Chapter I: On Water and Its Compounds (3)

This formula is very clearly understood from the fact that the
co-efficient of solubility of gases is that quantity measured at
0° and 760 mm., which is absorbed at a pressure of 760 mm. by one
volume of a liquid. If _n_ cubic centimetres of water absorb _m_
cubic centimetres of a gas, then one cubic centimetre absorbs
_m_/_n_. If _m_/_n_ c.c. of a gas are absorbed under a pressure
of _h_ mm., then, according to the law of the variation of
solubility of a gas with the pressure, there would he dissolved,
under a pressure of 760 mm., a quantity varying in the same ratio
to _m_/_n_ as 760 : _h_. In determining the residual volume of gas
its moisture (note 1) must be taken into consideration.

Below are given the number of grams of several substances
saturating 100 grams of water--that is, their co-efficients of
solubility by weight at three different temperatures:--

+----------------------------------------------+--------+---------+
| | | |
| At 0° | At 20° | At 100° |
+----------------------------------------------+--------+---------+
| {Oxygen, O_{2} 6/1000 | 4/1000 | -- |
|Gases {Carbonic anhydride, CO_{2} 35/100 | 18/100 | -- |
| {Ammonia, NH_{3} 90·0 | 51·8 | 7·3 |
| {Phenol, C_{6}H_{6}O 4·9 | 5·2 | [oo] |
|Liquids {Amyl alcohol, C_{5}H_{12}O 4·4 | 2·9 | -- |
| {Sulphuric acid, H_{2}SO_{4} [oo] | [oo] | [oo] |
| {Gypsum, CaSO_{4},2H_{2}O 1/5 | 1/4 | 1/5 |
| {Alum, AlKS_{2}O_{8},12H_{2}O 3·3 | 15·4 | 357·5 |
|Solids {Anhydrous sodium sulphate, 4·5 | 20 | 43 |
| { Na_{2}SO_{4} | | |
| {Common Salt, NaCl 35·7 | 36·0 | 39·7 |
| {Nitre, KNO_{3} 13·3 | 31·7 | 246·0 |
+----------------------------------------------+--------+---------+

Sometimes a substance is so slightly soluble that it may be
considered as insoluble. Many such substances are met with both
in solids and liquids, and such a gas as oxygen, although it
does dissolve, does so in so small a proportion by weight that
it might be considered as zero did not the solubility of even
so little oxygen play an important part in nature (as in the
respiration of fishes) and were not an infinitesimal quantity
of a gas by weight so easily measured by volume. The sign [oo],
which stands on a line with sulphuric acid in the above table,
indicates that it intermixes with water in all proportions.
There are many such cases among liquids, and everybody knows,
for instance, that spirit (absolute alcohol) can be mixed in any
proportion with water.

[22] Just as the existence must he admitted of substances which are
completely undecomposable (chemically) at the ordinary
temperature--and of substances which are entirely non-volatile
at such a temperature (as wood and gold), although capable
of decomposing (wood) or volatilising (gold) at a higher
temperature--so also the existence must be admitted of substances
which are totally insoluble in water without some degree of
change in their state. Although mercury is partially volatile at
the ordinary temperature, there is no reason to think that it
and other metals are soluble in water, alcohol, or other similar
liquids. However, mercury forms solutions, as it dissolves
other metals. On the other hand, there are many substances
found in nature which are so very slightly soluble in water,
that in ordinary practice they may be considered as insoluble
(for example, barium sulphate). For the comprehension of that
general plan according to which a change of state of substances
(combined or dissolved, solid, liquid, or gaseous) takes place,
it is very important to make a distinction at this boundary
line (on approaching zero of decomposition, volatility, or
solubility) between an insignificant amount and zero, but the
present methods of research and the data at our disposal at the
present time only just touch such questions (by studying the
electrical conductivity of dilute solutions and the development
of micro-organisms in them). It must be remarked, besides, that
water in a number of cases does not dissolve a substance as
such, but acts on it chemically and forms a soluble substance.
Thus glass and many rocks, especially if taken as powder, are
chemically changed by water, but are not directly soluble in it.

Substances which are easily soluble in water bear a certain resemblance to it. Thus sugar and salt in many of their superficial features remind one of ice. Metals, which are not soluble in water, have no points in common with it, whilst on the other hand they dissolve each other in a molten state, forming alloys, just as oily substances dissolve each other; for example, tallow is soluble in petroleum and in olive oil, although they are all insoluble in water. From this it is evident that the _analogy of substances forming a solution_ plays an important part, and as aqueous and all other solutions are liquids, there is good reason to believe that in the process of solution solid and gaseous substances change in a physical sense, passing into a liquid state. These considerations elucidate many points of solution--as, for instance, the variation of the co-efficient of solubility with the temperature and the evolution or absorption of heat in the formation of solutions.

The solubility--that is, the quantity of a substance necessary for saturation--_varies with the temperature_, and, further, with an increase in temperature the solubility of solid substances generally increases, and that of gases decreases; this might be expected, as solid substances by heating, and gases by cooling, approach to a liquid or dissolved state.[23] A graphic method is often employed to express the variation of solubility with temperature. On the axis of abscissæ or on a horizontal line, temperatures are marked out and perpendiculars are raised corresponding with each temperature, whose length is determined by the solubility of the salt at that temperature--expressing, for instance, one part by weight of a salt in 100 parts of water by one unit of length, such as a millimetre. By joining the summits of the perpendiculars, a curve is obtained which expresses the degree of solubility at different temperatures. For solids, the curve is generally an ascending one--_i.e._ recedes from the horizontal line with the rise in temperature. These curves clearly show by their inclination the degree of rapidity of increase in solubility with the temperature. Having determined several points of a curve--that is, having made a determination of the solubility for several temperatures--the solubility at intermediary temperatures may be determined from the form of the curve so obtained; in this way the empirical law of solubility may be examined.[24] The results of research have shown that the solubility of certain salts--as, for example, common table salt--varies comparatively little with the temperature; whilst for other substances the solubility increases by equal amounts for equal increments of temperature. Thus, for example, for the saturation of 100 parts of water by potassium chloride there is required at 0°, 29·2 parts, at 20°, 34·7, at 40°, 40·2, at 60°, 45·7; and so on, for every 10° the solubility increases by 2·75 parts by weight of the salt. Therefore the solubility of the potassium chloride in water may be expressed by a direct equation: _a_ = 29·2 + 0·275_t_, where _a_ represents the solubility at _t_°. For other salts, more complicated equations are required. For example, for nitre: _a_ = 13·3 + 0·574_t_ + 0·01717_t_^2 + 0·0000036_t_^3, which shows that when _t_ = 0° _a_ = 13·3, when _t_ = 10° _a_ = 20·8, and when _t_ = 100° _a_ = 246·0.

[23] Beilby (1883) experimented on paraffin, and found that one litre
of solid paraffin at 21° weighed 874 grams, and when liquid, at
its melting-point 38°, 783 grams, at 49°, 775 grams, and at 60°,
767 grams, from which the weight of a litre of liquefied paraffin
would be 795·4 grams at 21° if it could remain liquid at that
temperature. By dissolving solid paraffin in lubricating oil at
21° Beilby found that 795·6 grams occupy one cubic decimetre,
from which he concluded that the solution contained liquefied
paraffin.

[24] Gay-Lussac was the first to have recourse to such a graphic
method of expressing solubility, and he considered, in accordance
with the general opinion, that by joining up the summits of the
ordinates in one harmonious curve it is possible to express the
entire change of solubility with the temperature. Now, there are
many reasons for doubting the accuracy of such an admission, for
there are undoubtedly critical points in curves of solubility
(for example, of sodium sulphate, as shown further on), and it
may be that definite compounds of dissolved substances with
water, in decomposing within known limits of temperature, give
critical points more often than would be imagined; it may even
be, indeed, that instead of a continuous curve, solubility should
be expressed--if not always, then not unfrequently--by straight
or broken lines. According to Ditte, the solubility of sodium
nitrate, NaNO_{3}, is expressed by the following figures per 100
parts of water:--

0° 4° 10° 15° 21° 29° 36° 51° 68°
66·7 71·0 76·3 80·6 85·7 92·9 99·4 113·6 125·1

In my opinion (1881) these data should be expressed with
exactitude by a straight line, 67·5 + 0·87_t_, which entirely
agrees with the results of experiment. According to this
the figure expressing the solubility of salt at 0° exactly
coincides with the composition of a definite chemical
compound--NaNO_{3},7H_{2}O. The experiments made by Ditte
showed that all saturated solutions between 0° and -15·7° have
such a composition, and that at the latter temperature the
solution completely solidifies into one homogeneous whole.
Between 0° and -15·7° the solution NaNO_{3},7H_{2}O does not
deposit either salt or ice. Thus the solubility of sodium
nitrate is expressed by a broken straight line. In recent times
(1888) Étard discovered a similar phenomenon in many of the
sulphates. Brandes, in 1830, shows a diminution in solubility
below 100° for manganese sulphate. The percentage by weight
(_i.e._ per 100 parts of the solution, and not of water) of
saturation for ferrous sulphate, FeSO_{4}, from -2° to +65° =
13·5 + 0·3784_t_--that is, the solubility of the salt increases.
The solubility remains constant from 65° to 98° (according to
Brandes the solubility then increases; this divergence of opinion
requires proof), and from 98° to 150° it falls as = 104·35 -
0·6685_t_. Hence, at about +156° the solubility should = 0, and
this has been confirmed by experiment. I observe, on my part,
that Étard's formula gives 38·1 p.c. of salt at 65° and 38·8
p.c. at 92°, and this maximum amount of salt in the solution
very nearly corresponds with the composition FeSO_{4},14H_{2}O,
which requires 37·6 p.c. From what has been said, it is evident
that the data concerning solubility require a new method of
investigation, which should have in view the entire scale of
solubility--from the formation of completely solidified solutions
(cryohydrates, which we shall speak of presently) to the
separation of salts from their solutions, if this is accomplished
at a higher temperature (for manganese and cadmium sulphates
there is an entire separation, according to Étard), or to the
formation of a constant solubility (for potassium sulphate the
solubility, according to Étard, remains constant from 163° to
220° and equals 24·9 p.c.) (See Chapter XIV., note 50, solubility
of CaCl_{2}.)

Curves of solubility give the means of estimating the _amount of salt separated_ by the cooling to a known extent of a solution saturated at a given temperature. For instance, if 200 parts of a solution of potassium chloride in water saturated at a temperature of 60° be taken, and it be asked how much of the salt will be separated by cooling the solution to 0°, if its solubility at 60° = 45·7 and at 0° = 29·2? The answer is obtained in the following manner: At 60° a saturated solution contains 45·7 parts of potassium chloride per 100 parts by weight of water, consequently 145·7 parts by weight of the solution contain 45·7 parts, or, by proportion, 200 parts by weight of the solution contain 62·7 parts of the salt. The amount of salt remaining in solution at 0° is calculated as follows; In 200 grams taken there will be 137·3 grams of water; consequently, this amount of water is capable of holding only 40·1 grams of the salt, and therefore in lowering the temperature from 60° to 0° there should separate from the solution 62·7-40·1 = 22·6 grams of the dissolved salt.

The difference in the solubility of salts, &c., with a rise or fall of temperature is often taken advantage of, especially in technical work, for the separation of salts, in intermixture from each other. Thus a mixture of potassium and sodium chlorides (this mixture is met with in nature at Stassfurt) is separated from a saturated solution by subjecting it alternately to boiling (evaporation) and cooling. The sodium chloride separates out in proportion to the amount of water expelled from the solution by boiling, and is removed, whilst the potassium chloride separates out on cooling, as the solubility of this salt rapidly decreases with a lowering in temperature. Nitre, sugar, and many other soluble substances are purified (refined) in a similar manner.

Although in the majority of cases the solubility of solids increases with the temperature, yet there are some solid substances whose solubilities decrease on heating. Glauber's salt, or sodium sulphate, forms a particularly instructive example of the case in question. If this salt be taken in an ignited state (deprived of its water of crystallisation), then its solubility in 100 parts of water varies with the temperature in the following manner: at 0°, 5 parts of the salt form a saturated solution; at 20°, 20 parts of the salt, at 33° more than 50 parts. The solubility, as will be seen, increases with the temperature, as is the case with nearly all salts; but starting from 33° it suddenly diminishes, and at a temperature of 40°, less than 50 parts of the salt dissolve, at 60° only 45 parts of the salt, and at 100° about 43 parts of the salt in 100 parts of water. This phenomenon may be traced to the following facts: Firstly, that this salt forms various compounds with water, as will be afterwards explained; secondly, that at 33° the compound Na_{2}SO_{4} + 10H_{2}O formed from the solution at lower temperatures, melts; and thirdly, that on evaporation at a temperature above 33° an anhydrous salt, Na_{2}SO_{4} separates out. It will be seen from this example how complicated such an apparently simple phenomenon as solution really is; and all data concerning solutions lead to the same conclusion. This complexity becomes evident in investigating the _heat of solution_. If solution consisted of a physical change only, then in the solution of gases there would be evolved--and in the solution of solids, there would be absorbed--just that amount of heat corresponding to the change of state; but in reality a large amount of heat is always evolved in solution, depending on the fact that in the process of solution chemical combination takes place accompanied by an evolution of heat. Seventeen grams of ammonia (this weight corresponds with its formula NH_{3}), in passing from a gaseous into a liquid state, evolve 4,400 units of heat (latent heat); that is, the quantity of heat necessary to raise the temperature of 4,400 grams of water 1°. The same quantity of ammonia, in dissolving in an excess of water, evolves twice as much heat--namely 8,800 units--showing that the combination with water is accompanied by the evolution of 4,400 units of heat. Further, the chief part of this heat is separated in dissolving in small quantities of water, so that 17 grams of ammonia, in dissolving in 18 grams of water (this weight corresponds with its composition H_{2}O), evolve 7,535 units of heat, and therefore the formation of the solution NH_{3} + H_{2}O evolves 3,135 units of heat beyond that due to the change of state. As in the solution of gases, the heat of liquefaction (of physical change of state) and of chemical combination with water are both positive (+), therefore in the _solution of gases_ in water a _heat effect_ is always observed. This phenomenon is different in the solution of solid substances, because their passage from a solid to a liquid state is accompanied by an absorption of heat (negative,-heat), whilst their chemical combination with water is accompanied by an evolution of heat (+ heat); consequently, their sum may either be a cooling effect, when the positive (chemical) portion of heat is less than the negative (physical), or it may be, on the contrary, a heating effect. This is actually the case. 124 grams of sodium thiosulphate (employed in photography) Na_{2}S_{2}O_{3},5H_{2}O in melting (at 48°) absorbs 9,700 units of heat, but in dissolving in a large quantity of water at the ordinary temperature it absorbs 5,700 units of heat, which shows the evolution of heat (about + 4,000 units), notwithstanding the cooling effect observed in the process of solution, in the act of the chemical combination of the salt with water.[25] But in most cases solid substances in dissolving in water evolve heat, notwithstanding the passage into a liquid state, which indicates so considerable an evolution of (+) heat in the act of combination with water that it exceeds the absorption of (-) heat dependent on the passage into a liquid state, Thus, for instance, calcium chloride, CaCl_{2}, magnesium sulphate, MgSO_{4}, and many other salts evolve heat in dissolving; for example, 60 grams of magnesium sulphate evolve about 10,000 units of heat. Therefore, _in the solution of solid bodies_ either a cooling[26] or a heating[27] effect is produced, according to the difference of the reacting affinities. When they are considerable--that is, when water is with difficulty separated from the resultant solution, and only with a rise of temperature (such substances absorb water vapour)--then much heat is evolved in the process of solution, just as in many reactions of direct combination, and therefore a considerable heating of the solution is observed. Of such a kind, for instance, is the solution of sulphuric acid (oil of vitriol H_{2}SO_{4}), and of caustic soda (NaHO), &c., in water.[28]

[25] The latent heat of fusion is determined at the temperature of
fusion, whilst solution takes place at the ordinary temperature,
and one must think that at this temperature the latent heat
would be different, just as the latent heat of evaporation
varies with the temperature (see Note 11). Besides which, in
dissolving, disintegration of the particles of both the solvent
and the substance dissolved takes place, a process which in its
mechanical aspect resembles evaporation, and therefore must
consume much heat. The heat emitted in the solution of a solid
must therefore be considered (Personne) as composed of three
factors--(1) positive, the effect of combination; (2) negative,
the effect of transference into a liquid state; and (3) negative,
the effect of disintegration. In the solution of a liquid by
a liquid the second factor is removed; and therefore, if the
heat evolved in combination is greater than that absorbed in
disintegration a heating effect is observed, and in the reverse
case a cooling effect; and, indeed, sulphuric acid, alcohol, and
many liquids evolve heat in dissolving in each other. But the
solution of chloroform in carbon bisulphide (Bussy and Binget),
or of phenol (or aniline) in water (Alexéeff), produces cold.
In the solution of a small quantity of water in acetic acid
(Abasheff), or hydrocyanic acid (Bussy and Binget), or amyl
alcohol (Alexéeff), cold is produced, whilst in the solution of
these substances in an excess of water heat is evolved.

The relation existing between the solubility of solid bodies and
the heat and temperature of fusion and solution has been studied
by many investigators, and more recently (1893) by Schröder,
who states that in the solution of a solid body in a solvent
which does not act chemically upon it, a very simple process
takes place, which differs but little from the intermixture of
two gases which do not react chemically upon each other. The
following relation between the heat of solution _Q_ and the
heat of fusion _p_ may then be taken: _P_/_T__{0} = _Q_/_T_ =
constant, where _T__{0} and _T_ are the absolute (from -273°)
temperatures of fusion and saturation. Thus, for instance, in the
case of naphthalene the calculated and observed magnitudes of the
heat of solution differ but slightly from each other.

The fullest information concerning the solution of liquids
in liquids has been gathered by W. T. Alexéeff (1883-1885);
these data are, however, far from being sufficient to solve
the mass of problems respecting this subject. He showed that
two liquids which dissolve in each other, intermix together in
all proportions at a certain temperature. Thus the solubility
of phenol, C_{6}H_{6}O, in water, and the converse, is limited
up to 70°, whilst above this temperature they intermix in all
proportions. This is seen from the following figures, where p
is the percentage amount of phenol and _t_ the temperature at
which the solution becomes turbid--that is, that at which it is
saturated:--

_p_ = 7·12 10·20 15·31 26·15 28·55 36·70 48·86 61·15 71·97
_t_ = 1° 45° 60° 67° 67° 67° 65° 53° 20°

It is exactly the same with the solution of benzene, aniline,
and other substances in molten sulphur. Alexéeff discovered a
similar complete intermixture for solutions of secondary butyl
alcohol in water at about 107°; at lower temperatures the
solubility is not only limited, but between 50° and 70° it is at
its minimum, both for solutions of the alcohol in water and for
water in the alcohol; and at a temperature of 5° both solutions
exhibit a fresh change in their scale of solubility, so that a
solution of the alcohol in water which is saturated between 5°
and 40° will become turbid when heated to 60°. In the solution of
liquids in liquids, Alexéeff observed a lowering in temperature
(an absorption of heat) and an absence of change in specific
heat (calculated for the mixture) much more frequently than had
been done by previous observers. As regards his hypothesis (in
the sense of a mechanical and not a chemical representation of
solutions) that substances in solution preserve their physical
states (as gases, liquids, or solids), it is very doubtful, for
it would necessitate admitting the presence of ice in water or
its vapour.

From what has been said above, it will be clear that even in so
very simple a case as solution, it is impossible to calculate
the heat emitted by chemical action alone, and that the chemical
process cannot be separated from the physical and mechanical.

[26] The cooling effect produced in the solution of solids (and also in
the expansion of gases and in evaporation) is applied to the
_production of low temperatures_. Ammonium nitrate is very often
used for this purpose; in dissolving in water it absorbs 77 units
of heat per each part by weight. On evaporating the solution thus
formed, the solid salt is re-obtained. The application of the
various _freezing mixtures_ is based on the same principle. Snow
or broken ice frequently enters into the composition of these
_mixtures_, advantage being taken of its latent heat of fusion in
order to obtain the lowest possible temperature (without altering
the pressure or employing heat, as in other methods of obtaining
a low temperature). For laboratory work recourse is most often
had to a mixture of three parts of snow and one part of common
salt, which causes the temperature to fall from 0° to -21° C.
Potassium thiocyanate, KCNS, mixed with water (3/4 by weight of
the salt) gives a still lower temperature. By mixing ten parts of
crystallised calcium chloride, CaCl_{2},6H_{2}O, with seven parts
of snow, the temperature may even fall from 0° to -55°.

[27] The heat which is evolved in solution, or even in the dilution of
solutions, is also sometimes made use of in practice. Thus
caustic soda (NaHO), in dissolving or on the addition of water to
a strong solution of it, evolves so much heat that it can replace
fuel. In a steam boiler, which has been previously heated to
the boiling point, another boiler is placed containing caustic
soda, and the exhaust steam is made to pass through the latter;
the formation of steam then goes on for a somewhat long period
of time without any other heating. Norton makes use of this for
smokeless street locomotives.

[28]

The temperatures obtained by mixing monohydrated sulphuric acid,
H_{2}SO_{4}, with different quantities of water, are shown on
the lowest curve in fig. 17, the relative proportions of both
substances being expressed in percentages by weight along the
horizontal axis. The greatest rise of temperature is 149°. It
corresponds with the greatest evolution of heat (given on the
middle curve) corresponding with a definite volume (100 c.c.)
of the solution produced. The top curve expresses the degree
of contraction, which also corresponds with 100 volumes of
the solution produced. The greatest contraction, as also the
greatest rise of temperature, corresponds with the formation of a
trihydrate, H_{2}SO_{4},2H_{2}O (= 73·1 p.c. H_{2}SO_{4}), which
very likely repeats itself in a similar form in other solutions,
although all the phenomena (of contraction, evolution of heat,
and rise of temperature) are very complex and are dependent
on many circumstances. One would think, however, judging from
the above examples, that all other influences are feebler in
their action than chemical attraction, especially when it is so
considerable as between sulphuric acid and water.

Solution is a reversible reaction; for, if the water be expelled from a solution, the substance originally taken is obtained again. But it must be borne in mind that the expulsion of the water taken for solution is not always accomplished with equal facility, because water has different degrees of chemical affinity for the substance dissolved. Thus, if a solution of sulphuric acid, which mixes with water in all proportions, be heated, it will be found that very different degrees of heat are required to expel the water. When it is in a large excess, water is given off at a temperature slightly above 100°, but if it be in but a small proportion there is such an affinity between it and the sulphuric acid that at 120°, 150°, 200°, and even at 300°, water is still retained by the sulphuric acid. The bond between the remaining quantity of water and the sulphuric acid is evidently stronger than the bond between the sulphuric acid and the excess of water. The force acting in solutions is consequently of different intensity, starting from so feeble an attraction that the properties of water--as, for instance, its power of evaporation--are but very little changed, and ending with cases of strong attraction between the water and the substance dissolved in or chemically combined with it. In consideration of the very important significance of the phenomena, and of the cases of the breaking up of solutions with separation of water or of the substance dissolved from them, we shall further discuss them separately, after having acquainted ourselves with certain peculiarities of the solution of gases and of solid bodies.

The solubility of gases, which is usually measured by the volume of gas[29] (at 0° and 760 mm. pressure) per 100 volumes of water, varies not only with the nature of the gas (and also of the solvent), and with the temperature, but also with the pressure, because gases themselves change their volume considerably with the pressure. As might be expected, (1) gases which are easily liquefied (by pressure and cold) are more soluble than those which are liquefied with difficulty. Thus, in 100 volumes of water only two volumes of hydrogen dissolve at 0° and 760 mm., three volumes of carbonic oxide, four volumes of oxygen, &c., for these are gases which are liquefied with difficulty; whilst there dissolve 180 volumes of carbonic anhydride, 130 of nitrous oxide, and 437 of sulphurous anhydride, for these are gases which are rather easily liquefied. (2) The solubility of a gas is diminished by heating, which is easily intelligible from what has been said previously--the elasticity of a gas becomes greater, it is removed further from a liquid state. Thus 100 volumes of water at 0° dissolve 2·5 volumes of air, and at 20° only 1·7 volume. For this reason cold water, when brought into a warm room, parts with a portion of the gas dissolved in it.[30] (3) The quantity of the gas dissolved varies directly with the pressure. This rule is called the _law of Henry and Dalton_, and is applicable to those gases which are little soluble in water. Therefore a gas is separated from its solution in water in a vacuum, and water saturated with a gas under great pressure parts with it if the pressure be diminished. Thus many mineral springs are saturated underground with carbonic anhydride under the great pressure of the column of water above them. On coming to the surface, the water of these springs boils and foams on giving up the excess of dissolved gas. Sparkling wines and aërated waters are saturated under pressure with the same gas. They hold the gas so long as they are in a well-corked vessel. When the cork is removed and the liquid comes in contact with air at a lower pressure, part of the gas, unable to remain in solution at a lower pressure, is separated as froth with the hissing sound familiar to all. It must be remarked that the law of Henry and Dalton belongs to the class of _approximate laws_, like the laws of gases (Gay-Lussac's and Mariotte's) and many others--that is, it expresses only a portion of a complex phenomenon, the limit towards which the phenomenon aims. The matter is rendered complicated from the influence of the degree of solubility and of affinity of the dissolved gas for water. Gases which are little soluble--for instance, hydrogen, oxygen, and nitrogen--follow the law of Henry and Dalton the most closely. Carbonic anhydride exhibits a decided deviation from the law, as is seen from the determinations of Wroblewski (1882). He showed that at 0° a cubic centimetre of water absorbs 1·8 cubic centimetre of the gas under a pressure of one atmosphere; under 10 atmospheres, 16 cubic centimetres (and not 18, as it should be according to the law); under 20 atmospheres, 26·6 cubic centimetres (instead of 36), and under 30 atmospheres, 33·7 cubic centimetres.[31] However, as the researches of Sechenoff show, the absorption of carbonic anhydride within certain limits of change of pressure, and at the ordinary temperature, by water--and even by solutions of salts which are not chemically changed by it, or do not form compounds with it--very closely follows the law of Henry and Dalton, so that the chemical bond between this gas and water is so feeble that the breaking up of the solution with separation of the gas is accomplished by a decrease of pressure alone.[32] The case is different if a considerable affinity exists between the dissolved gas and water. Then it might even be expected that the gas would not be entirely separated from water in a vacuum, as should be the case with gases according to the law of Henry and Dalton. Such gases--and, in general, all those which are very soluble--exhibit a distinct deviation from the law of Henry and Dalton. As examples, ammonia and hydrochloric acid gas may be taken. The former is separated by boiling and decrease of pressure, while the latter is not, but they both deviate distinctly from the law.

+---------------+-----------------+--------------------+
|Pressure in mm.|Ammonia dissolved| Hydrochloric acid |
| of mercury | in 100 grams of |gas dissolved in 100|
| | water at 0° |grams of water at 0°|
+---------------+-----------------+--------------------+
| | Grams | Grams |
| 100 | 28·0 | 65·7 |
| 500 | 69·2 | 78·2 |
| 1,000 | 112·6 | 85·6 |
| 1,500 | 165·6 | -- |
+---------------+-----------------+--------------------+

[29] If a volume of gas _v_ be measured under a pressure of _h_ mm. of
mercury (at 0°) and at a temperature _t_° Centigrade, then,
according to the combined laws of Boyle, Mariotte, and of
Gay-Lussac, its volume at 0° and 760 mm. will equal the product
of _v_ into 760 divided by the product of _h_ into 1 + _a__t_°,
where _a_ is the co-efficient of expansion of gases, which is
equal to 0·00367. The weight of the gas will be equal to its
volume at 0° and 760 mm. multiplied by its density referred to
air and by the weight of one volume of air at 0° and 760 mm.
The weight of one litre of air under these conditions being =
1·293 gram. If the density of the gas be given in relation to
hydrogen this must be divided by 14·4 to bring it in relation to
air. If the gas be measured when saturated with aqueous vapour,
then it must be reduced to the volume and weight of the gas when
dry, according to the rules given in Note 1. If the pressure
be determined by a column of mercury having a temperature _t_,
then by dividing the height of the column by 1 + 0·00018_t_ the
corresponding height at 0° is obtained. If the gas be enclosed in
a tube in which a liquid stands above the level of the mercury,
the height of the column of the liquid being = H and its density
= D, then the gas will be under a pressure which is equal to the
barometric pressure less HD/13·59, where 13·59 is the density of
mercury. By these methods the _quantity of a gas_ is determined,
and its observed volume reduced to normal conditions or to parts
by weight. The physical data concerning vapours and gases must be
continually kept in sight in dealing with and measuring gases.
The student must become perfectly familiar with the calculations
relating to gases.

[30] According to Bunsen, Winkler, Timofeeff, and others, 100 vols. of
water under a pressure of one atmosphere absorb the following
volumes of gas (measured at 0° and 760 mm.):--

1 2 3 4 5 6 7 8 9 10 11
0° 4·82 2·35 2·15 179·7 3·54 130·5 437·1 688·6 5·4 104960 7·38
20° 3·10 1·54 1·83 90·1 2·32 67·0 290·5 362·2 3·5 65400 4·71

1, oxygen; 2, nitrogen; 3, hydrogen; 4, carbonic anhydride;
5, carbonic oxide; 6, nitrous oxide; 7, hydrogen sulphide; 8,
sulphurous anhydride; 9, marsh gas; 10, ammonia; 11, nitric
oxide. The decrease of solubility with a rise of temperature
varies for different gases; it is greater, the greater the
molecular weight of the gas. It is shown by calculation that
this decrease varies (Winkler) as the cube root of the molecular
weight of the gas. This is seen from the following table:

+--------------+-------------+---------------+
| Decrease of | Cube root of| Ratio between |
| solubility | molecular | decrease and |
| per 20° in | weight. | cube root of |
| per cent. | | mol. wt. |
+--------------+-------------+---------------+
| H_{2} 15·32 | 1·259 | 12·17 |
| N_{2} 34·33 | 3·037 | 11·30 |
| CO 34·44 | 3·037 | 11·34 |
| NO 36·24 | 3·107 | 11·66 |
| O_{2} 36·55 | 3·175 | 11·51 |
+--------------+-------------+---------------+

The decrease in the coefficient of absorption with the
temperature must be connected with a change in the physical
properties of the water. Winkler (1891) remarked a certain
relation between the internal friction and the coefficient of
absorption at various temperatures.

[31] These figures show that the co-efficient of solubility decreases
with an increase of pressure, notwithstanding that the carbonic
anhydride approaches a liquid state. As a matter of fact,
liquefied carbonic anhydride does not intermix with water,
and does not exhibit a rapid increase in solubility at its
temperature of liquefaction. This indicates, in the first place,
that solution does not consist in liquefaction, and in the
second place that the solubility of a substance is determined
by a peculiar attraction of water for the substance dissolving.
Wroblewski even considered it possible to admit that a dissolved
gas retains its properties as a gas. This he deduced from
experiments, which showed that the rate of diffusion of gases
in a solvent is, for gases of different densities, inversely
proportional to the square roots of their densities, just as
the velocities of gaseous molecules (see Note 34). Wroblewski
showed the affinity of water, H_{2}O, for carbonic anhydride,
CO_{2}, from the fact that on expanding moist compressed carbonic
anhydride (compressed at 0° under a pressure of 10 atmospheres)
he obtained (a fall in temperature takes place from the
expansion) a very unstable definite crystalline compound, CO_{2}
+ 8H_{2}O.

[32] As, according to the researches of Roscoe and his collaborators,
ammonia exhibits a considerable deviation at low temperatures
from the law of Henry and Dalton, whilst at 100° the deviation
is small, it would appear that the dissociating influence of
temperature affects all gaseous solutions; that is, at high
temperatures, the solutions of all gases will follow the law, and
at lower temperatures there will in all cases be a deviation from
it.

It will be remarked, for instance, from this table that whilst the pressure increased 10 times, the solubility of ammonia only increased 4-1/2 times.

A number of examples of such cases of the absorption of gases by liquids might be cited which do not in any way, even approximately, agree with the laws of solubility. Thus, for instance, carbonic anhydride is absorbed by a solution of caustic potash in water, and if sufficient caustic potash be present it is not separated from the solution by a decrease of pressure. This is a case of more intimate chemical combination. A correlation less completely studied, but similar and clearly chemical, appears in certain cases of the solution of gases in water, and we shall afterwards find an example of this in the solution of hydrogen iodide; but we will first stop to consider a remarkable application of the law of Henry and Dalton[33] in the case of the solution of a mixture of two gases, and this we must do all the more because the phenomena which there take place cannot be foreseen without a clear theoretical representation of the nature of gases.[34]

[33] The ratio between the pressure and the amount of gas dissolved
was discovered by Henry in 1805, and Dalton in 1807 pointed
out the adaptability of this law to cases of gaseous mixtures,
introducing the conception of partial pressures which is
absolutely necessary for a right comprehension of Dalton's law.
The conception of partial pressures essentially enters into
that of the diffusion of vapours in gases (footnote 1); for
the pressure of damp air is equal to the sum of the pressures
of dry air and of the aqueous vapour in it, and it is admitted
as a corollary to Dalton's law that evaporation in dry air
takes place as in a vacuum. It is, however, necessary to remark
that the volume of a mixture of two gases (or vapours) is only
approximately equal to the sum of the volumes of its constituents
(the same, naturally, also refers to their pressures)--that is to
say, in mixing gases a change of volume occurs, which, although
small, is quite apparent when carefully measured. For instance,
in 1888 Brown showed that on mixing various volumes of sulphurous
anhydride (SO_{2}) with carbonic anhydride (at equal pressures
of 760 mm. and equal temperatures) a decrease of pressure of
3·9 millimetres of mercury was observed. The possibility of a
chemical action in similar mixtures is evident from the fact that
equal volumes of sulphurous and carbonic anhydrides at -19° form,
according to Pictet's researches in 1888, a liquid which may be
regarded as an unstable chemical compound, or a solution similar
to that given when sulphurous anhydride and water combine to an
unstable chemical whole.

[34] The origin of the kinetic theory of gases now generally accepted,
according to which they are animated by a rapid progressive
motion, is very ancient (Bernouilli and others in the last
century had already developed a similar representation), but
it was only generally accepted after the mechanical theory of
heat had been established, and after the work of Krönig (1855),
and especially after its mathematical side had been worked out
by Clausius and Maxwell. The pressure, elasticity, diffusion,
and internal friction of gases, the laws of Boyle, Mariotte,
and of Gay-Lussac and Avogadro-Gerhardt are not only explained
(deduced) by the kinetic theory of gases, but also expressed
with perfect exactitude; thus, for example, the magnitude of
the internal friction of different gases was foretold with
exactitude by Maxwell, by applying the theory of probabilities
to the impact of gaseous particles. The kinetic theory of gases
must therefore be considered as one of the most brilliant
acquisitions of the latter half of the present century. The
velocity of the progressive motion of the particles of a gas, one
cubic centimetre of which weighs _d_ grams, is found, according
to the theory, to be equal to the square root of the product of
3_pDq_ divided by _d_, where _p_ is the pressure under which _d_
is determined expressed in centimetres of the mercury column,
_D_ the weight of a cubic centimetre of mercury in grams (_D_
= 13·59, _p_ = 76, consequently the normal pressure = 1,033
grams on a sq. cm.), and _g_ the acceleration of gravity in
centimetres (_g_ = 980·5, at the sea level and long. 45° = 981·92
at St. Petersburg; in general it varies with the longitude and
altitude of the locality). Therefore, at 0° the velocity of
hydrogen is 1,843, and of oxygen 461, metres per second. This
is the average velocity, and (according to Maxwell and others)
it is probable that the velocities of individual particles
are different; that is, they occur in, as it were, different
conditions of temperature, which it is very important to take
into consideration in investigating many phenomena proper to
matter. It is evident from the above determination of the
velocity of gases, that different gases at the same temperature
and pressure have average velocities, which are inversely
proportional to the square roots of their densities; this is also
shown by direct experiment on the flow of gases through a fine
orifice, or through a porous wall. This _dissimilar velocity of
flow_ for different gases is frequently taken advantage of in
chemical researches (see Chap. II. and also Chap. VII.) in order
to separate two gases having different densities and velocities.
The difference of the velocity of flow of gases also determines
the phenomenon cited in the following footnote for demonstrating
the existence of an internal motion in gases.

If for a certain mass of a gas which fully and exactly follows
the laws of Mariotte and Gay-Lussac the temperature _t_ and the
pressure _p_ be changed simultaneously, then the entire change
would be expressed by the equation _pv_ = _C_(1 + _at_), or,
what is the same, _pv_ = _RT_, where _T_ = _t_ + 273 and _C_
and _R_ are constants which vary not only with the units taken
but with the nature of the gas and its mass. But as there are
discrepancies from both the fundamental laws of gases (which
will be discussed in the following chapter), and as, on the
one hand, a certain attraction between the gaseous molecules
must be admitted, while on the other hand the molecules of
gases themselves must occupy a portion of a space, hence for
ordinary gases, within any considerable variation of pressure and
temperature, recourse should be had to Van der Waal's formula--

(_p_ + _a_/_v_^2)(_v_-_p_) = R(1 + _at_)

where _a_ is the true co-efficient of expansion of gases.

The formula of Van der Waals has an especially important
significance in the case of the passage of a gas into a liquid
state, because the fundamental properties of both gases and
liquids are equally well expressed by it, although only in their
general features.

The further development of the questions referring to the
subjects here touched on, which are of especial interest for the
theory of solutions, must be looked for in special memoirs and
works on theoretical and physical chemistry. A small part of this
subject will be partially considered in the footnotes of the
following chapter.

_The law of partial pressures_ is as follows:--The solubility of gases in intermixture with each other does not depend on the influence of the total pressure acting on the mixture, but on the influence of that portion of the total pressure which is due to the volume of each given gas in the mixture. Thus, for instance, if oxygen and carbonic anhydride were mixed in equal volumes and exerted a pressure of 760 millimetres, then water would dissolve so much of each of these gases as would be dissolved if each separately exerted a pressure of half an atmosphere, and in this case, at 0° one cubic centimetre of water would dissolve 0·02 cubic centimetre of oxygen and 0·90 cubic centimetre of carbonic anhydride. If the pressure of a gaseous mixture equals _h_, and in _n_ volumes of the mixture there be _a_ volumes of a given gas, then its solution will proceed as though this gas were dissolved under a pressure (_h_ × _a_)/_n_. That portion of the pressure under influence of which the solution proceeds is termed the 'partial' pressure.

In order to clearly understand the cause of the law of partial pressures, an explanation must be given of the fundamental properties of gases. Gases are elastic and disperse in all directions. We are led from what we know of gases to the assumption that these fundamental properties of gases are due to a rapid progressive motion, in all directions, which is proper to their smallest particles (molecules).[35] These molecules in impinging against an obstacle produce a pressure. The greater the number of molecules impinging against an obstacle in a given time, the greater the pressure. The pressure of a separate gas or of a gaseous mixture depends on the sum of the pressures of all the molecules, on the number of blows in a unit of time on a unit of surface, and on the mass and velocity (or the _vis viva_) of the impinging molecules. The nature of the different molecules is of no account; the obstacle is acted on by a pressure due to the sum of their _vis viva_. But, in a chemical action such as the solution of gases, the nature of the impinging molecules plays, on the contrary, the most important part. In impinging against a liquid, a portion of the gas enters into the liquid itself, and is held by it so long as other gaseous molecules impinge against the liquid--exert a pressure on it. As regards the solubility of a given gas, for the number of blows it makes on the surface of a liquid, it is immaterial whether other molecules of gases impinge side by side with it or not. Hence, the solubility of a given gas will be proportional, not to the total pressure of a gaseous mixture, but to that portion of it which is due to the given gas separately. Moreover, the saturation of a liquid by a gas depends on the fact that the molecules of gases that have entered into a liquid do not remain at rest in it, although they enter in a harmonious kind of motion with the molecules of the liquid, and therefore they throw themselves off from the surface of the liquid (just like its vapour if the liquid be volatile). If in a unit of time an equal number of molecules penetrate into (leap into) a liquid and leave (or leap out of) a liquid, it is saturated. It is a case of mobile equilibrium, and not of rest. Therefore, if the pressure be diminished, the number of molecules departing from the liquid will exceed the number of molecules entering into the liquid, and a fresh state of mobile equilibrium only takes place under a fresh equality of the number of molecules departing from and entering into the liquid. In this manner the main features of the solution are explained, and furthermore of that special (chemical) attraction (penetration and harmonious motion) of a gas for a liquid, which determines both the measure of solubility and the degree of stability of the solution produced.

[35] Although the actual motion of gaseous molecules, which is accepted
by the kinetic theory of gases, cannot be seen, yet its existence
may be rendered evident by taking advantage of the difference in
the velocities undoubtedly belonging to different gases which
are of different densities under equal pressures. The molecules
of a light gas must move more rapidly than the molecules of
a heavier gas in order to produce the same pressure. Let us
take, therefore, two gases--hydrogen and air; the former is
14·4 times lighter than the latter, and hence the molecules of
hydrogen must move almost four times more quickly than air (more
exactly 3·8, according to the formula given in the preceding
footnote). Consequently, if a porous cylinder containing air is
introduced into an atmosphere of hydrogen, then in a given time
the volume of hydrogen which succeeds in entering the cylinder
will be greater than the volume of air leaving the cylinder, and
therefore the pressure inside the cylinder will rise until the
gaseous mixture (of air and hydrogen) attains an equal density
both inside and outside the cylinder. If now the experiment
be reversed and air surround the cylinder, and hydrogen be
inside the cylinder, then more gas will leave the cylinder than
enters it, and hence the pressure inside the cylinder will be
diminished. In these considerations we have replaced the idea of
the number of molecules by the idea of volumes. We shall learn
subsequently that equal volumes of different gases contain an
equal number of molecules (the law of Avogadro-Gerhardt), and
therefore instead of speaking of the number of molecules we can
speak of the number of volumes. If the cylinder be partially
immersed in water the rise and fall of the pressure can be
observed directly, and the experiment consequently rendered
self-evident.

The consequences of the law of partial pressures are exceedingly numerous and important. All liquids in nature are in contact with the atmosphere, which, as we shall afterwards see more fully, consists of an intermixture of gases, chiefly four in number--oxygen, nitrogen, carbonic anhydride, and aqueous vapour. 100 volumes of air contain, approximately, 78 volumes of nitrogen, and about 21 volumes of oxygen; the quantity of carbonic anhydride, by volume, does not exceed 0·05. Under ordinary circumstances, the quantity of aqueous vapour is much greater than this, but it varies of course with climatic conditions. We conclude from these numbers that the solution of nitrogen in a liquid in contact with the atmosphere will proceed under a partial pressure of (78/100) × 760 mm. if the atmospheric pressure equal 760 mm.; similarly, under a pressure of 600 mm. of mercury, the solution of oxygen will proceed under a partial pressure of about 160 mm., and the solution of carbonic anhydride only under the very small pressure of 0·4 mm. As, however, the solubility of oxygen in water is twice that of nitrogen, the ratio of O to N dissolved in water will be greater than the ratio in air. It is easy to calculate what quantity of each of the gases will be contained in water, and taking the simplest case we will calculate what quantity of oxygen, nitrogen, and carbonic anhydride will be dissolved from air having the above composition at 0° and 760 mm. pressure. Under a pressure of 760 mm. 1 cubic centimetre of water dissolves 0·0203 cubic centimetre of nitrogen or under the partial pressure of 600 mm. it will dissolve 0·0203 × 600/760, or 0·0160 cubic centimetre; of oxygen 0·0411 × 160/760, or 0·0086 cubic centimetre; of carbonic anhydride 1·8 × 0·4/760 or 0·00095 cubic centimetre: hence, 100 cubic centimetres of water will contain at 0° altogether 2·55 cubic centimetres of atmospheric gases, and 100 volumes of air dissolved in water will contain about 62 p.c. of nitrogen, 34 p.c. of oxygen, and 4 p.c. of carbonic anhydride. The water of rivers, wells, &c. usually contains more carbonic anhydride. This proceeds from the oxidation of organic substances falling into the water. The amount of oxygen, however, dissolved in water appears to be actually about 1/3 the dissolved gases, whilst air contains only 1/5 of it by volume.