions is not large, so, owing to the
insufficient accuracy of observations, a proportionality between
this change and a change of composition may, in a first rough
approximation and especially within narrow limits of change
of composition, easily be imagined in cases where it does not
even exist. The conclusion of Michel and Kraft is particularly
instructive in this respect; in 1854, on the basis of their
incomplete researches, they supposed that the increment of the
specific gravity of solutions was proportional to the increment
of a salt in a given volume of a solution, which is only true
for determinations of specific gravity which are exact to
the second decimal place--an accuracy insufficient even for
technical determinations. Accurate measurements do not confirm
a proportionality either in this case or in many others where
a ratio has been generally accepted; as, for example, for the
rotatory power (with respect to the plane of polarisation)
of solutions, and for their capillarity, &c. Nevertheless,
such a method is not only still made use of, but even has its
advantages when applied to solutions within a limited scope--as,
for instance, very weak solutions, and for a first acquaintance
with the phenomena accompanying solution, and also as a means
for facilitating the application of mathematical analysis to
the investigation of the phenomenon of solution. Judging by the
results obtained in my researches on the specific gravity of
solutions, I think that in many cases it would be nearer the
truth to take the change of properties as proportional, not to
the amount of a substance dissolved, but to the product of this
quantity and the amount of water in which it is dissolved; the
more so since many chemical relations vary in proportion to the
reacting masses, and a similar ratio has been established for
many phenomena of attraction studied by mechanics. This product
is easily arrived at when the quantity of water in the solutions
to be compared is constant, as is shown in investigating the fall
of temperature in the formation of ice (_see_ footnote 49, p. 91).

[45] All the different forms of chemical reaction may be said to take
place in the process of solution. (1) _Combinations_ between
the solvent and the substance dissolved, which are more or less
stable (more or less dissociated). This form of reaction is the
most probable, and is that most often observed. (2) Reactions
of _substitution_ or of _double decomposition_ between the
molecules. Thus it may be supposed that in the solution of
sal ammoniac, NH_{4}Cl, the action of water produces ammonia,
NH_{4}HO, and hydrochloric acid, HCl, which are dissolved in
the water and simultaneously attract each other. As these
solutions and many others do indeed exhibit signs, which are
sometimes indisputable, of similar double decompositions (thus
solutions of sal-ammoniac yield a certain amount of ammonia),
it is probable that this form of reaction is more often met
with than is generally thought. (3) Reactions of _isomerism_ or
_replacement_ are also probably met with in solution, all the
more as here molecules of different kinds come into intimate
contact, and it is very likely that the configuration of the
atoms in the molecules under these influences is somewhat
different from what it was in its original and isolated state.
One is led to this supposition especially from observations made
on solutions of substances which rotate the plane of polarisation
(and observations of this kind are very sensitive with respect
to the atomic structure of molecules), because they show, for
example (according to Schneider, 1881), that strong solutions
of malic acid rotate the plane of polarisation to the right,
whilst its ammonium salts in all degrees of concentration
rotate the plane of polarisation to the left. (4) Reactions of
_decomposition_ under the influences of solution are not only
rational in themselves, but have in recent years been recognised
by Arrhenius, Ostwald, and others, particularly on the basis of
electrolytic determinations. If a portion of the molecules of a
solution occur in a condition of decomposition, the other portion
may occur in a yet more complex state of combination, just as the
velocity of the motion of different gaseous molecules may be far
from being the same (_see_ Note 34, p. 81).

It is, therefore, very probable that the reactions taking place
in solution vary both quantitatively and qualitatively with
the mass of water in the solution, and the great difficulty
in arriving at a definite conclusion as to the nature of the
chemical relations which take place in the process of solution
will be understood, and if besides this the existence of a
physical process, like the sliding between and interpenetration
of two homogeneous liquids, be also recognised in solution,
then the complexity of the problem as to the actual nature of
solutions, which is now to the fore, appears in its true light.
However, the efforts which are now being applied to the solution
of this problem are so numerous and of such varied aspect that
they will afford future investigators a vast mass of material
towards the construction of a complete theory of solution.

For my part, I am of opinion that the study of the physical
properties of solutions (and especially of weak ones) which now
obtains, cannot give any fundamental and complete solution of
the problem whatever (although it should add much to both the
provinces of physics and chemistry), but that, parallel with it,
should be undertaken the study of the influence of temperature,
and especially of low temperatures, the application to solutions
of the mechanical theory of heat, and the comparative study of
the chemical properties of solutions. The beginning of all this
is already established, but it is impossible to consider in so
short an exposition of chemistry the further efforts of this kind
which have been made up to the present date.

The feeble development of the chemical affinities acting in solutions of solids becomes evident from those multifarious methods by which _their solutions are decomposed_, whether they be saturated or not. On heating (absorption of heat), on cooling, and by internal forces alone, aqueous solutions in many cases separate into their components or their definite compounds with water. The water contained in solutions is removed from them as vapour, or, by freezing, in the form of ice,[46] but the _tension of the vapour of water_[47] held in solution is less than that of water in a free state, and the _temperature of the formation of ice_ from solutions is lower than 0°. Further, both the diminution of vapour tension and the lowering of the freezing point proceed, in dilute solutions, almost in proportion to the amount of a substance dissolved.[48] Thus, if per 100 grams of water there be in solution 1, 5, 10 grams of common salt (NaCl), then at 100° the vapour tension of the solutions decreases by 4, 21, 43 mm. of the barometric column, against 760 mm., or the vapour tension of water, whilst the freezing points are -0·58°, -2·91°, and -6·10° respectively. The above figures[49] are almost proportional to the amounts of salt in solution (1, 5, and 10 per 100 of water). Furthermore, it has been shown by experiment that the ratio of the diminution of vapour tension to the vapour tension of water at different temperatures in a given solution is an almost constant quantity,[50] and that for every (dilute) solution the ratio between the diminution of vapour tension and of the freezing point is also a tolerably constant quantity.[51]

[46] If solutions are regarded as being in a state of dissociation
(_see_ footnote 19, p. 64) it would be expected that they would
contain free molecules of water, which form one of the products
of the decomposition of those definite compounds whose formation
is the cause of solution. In separating as ice or vapour, water
makes, with a solution, a heterogeneous system (made up of
substances in different physical states) similar, for instance,
to the formation of a precipitate or volatile substance in
reactions of double decomposition.

[47] If the substance dissolved is non-volatile (like salt or sugar),
or only slightly volatile, then the whole of the tension of
the vapour given off is due to the water, but if a solution
of a volatile substance--for instance, a gas or a volatile
liquid--evaporates, then only a portion of the pressure belongs
to the water, and the whole pressure observed consists of the sum
of the pressures of the vapours of the water and of the substance
dissolved. The majority of researches bear on the first case,
which will be spoken of presently, and the observations of D. P.
Konovaloff (1881) refer to the second case. He showed that in the
case of two volatile liquids, mutually soluble in each other,
forming two layers of saturated solutions (for example, ether
and water, Note 20, p. 67), both solutions have an equal vapour
tension (in the case in point the tension of both is equal to 431
mm. of mercury at 19·8°). Further, he found that for solutions
which are formed in all proportions, the tension is either
greater (solutions of alcohol and water) or less (solutions of
formic acid) than that which answers to the rectilinear change
(proportional to the composition) from the tension of water
to the tension of the substance dissolved; thus, the tension,
for example, of a 70 p.c. solution of formic acid is less, at
all temperatures, than the tension of water and of formic acid
itself. In this case the tension of a solution is never equal to
the sum of the tensions of the dissolving liquids, as Regnault
already showed when he distinguished this case from that in
which a mixture of liquids, which are insoluble in each other,
evaporates. From this it is evident that a mutual action occurs
in solution, which diminishes the vapour tensions proper to the
individual substances, as would be expected on the supposition of
the formation of compounds in solutions, because the elasticity
then always diminishes.

[48] This amount is usually expressed by the weight of the substance
dissolved per 100 parts by weight of water. Probably it would
be better to express it by the quantity of the substance in a
definite volume of the solution--for instance, in a litre--or
by the ratios of the number of molecules of water and of the
substance dissolved.

[49] The variation of the vapour tension of solutions has been
investigated by many. The best known researches are those of
Wüllner in Germany (1858-1860) and of Tamman in Russia (1887).
The researches on the temperature of the formation of ice from
various solutions are also very numerous; Blagden (1788),
Rüdorff (1861), and De Coppet (1871) established the beginning,
but this kind of investigation takes its chief interest from
the work of Raoult, begun in 1882 on aqueous solutions, and
afterwards continued for solutions in various other easily frozen
liquids--for instance, benzene, C_{6}H_{6} (melts at 4·96°),
acetic acid, C_{2}H_{4}O_{2} (16·75°), and others. An especially
important interest is attached to these cryoscopic investigations
of Raoult in France on the depression of the freezing point,
because he took solutions of many well-known carbon-compounds
and discovered a simple relation between the molecular weight
of the substances and the temperature of crystallisation of the
solvent, which enabled this kind of research to be applied to
the investigation of the nature of substances. We shall meet
with the application of this method later on (_see also_ Chapter
VII.), and at present will only cite the deduction arrived at
from these results. The solution of one-hundredth part of that
molecular gram weight which corresponds with the formula of a
substance dissolved (for example, NaCl = 58·5, C_{2}H_{6}O = 46,
&c.) in 100 parts of a solvent lowers the freezing point of its
solution in water 0·185°, in benzene 0·49°, and in acetic acid
O·39°, or twice as much as with water. And as in weak solutions
the depression or fall of freezing point is proportional to the
amount of the substance dissolved, it follows that the fall of
freezing point for all other solutions may be calculated from
this rule. So, for instance, the weight which corresponds with
the formula of acetone, C_{3}H_{6}O is 58; a solution containing
2·42, 6·22, and 12·35 grams of acetone per 100 grams of water,
forms ice (according to the determinations of Beckmann) at
0·770°, 1·930°, and 3·820°, and these figures show that with
a solution containing 0·58 gram of acetone per 100 of water
the fall of the temperature of the formation of ice will be
0·185°, 0·180°, and 0·179°. It must be remarked that the law of
proportionality between the fall of temperature of the formation
of ice, and the composition of a solution, is in general only
approximate, and is only applicable to weak solutions (Pickering
and others).

We will here remark that the theoretical interest of this subject
was strengthened on the discovery of the connection existing
between the fall of tension, the fall of the temperature of the
formation of ice, of osmotic pressure (Van't Hoff, Note 19),
and of the electrical conductivity of solutions, and we will
therefore supplement what we have already said on the subject by
some short remarks on the method of cryoscopic investigations,
although the details of the subject form the subject of more
special works on physical chemistry (such as Ostwald's _Lehrbuch
der allgemeinen Chemie_, 1891-1894, 2 vols.)

In order to determine the _temperature of the formation of
ice_ (or of crystallisation of other solvents), a solution
of known strength is prepared and poured into a cylindrical
vessel surrounded by a second similar vessel, leaving a layer
of air between the two, which, being a bad conductor, prevents
any rapid change of temperature. The bulb of a sensitive and
corrected thermometer is immersed in the solution, and also a
bent platinum wire for stirring the solution; the whole is then
cooled (by immersing the apparatus in a freezing mixture), and
the temperature at which ice begins to separate observed. If
the temperature at first falls slightly lower, it nevertheless
becomes constant when ice begins to form. By then allowing the
liquid to get just warm, and again observing the temperature of
the formation of ice, an exact determination may be arrived at.
It is still better to take a large mass of solution, and induce
the formation of the first crystals by dropping a small lump
of ice into the solution already partially over-cooled. This
only imperceptibly changes the composition of the solution. The
observation should be made at the point of formation of only a
very small amount of crystals, as otherwise the composition of
the solution will become altered from their separation. Every
precaution must be taken to prevent the access of moisture to the
interior of the apparatus, which might also alter the composition
of the solution or properties of the solvent (for instance, when
using acetic acid).

With respect to the depression of dilute solutions it is
known--(1) That the depression increases in almost direct
proportion to the amount of the substance in solution (always
per 100 parts of water), for example, for KCl when the solution
contains 1 part of salt (per 100 parts of water) the depression =
0·45°, when the solution contains 2 parts of salt = 0·90°, with
10 parts of salt = 4·4°. (2) The greater the molecular weight
expressed by the formula (see Chapter VII.), and designated
by M, the less, under other similar conditions, will be the
depression _d_, and therefore if the concentration of a solution
(the amount by weight of substance dissolved per 100 parts of
water) be designated by _p_, then the fraction M_d_/_p_ or the
molecular depression for a given class of substances will be a
constant quantity; for example, in the case of methyl alcohol in
water 17·3, for acetone about 18·0, for sugar about 18·5. (3) In
general the molecular depression for substances whose solutions
do not conduct an electric current is about 18·5, while for
acids, salts, and such like substances whose solutions do conduct
electricity, it is _i_ times greater; for instance, for HCl, KI,
HNO_{3}, KHO, &c., about 36 (_i_ is nearly 2), for borax about
66, and so on where _i_ varies in the same manner as it does in
the case of the osmotic pressure of solutions (Note 19). (4)
Different solvents (water, acetic acid, benzene, &c.) have each
their corresponding constants of molecular depression (which have
a certain remote connection with their molecular weight); for
example, for acetic acid the molecular depression is about 39 and
not 19 (as it is for water), for benzene 49, for methyl alcohol
about 17, &c. (5) If the molecular weight M of a substance be
unknown, then in the case of non-conductors of electricity or for
a given group, it may be found by determining the depression,
_d_, for a given concentration, _p_; for example, in the case of
peroxide of hydrogen, which is a non-conductor of electricity,
the molecular weight, M, was found to be nearly 34, _i.e._ equal
to H_{2}O_{2}.

Similar results have also been found for the fall in the
vapour tension of solutions (Note 51), and for the rise of
their boiling points (hence these data may also serve for
determining the molecular weight of a substance in solution,
as is shortly described in Chapter VII., Note 27 bis). And as
these conclusions are also applicable in the case of osmotic
pressure (Note 19), and a variation in the magnitude of _i_, in
passing from solutions which do not conduct an electric current
to those which do conduct electricity is everywhere remarked,
so it was natural to here seek that causal connection which
Arrhenius (1888), Ostwald, and others expected to find in the
supposition that a portion of the substance of the electrolyte
is already decomposed in the very act of solution, into its
ions (for example, NaCl into Na and Cl), or into the atoms of
those individual substances which make their appearance in
electrolysis, and in this way to explain the fact that _i_ is
greater for those bodies which conduct an electric current.
We will not consider here this supposition, known as the
hypothesis of 'electrolytic dissociation,' not only because
it wholly belongs to that special branch--physical chemistry,
and gives scarcely any help towards explaining the chemical
relations of solutions (particularly their passage into definite
compounds, their reactions, and their very formation), but
also because--(1) all the above data (for constant depression,
osmotic pressure, &c.) only refer to dilute solutions, and are
not applicable to strong solutions; whilst the chemical interest
in strong solutions is not less than in dilute solutions, and
the transition from the former into the latter is consecutive
and inevitable; (2) because in all homogeneous bodies (although
it may be insoluble and not an electrolyte) a portion of the
atoms may he supposed (Clausius) to be passing from one particle
to another (Chapter X., Note 28), and as it were dissociated,
but there are no reasons for believing that such a phenomenon
is proper to the solutions of electrolytes only; (3) because no
essential mark of difference is observed between the solution of
electrolytes and non-conductors, although it might be expected
there would be according to Arrhenius' hypothesis; (4) because it
is most reasonable to suppose the formation of new, more complex,
but unstable and easily dissociated compounds in the act of
solution, than a decomposition, even partial, of the substances
taken; (5) because if Arrhenius' hypothesis be accepted it
becomes necessary to admit the existence in solutions of free
ions, like the atoms Cl or Na, without any apparent expenditure
of the energy necessary for their disruption, and if in this case
it can be explained why _i_ then = 2, it is not at all clear why
solutions of MgSO_{4} give _i_ = 1, although the solution does
conduct an electric current; (6) because in dilute solutions,
the approximative proportionality between the depression and
concentration may be recognised, while admitting the formation
of hydrates, with as much right as in admitting the solution
of anhydrous substances, and if the formation of hydrates be
recognised it is easier to admit that a portion of these hydrates
is decomposed than to accept the breaking-up into ions; (7)
because the best conductors of electricity are solutions like the
sulphates in which it is necessary to recognise the formation
of associated systems or hydrates; (8) because the cause of
electro-conductivity can be sooner looked for in this affinity
and this combination of the substance dissolved with the solvent,
as is seen from the fact, that (D. P. Konovaloff) neither aniline
nor acetic acid alone conduct an electric current, a solution
of aniline in water conducts it badly (and here the affinity is
very small), while a solution of aniline in acetic acid forms a
good electrolyte, in which, without doubt, chemical forces are
acting, bringing aniline, like ammonia, into combination with the
acetic acid; which is evident from the researches made by Prof.
Konovaloff upon mixtures (solutions) of aniline and other amines;
and, lastly, (9) because I, together with many of the chemists
of the present day, cannot regard the hypothesis of electrolytic
dissociation in the form given to it up to now by Arrhenius and
Ostwald, as answering to the sum total of the chemical data
respecting solutions and dissociation in general. Thus, although
I consider it superfluous to discuss further the evolution of
the above theory of solutions, still I think that it would he
most useful for students of chemistry to consider all the data
referring to this subject, which can be found in the _Zeitschrift
für physikalische Chemie_, 1888-1894.

[50] This fact, which was established by Gay-Lussac, Pierson, and
v. Babo, is confirmed by the latest observations, and enables us
to express not only the fall of tension (_p_-_p_´) itself, but
its ratio to the tension of water (_p_-_p_´)/_p_. It is to be
remarked that in the absence of any chemical action, the fall of
pressure is either very small, or does not exist at all (note
33), and is not proportional to the quantity of the substance
added. As a rule, the tension is then equal, according to the law
of Dalton, to the sum of the tensions of the substances taken.
Hence liquids which are insoluble in each other (for example,
water and chloride of carbon) present a tension equal to the sum
of their individual tensions, and therefore such a mixture boils
at a lower temperature than the more volatile liquid (Magnus,
Regnault).

[51] If, in the example of common salt, the fall of tension be divided
by the tension of water, a figure is obtained which is nearly
105 times less than the magnitude of the fall of temperature of
formation of ice. This correlation was theoretically deduced
by Goldberg, on the basis of the application of the mechanical
theory of heat, and is repeated by many investigated solutions.

The diminution of the vapour tension of solutions explains the rise in boiling point due to the solution of solid non-volatile bodies in water. The temperature of a vapour is the same as that of the solution from which it is generated, and therefore it follows that the aqueous vapour given off from a solution will be superheated. A saturated solution of common salt boils at 108·4°, a solution of 335 parts of nitre in 100 parts of water at 115·9°, and a solution of 325 parts of potassium chloride in 100 parts of water at 179°, if the temperature of ebullition be determined by immersing the thermometer bulb in the liquid itself. This is another proof of the bond which exists between water and the substance dissolved. And this bond is seen still more clearly in those cases (for example, in the solution of nitric or formic acid in water) where the solution boils at a higher temperature than either water or the volatile substance dissolved in it. For this reason the solutions of certain gases--for instance, hydriodic or hydrochloric acid--boil above 100°.

The separation of ice from solutions[52] explains both the phenomenon, well known to sailors, that the ice formed from salt water gives fresh water, and also the fact that by freezing, just as by evaporation, a solution is obtained which is richer in salts than before. This is taken advantage of in cold countries for obtaining a liquor from sea water, which is then evaporated for the extraction of salt.

[52] Fritzsche showed that solutions of certain colouring matters yield
colourless ice, which clearly proves the passage of water only
into a solid state, without any intermixture of the substance
dissolved, although the possibility of the admixture in certain
other cases cannot be denied.

On the removal of part of the water from a solution (by evaporation or the separation of ice), a saturated solution should be obtained, and then the solid substance dissolved should separate out. Solutions saturated at a certain temperature should also separate out a corresponding portion of the substance dissolved if they be reduced, by cooling,[53] to a temperature at which the water can no longer hold the former quantity of the substance in solution. If this separation, by cooling a saturated solution or by evaporation, take place slowly, _crystals_ of the substance dissolved are in many cases formed; and this is the method by which crystals of soluble salts are usually obtained. Certain solids very easily separate out from their solutions in perfectly formed crystals, which may attain very large dimensions. Such are nickel sulphate, alum, sodium carbonate, chrome-alum, copper sulphate, potassium ferricyanide, and a whole series of other salts. The most remarkable circumstance in this is that many solids in separating out from an aqueous solution retain a portion of water, forming crystallised solid substances which contain water. A portion of the water previously in the solution remains in the separated crystals. The water which is thus retained is called the _water of crystallisation_. Alum, copper sulphate, Glauber's salt, and magnesium sulphate contain such water, but neither sal-ammoniac, table salt, nitre, potassium chlorate, silver nitrate, nor sugar, contains any water of crystallisation. One and the same substance may separate out from a solution with or without water of crystallisation, according to the temperature at which the crystals are formed. Thus common salt in crystallising from its solution in water at the ordinary or at a higher temperature does not contain water of crystallisation. But if its separation from the solution takes place at a low temperature, namely below -5°, then the crystals contain 38 parts of water in 100 parts. Crystals of the same substance which separate out at different temperatures may contain different amounts of water of crystallisation. This proves to us that a solid dissolved in water may form various compounds with it, differing in their properties and composition, and capable of appearing in a solid separate form like many ordinary definite compounds. This is indicated by the numerous properties and phenomena connected with solutions, and gives reason for thinking that there exist in solutions themselves such compounds of the substance dissolved, and the solvent or compounds similar to them, only in a liquid partly decomposed form. Even the _colour of solutions_ may often confirm this opinion. Copper sulphate forms crystals having a blue colour and containing water of crystallisation. If the water of crystallisation be removed by heating the crystals to redness, a colourless anhydrous substance is obtained (a white powder). From this it may be seen that the blue colour belongs to the compound of the copper salt with water. Solutions of copper sulphate are all blue, and consequently they contain a compound similar to the compound formed by the salt with its water of crystallisation. Crystals of cobalt chloride when dissolved in an anhydrous liquid--like alcohol, for instance--give a blue solution, but when they are dissolved in water a red solution is obtained. Crystals from the aqueous solution, according to Professor Potilitzin, contain six times as much water (CoCl_{2},6H_{2}O) for a given weight of the salt, as those violet crystals (CoCl_{2},H_{2}O) which are formed by the evaporation of an alcoholic solution.

[53] As the solubility of certain substances (for example, coniine,
cerium sulphate, and others) decreases with a rise of temperature
(between certain limits--see, for example, note 24), so these
substances do not separate from their saturated solutions on
cooling but on heating. Thus a solution of manganese sulphate,
saturated at 70°, becomes cloudy on further heating. The point at
which a substance separates from its solution with a change of
temperature gives an easy means of determining the co-efficient
of solubility, and this was taken advantage of by Prof. Alexéeff
for determining the solubility of many substances. The phenomenon
and method of observation are here essentially the same as in
the determination of the temperature of formation of ice. If a
solution of a substance which separates out on heating be taken
(for example, the sulphate of calcium or manganese), then at a
certain fall of temperature ice will separate out from it, and
at a certain rise of temperature the salt will separate out.
From this example, and from general considerations, it is clear
that the separation of a substance dissolved from a solution
should present a certain analogy to the separation of ice from a
solution. In both cases, a heterogeneous system of a solid and a
liquid is formed from a homogeneous (liquid) system.

That solutions contain particular compounds with water is further shown by the phenomena of supersaturated solutions, of so-called cryohydrates, of solutions of certain acids having constant boiling points, and the properties of compounds containing water of crystallisation whose data it is indispensable to keep in view in the consideration of solutions.

Supersaturated solutions exhibit the following phenomena:--On the refrigeration of a saturated solution of certain salts,[54] if the liquid be brought under certain conditions, the excess of the solid may sometimes remain in solution and not separate out. A great number of substances, and more especially sodium sulphate, Na_{2}SO_{4}, or Glauber's salt, easily form supersaturated solutions. If boiling water be saturated with this salt, and the solution be poured off from any remaining undissolved salt, and, the boiling being still continued, the vessel holding the solution be well closed by cotton wool, or by fusing up the vessel, or by covering the solution with a layer of oil, then it will he found that this saturated solution does not separate out any Glauber's salt whatever on cooling down to the ordinary or even to a much lower temperature; although without the above precautions a salt separates out on cooling, in the form of crystals, which contain Na_{2}SO_{4},10H_{2}O--that is, 180 parts of water for 142 parts of anhydrous salt. The supersaturated solution may be moved about or shaken inside the vessel holding it, and no crystallisation will take place; the salt remains in the solution in as large an amount as at a higher temperature. If the vessel holding the supersaturated solution be opened and a crystal of Glauber's salt be thrown in, crystallisation suddenly takes place.[55] A considerable rise in temperature is noticed during this rapid separation of crystals, which is due to the fact that the salt, previously in a liquid state, passes into a solid state. This bears some resemblance to the fact that water maybe cooled below 0° (even to -10°) if it be left at rest, under certain circumstances, and evolves heat in suddenly crystallising. Although from this point of view there is a resemblance, yet in reality the phenomenon of supersaturated solutions is much more complicated. Thus, on cooling, a saturated solution of Glauber's salt deposits crystals containing Na_{2}SO_{4},7H_{2}0,[56] or 126 parts of water per 142 parts of anhydrous salt, and not 180 parts of water, as in the above-mentioned salt. The crystals containing 7H_{2}O are distinguished for their instability; if they stand in contact not only with crystals of Na_{2}SO_{4},10H_{2}O, but with many other substances, they immediately become opaque, forming a mixture of anhydrous and deca-hydrated salts. It is evident that between water and a soluble substance there may be established different kinds of greater or less stable equilibrium, of which solutions form a particular case.[57]

[54] Those salts which separate out with water of crystallisation and
give several crystallohydrates form supersaturated solutions with
the greatest facility, and the phenomenon is much more common
than was previously imagined. The first data were given in the
last century by Loewitz, in St. Petersburg. Numerous researches
have proved that supersaturated solutions do not differ from
ordinary solutions in any of their essential properties. The
variations in specific gravity, vapour tension, formation of ice,
&c., take place according to the ordinary laws.

[55] Inasmuch as air, as has been shown by direct experiment, contains,
although in very small quantities, minute crystals of salts,
and among them sodium sulphate, air can bring about the
crystallisation of a supersaturated solution of sodium sulphate
in an open vessel, but it has no effect on saturated solutions of
certain other salts; for example, lead acetate. According to the
observations of De Boisbaudran, Gernez, and others, isomorphous
salts (analogous in composition) are capable of inducing
crystallisation. Thus, a supersaturated solution of nickel
sulphate crystallises by contact with crystals of sulphates of
other metals analogous to it, such as those of magnesium, cobalt,
copper, and manganese. The crystallisation of a supersaturated
solution, set up by the contact of a minute crystal, starts from
it in rays with a definite velocity, and it is evident that the
crystals as they form propagate the crystallisation in definite
directions. This phenomenon recalls the evolution of organisms
from germs. An attraction of similar molecules ensues, and they
dispose themselves in definite similar forms.

[56] At the present time a view is very generally accepted, which
regards supersaturated solutions as homogeneous systems, which
pass into heterogeneous systems (composed of a liquid and a
solid substance), in all respects exactly resembling the passage
of water cooled below its freezing point into ice and water,
or the passage of crystals of rhombic sulphur into monoclinic
crystals, and of the monoclinic crystals into rhombic. Although
many phenomena of supersaturation are thus clearly understood,
yet the spontaneous formation of the unstable hepta-hydrated salt
(with 7H_{2}O), in the place of the more stable deca-hydrated
salt (with mol. 10H_{2}O), indicates a property of a saturated
solution of sodium sulphate which obliges one to admit that
it has a different structure from an ordinary solution.
Stcherbacheff asserts, on the basis of his researches, that
a solution of the deca-hydrated salt gives, on evaporation,
without the aid of heat, the deca-hydrated salt, whilst after
heating above 33° it forms a supersaturated solution and the
hepta-hydrated salt. But in order that this view should be
accepted, some facts must be discovered distinguishing solutions
(which are, according to this view, isomeric) containing the
hepta-hydrated salt from those containing the deca-hydrated
salt, and all efforts in this direction (the study of the
properties of the solutions) have given negative results. As
some crystallohydrates of salts (alums, sugar of lead, calcium
chloride) melt straightway (without separating out anything),
whilst others (like Na_{2}SO_{4},10H_{2}O) are broken up, then
it may be that the latter are only in a state of equilibrium at
a higher temperature than their melting point. It may here be
observed that in melting crystals of the deca-hydrated salt,
there is formed, besides the solid anhydrous salt, a saturated
solution giving the hepta-hydrated salt, so that this passage
from the deca-to the hepta-hydrated salt, and the reverse,
takes place with the formation of the anhydrous (or, it may be,
monohydrated) salt.

Moreover, supersaturation (Potilitzin, 1889) only takes
place with those substances which are capable of giving
several modifications or several crystallohydrates, _i.e._
supersaturated solutions separate out, besides the stable normal
crystallohydrate, hydrates containing less water and also the
anhydrous salt. This degree of saturation acts upon the substance
dissolved in a like manner to heat. Sulphate of nickel in a
solution at 15° to 20° separates out rhombic crystals with
7H_{2}O, at 30° to 40° cubical crystals, with 6H_{2}O, at 50° to
70° monoclinic crystals, also containing 6H_{2}O. Crystals of
the same composition separate out from supersaturated solutions
at one temperature (17° to 19°), but at different degrees of
saturation, as was shown by Lecoq de Boisbaudran. The capacity
to voluntarily separate out slightly hydrated or anhydrous salts
by the introduction of a crystal into the solution is common to
all supersaturated solutions. If a salt forms a supersaturated
solution, then one would expect, according to this view, that
it should exist in the form of several hydrates or in several
modifications. Thus Potilitzin concluded that chlorate of
strontium, which easily gives supersaturated solutions, should
be capable of forming several hydrates, besides the anhydrous
salt known; and he succeeded in discovering the existence
of two hydrates, Sr(ClO_{3})_{2},3H_{2}O and apparently
Sr(ClO_{3})_{2},8H_{2}O. Besides this, three modifications of the
common anhydrous salt were obtained, differing from each other
in their crystalline form. One modification separated out in the
form of rhombic octahedra, another in oblique plates, and a third
in long brittle prisms or plates. Further researches showed that
salts which are not capable of forming supersaturated solutions
such as the bromates of calcium, strontium, and barium, part
with their water of hydration with difficulty (they crystallise
with 1H_{2}O), and decompose very slowly in a vacuum or in dry
air. In other words the tension of dissociation is very small
in this class of hydrates. As the hydrates characterised by a
small dissociation tension are incapable of giving supersaturated
solutions, so conversely supersaturated solutions give hydrates
whose tension of dissociation is great (Potilitzin, 1893).

[57] _Emulsions_, like milk, are composed of a solution of glutinous
or similar substances, or of oily liquids suspended in a
liquid in the form of drops, which are clearly visible under a
microscope, and form an example of a mechanical formation which
resembles solution. But the difference from solutions is here
evident. There are, however, solutions which approach very near
to emulsions in the facility with which the substance dissolved
separates from them. It has long been known, for example, that
a particular kind of Prussian blue, KFe_{2}(CN)_{6}, dissolves
in pure water, but, on the addition of the smallest quantity
of either of a number of salts, it coagulates and becomes
quite insoluble. If copper sulphide (CuS), cadmium sulphide
(CdS), arsenic sulphide (As_{2}S_{5}) (the experiments with
these substances proceed with great ease, and the solution
obtained is comparatively stable), and many other metallic
sulphides, be obtained by a method of double decomposition (by
precipitating salts of these metals by hydrogen sulphide),
and be then carefully washed (by allowing the precipitate to
settle, pouring off the liquid, and again adding sulphuretted
hydrogen water), then, as was shown by Schulze, Spring, Prost,
and others, the previously insoluble sulphides pass into
transparent (for mercury, lead, and silver, reddish brown; for
copper and iron, greenish brown; for cadmium and indium, yellow;
and for zinc, colourless) solutions, which may be preserved
(the weaker they are the longer they keep) and even boiled, but
which, nevertheless, in time coagulate--that is, separate in an
insoluble form, and then sometimes become crystalline and quite
incapable of re-dissolving. Graham and others observed the power
shown by colloids (_see_ note 18) of forming similar _hydrosols
or solutions of gelatinous colloids_, and, in describing alumina
and silica, we shall again have occasion to speak of such
solutions.