from a physical and from a chemical point of view, and it is
more evident in solutions than in any other department of
chemistry how closely these provinces of natural science are
allied together. On the one hand solutions form a particular
case of a physico-mechanical interpenetration of homogeneous
substances, and a juxtaposition of the molecules of the substance
dissolved and of the solvent, similar to the juxtaposition which
is exhibited in homogeneous substances. From this point of view
this diffusion of solutions is exactly similar to the diffusion
of gases, with only this difference, that the nature and store of
energy are different in gases from what they are in liquids, and
that in liquids there is considerable friction, whilst in gases
there is comparatively little. The penetration of a dissolved
substance into water is likened to evaporation, and solution to
the formation of vapour. This resemblance was clearly expressed
even by Graham. In recent years the Dutch chemist, Van't Hoff,
has developed this view of solutions in great detail, having
shown (in a memoir in the _Transactions of the Swedish Academy
of Science_, Part 21, No. 17, 'Lois de l'équilibre chimique
dans l'état dilué, gazeux ou dissous,' 1886), that for dilute
solutions the _osmotic pressure_ follows the same laws of Boyle,
Mariotte, Gay-Lussac, and Avogadro-Gerhardt as for gases. The
osmotic pressure of a substance dissolved in water is determined
by means of membranes which allow the passage of water, but not
of a substance dissolved in it, through them. This property is
found in animal protoplasmic membranes and in porous substances
covered with an amorphous precipitate, such as is obtained by the
action of copper sulphate on potassium ferrocyanide (Pfeffer,
Traube). If, for instance, a one p.c. solution of sugar he placed
in such a vessel, which is then closed and placed in water, the
water passes through the walls of the vessel and increases the
pressure by 50 mm. of the barometric column. If the pressure be
artificially increased inside the vessel, then the water will be
expelled through the walls. De Vries found a convenient means
of determining _isotonic_ solutions (those presenting a similar
osmotic pressure) in the cells of plants. For this purpose a
portion of the soft part of the leaves of the _Tradescantis
discolor_, for instance, is cut away and moistened with the
solution of a given salt and of a given strength. If the osmotic
pressure of the solution taken be less than that of the sap
contained in the cells they will change their form or shrink; if,
on the other hand, the osmotic pressure be greater than that of
the sap, then the cells will expand, as can easily be seen under
the microscope. By altering the amount of the different salts in
solution it is possible to find for each salt the strength of
solution at which the cells begin to swell, and at which they
will consequently have an equal osmotic pressure. As it increases
in proportion to the amount of a substance dissolved per 100
parts of water, it is possible, knowing the osmotic pressure
of a given substance--for instance, sugar at various degrees
of concentration of solution--and knowing the composition of
isotonic solutions compared with sugar, to determine the osmotic
pressure of all the salts investigated. The osmotic pressure of
dilute solutions determined in this manner directly or indirectly
(from observations made by Pfeffer and De Vries) was shown to
follow the same laws as those of the pressure of gases; for
instance, by doubling or increasing the quantity of a salt (in
a given volume) _n_ times, the pressure is doubled or increases
_n_ times. So, for example, in a solution containing one part
of sugar per 100 parts of water the osmotic pressure (according
to Pfeffer) = 58·5 cm. of mercury, if 2 parts of sugar = 101·6,
if 4 parts = 208·2 and so on, which proves that the ratio is
true within the limits of experimental error. (2) Different
substances for equal strengths of solutions, show very different
osmotic pressures, just as gases for equal parts by weight in
equal volumes show different tensions. (3) If, for a given dilute
solution at 0°, the osmotic pressure equal _p_°, then at _t_°
it will be greater and equal to _p_°(1 + 0·00367_t_), _i.e._ it
increases with the temperature in exactly the same manner as the
tension of gases increases. (4) If in dilute solutions of such
substances as do not conduct an electric current (for instance,
sugar, acetone, and many other organic bodies) the substances
be taken in the ratio of their molecular weights (expressed by
their formulæ, see Chapter VII.), then not only will the osmotic
pressure be equal, but its magnitude will be determined by
that tension which would be proper to the vapours of the given
substances when they would be contained in the space occupied by
the solution, just as the tension of the vapours of molecular
quantities of the given substances will be equal, and determined
by the laws of Gay-Lussac, Mariotte, and Avogadro-Gerhardt. Those
formulæ (Chapter VII., Notes 23 and 24) by which the gaseous
state of matter is determined, may also be applied in the present
case. So, for example, the osmotic pressure _p_, in centimetres
of mercury, of a one per cent. solution of sugar, may be
calculated according to the formula for gases:
M_p_ = 6200_s_(273 + _t_),
where M is the molecular weight, _s_ the weight in grams of a
cubic centimetre of vapour, and _t_ its temperature. For sugar M
= 342 (because its molecular composition is C_{12}H_{22}O_{11}).
The specific gravity of the solution of sugar is 1·003, hence the
weight of sugar _s_ contained in a 1 per cent. solution = 0·01003
gram. The observation was made at _t_ = 14°. Hence, according
to the formula, we find _p_ = 52·2 centimetres. And experiments
carried on at 14° gave 53·5 centimetres, which is very near to
the above. (5) For the solutions of salts, acids, and similar
substances, which conduct an electric current, the calculated
pressure is usually (but not always in a definite or multiple
number of times) less than the observed by _i_ times, and this
_i_ for dilute solutions of MgSO_{4} is nearly 1, for CO_{2} = 1,
for KCl, NaCl, KI, KNO_{3} greater than 1, and approximates to 2,
for BaCl_{2}, MgCl_{2}, K_{2}CO_{3}, and others between 2 and 3,
for HCl, H_{2}SO_{4}, NaNO_{3}, CaN_{2}O_{6}, and others nearly
2 and so on. It should be remarked that the above deductions are
only applicable (and with a certain degree of accuracy) to dilute
solutions, and in this respect resemble the generalisations of
Michel and Kraft (see Note 44). Nevertheless, the arithmetical
relation found by Van't Hoff between the formation of vapours
and the transition into dilute solutions forms an important
scientific discovery, which should facilitate the explanation of
the nature of solutions, while the osmotic pressure of solutions
already forms a very important aspect of the study of solutions.
In this respect it is necessary to mention that Prof. Konovaloff
(1891, and subsequently others also) discovered the dependence
(and it may be a sufficient explanation) of the osmotic pressure
upon the differences of the tensions of aqueous vapours and
aqueous solutions; this, however, already enters into a special
province of physical chemistry (certain data are given in Note
49 and following), and to this physical side of the question
also belongs one of the extreme consequences of the resemblance
of osmotic pressure to gaseous pressure, which is that the
concentration of a uniform solution varies in parts which are
heated or cooled. Soret (1881) indeed observed that a solution
of copper sulphate containing 17 parts of the salt at 20° only
contained 14 parts after heating the upper portion of the tube
to 80° for a long period of time. This aspect of solution, which
is now being very carefully and fully worked out, may be called
the _physical_ side. Its other aspect is purely _chemical_, for
solution does not take place between any two substances, but
requires a special and particular attraction or affinity between
them. A vapour or gas permeates any other vapour or gas, but a
salt which dissolves in water may not be in the least soluble
in alcohol, and is quite insoluble in mercury. In considering
solutions as a manifestation of chemical force (and of chemical
energy), it must be acknowledged that they are here developed to
so feeble an extent that the definite compounds (that is, those
formed according to the law of multiple proportions) formed
between water and a soluble substance dissociate even at the
ordinary temperature, forming a homogeneous system--that is,
one in which both the compound and the products into which it
decomposes (water and the aqueous compound) occur in a liquid
state. The chief difficulty in the comprehension of solutions
depends on the fact that the mechanical theory of the structure
of liquids has not yet been so fully developed as the theory of
gases, and solutions are liquids. The conception of solutions
as liquid dissociated definite chemical compounds is based on
the following considerations: (1) that there exist certain
undoubtedly definite chemical crystallised compounds (such as
H_{2}SO_{4},H_{2}O; or NaCl,2H_{2}O; or CaCl_{2},6H_{2}O; &c.)
which melt on a certain rise of temperature, and then form true
solutions; (2) that metallic alloys in a molten condition are
real solutions, but on cooling they often give entirely distinct
and definite crystallised compounds, which are recognised by
the properties of alloys; (3) that between the solvent and the
substance dissolved there are formed, in a number of cases,
many undoubtedly definite compounds, such as compounds with
water of crystallisation; (4) that the physical properties of
solutions, and especially their specific gravities (a property
which can be very accurately determined), vary with a change in
composition, and in such a manner as would be required by the
formation of one or more definite but dissociating compounds.
Thus, for example, on adding water to fuming sulphuric acid its
density is observed to decrease until it attains the definite
composition H_{2}SO_{4}, or SO_{3} + H_{2}O, when the specific
gravity increases, although on further diluting with water it
again falls. Moreover (Mendeléeff, _The Investigation of Aqueous
Solutions from their Specific Gravities_, 1887), the increase
in specific gravity (_ds_), varies in all well-known solutions
with the proportion of the substance dissolved (_dp_), and this
dependence can be expressed by a formula (_ds_/_dp_ = A + B_p_)
between the limits of definite compounds whose existence in
solutions must be admitted, and this is in complete accordance
with the dissociation hypothesis. Thus, for instance, from
H_{2}SO_{4} to H_{2}SO_{4} + H_{2}O (both these substances exist
as definite compounds in a free state), the fraction _ds_/_dp_
= 0·0729-0·000749_p_ (where _p_ is the percentage amount of
H_{2}SO_{4}). For alcohol C_{2}H_{6}O, whose aqueous solutions
have been more accurately investigated than all others, the
definite compound C_{2}H_{6}O + 3H_{2}O, and others must be
acknowledged in its solutions.
The two aspects of solution above mentioned, and the hypotheses
which have as yet been applied to the examination of solutions,
although they have somewhat different starting points, will
doubtless in time lead to a general theory of solutions,
because the same common laws govern both physical and chemical
phenomena, inasmuch as the properties and motions of molecules,
which determine physical properties, depend on the motions and
properties of atoms, which determine chemical reactions. For
details of the questions dealing with theories of solution,
recourse must now be had to special memoirs and to works on
theoretical (physical) chemistry; for this subject forms one of
special interest at the present epoch of the development of our
science. In working out chiefly the chemical side of solutions, I
consider it to be necessary to reconcile the two aspects of the
question; this seems to me to be all the more possible, as the
physical side is limited to dilute solutions only, whilst the
chemical side deals mainly with strong solutions.
In the consideration of the process of solution, besides the conception
of diffusion, another fundamental conception is necessary--namely, that
of the _saturation of solutions_.
Just as moist air may be diluted with any desired quantity of dry air,
so also an indefinitely large quantity of a liquid solvent may be
taken, and yet a uniform solution will be obtained. But more than a
definite quantity of aqueous vapour cannot be introduced into a certain
volume of air at a certain temperature. The excess above the point of
saturation will remain in the liquid state.[20] The relation between
water and substances dissolved in it is similar. More than a definite
quantity of a substance cannot, at a certain temperature, dissolve in
a given quantity of water; the excess does not unite with the water.
Just as air or a gas becomes saturated with vapour, so water becomes
saturated with a substance dissolved in it. If an excess of a substance
be added to water which is already saturated with it, it will remain in
its original state, and will not diffuse through the water. The quantity
of a substance (either by volume with gases, or by weight with solids
and liquids) which is capable of saturating 100 parts of water is called
the _co-efficient of solubility_ or the _solubility_. In 100 grams of
water at 15°, there can be dissolved not more than 35·86 grams of
common salt. Consequently, its solubility at 15° is equal to 35·86.[21]
It is most important to turn attention to the _existence of the solid
insoluble substances of nature_, because on them depends the shape
of the substances of the earth's surface, and of plants and animals.
There is so much water on the earth's surface, that were the surface of
substances formed of soluble matters it would constantly change, and
however substantial their forms might be, mountains, river banks and sea
shores, plants and animals, or the habitations and coverings of men,
could not exist for any length of time.[22]
[20] A system of (chemically or physically) re-acting substances in
different states of aggregation--for instance, some solid, others
liquid or gaseous--is termed a heterogeneous system. Up to now it
is only systems of this kind which can be subjected to detailed
examination in the sense of the mechanical theory of matter.
Solutions (_i.e._ unsaturated ones) form fluid homogeneous
systems, which at the present time can only be investigated with
difficulty.
In the case of limited solution of liquids in liquids, _the
difference between the solvent and the substance dissolved_ is
clearly seen. The former (that is, the solvent) may be added in
an unlimited quantity, and yet the solution obtained will always
be uniform, whilst only a definite saturating proportion of the
substance dissolved can be taken, We will take water and common
(sulphuric) ether. On shaking the ether with the water, it will
be remarked that a portion of it dissolves in the water. If the
ether be taken in such a quantity that it saturates the water
and a portion of it remains undissolved, then this remaining
portion will act as a solvent, and water will diffuse through it
and also form a saturated solution of water in the ether taken.
Thus two saturated solutions will be obtained. One solution
will contain ether dissolved in water, and the other solution
will contain water dissolved in ether. These two solutions will
arrange themselves in two layers, according to their density;
the ethereal solution of water will be on the top. If the upper
ethereal solution be poured off from the aqueous solution,
any quantity of ether may be added to it; this shows that the
dissolving substance is ether. If water be added to it, it is
no longer dissolved in it; this shows that water saturates the
ether--here water is the substance dissolved. If we act in the
same manner with the lower layer, we shall find that water is the
solvent and ether the substance dissolved. By taking different
amounts of ether and water, the degree of solubility of ether in
water, and of water in ether, may be easily determined. Water
approximately dissolves 1/10 of its volume of ether, and ether
dissolves a very small quantity of water. Let us now imagine that
the liquid poured in dissolves a considerable amount of water,
and that water dissolves a considerable amount of the liquid. Two
layers could not be formed, because the saturated solutions would
resemble each other, and therefore they would intermix in all
proportions. This is, consequently, a case of a phenomenon where
two liquids present considerable co-efficients of solubility
in each other, but where it is impossible to say what these
co-efficients are, because it is impossible to obtain a saturated
solution.
[21] The solubility, or co-efficient of solubility, of a substance is
determined by various methods. Either a solution is expressly
prepared with a clear excess of the soluble substance and
saturated at a given temperature, and the quantity of water and
of the substance dissolved in it determined by evaporation,
desiccation, or other means; or else, as is done with gases,
definite quantities of water and of the soluble substance are
taken and the amount remaining undissolved is determined.
[Illustration: FIG. 16.--Bunsen's absorptiometer. Apparatus for
determining the solubility of gases in liquids.]
The solubility of a gas in water is determined by means of an
apparatus called an _absorptiometer_ (fig. 16). It consists of an
iron stand _f_, on which an india-rubber ring rests. A wide
glass tube is placed on this ring, and is pressed down on it by
the ring _h_ and the screws _i i_. The tube is thus firmly fixed
on the stand. A cock _r_, communicating with a funnel _r_, passes
into the lower part of the stand. Mercury can be poured into the
wide tube through this funnel, which is therefore made of steel,
as copper would be affected by the mercury. The upper ring _h_
is furnished with a cover _p_, which can be firmly pressed down
on to the wide tube, and hermetically closes it by means of an
india-rubber ring. The tube _r r_ can be raised at will, and
so by pouring mercury into the funnel the height of the column
of mercury, which produces pressure inside the apparatus, can
be increased. The pressure can also be diminished at will, by
letting mercury out through the cock _r_. A graduated tube _e_,
containing the gas and liquid to be experimented on, is placed
inside the wide tube. This tube is graduated in millimetres
for determining the pressure, and it is calibrated for volume,
so that the number of volumes occupied by the gas and liquid
dissolving it can be easily calculated. This tube can also be
easily removed from the apparatus. The lower portion of this
tube when removed from the apparatus is shown to the right of
the figure. It will be observed that its lower end is furnished
with a male screw _b_, fitting in a nut _a_. The lower surface of
the nut _a_ is covered with india-rubber, so that on screwing up
the tube its lower end presses upon the india-rubber, and thus
hermetically closes the whole tube, for its upper end is fused
up. The nut _a_ is furnished with arms _c c_, and in the stand
_f_ there are corresponding spaces, so that when the screwed-up
internal tube is fixed into stand _f_, the arms _c c_ fix into
these spaces cut in _f_. This enables the internal tube to be
fixed on to the stand _f_. When the internal tube is fixed in the
stand, the wide tube is put into its right position, and mercury
and water are poured into the space between the two tubes, and
communication is opened between the inside of the tube _e_ and
the mercury between the interior and exterior tubes. This is done
by either revolving the interior tube _e_, or by a key turning
the nut about the bottom part of _f_. The tube _e_ is filled with
gas and water as follows: the tube is removed from the apparatus,
filled with mercury, and the gas to be experimented on is passed
into it. The volume of the gas is measured, the temperature and
pressure determined, and the volume it would occupy at 0° and
760 mm. calculated. A known volume of water is then introduced
into the tube. The water must be previously boiled, so as to be
quite freed from air in solution. The tube is then closed by
screwing it down on to the india-rubber on the nut. It is then
fixed on to the stand _f_, mercury and water are poured into
the intervening space between it and the exterior tube, which
is then screwed up and closed by the cover _p_, and the whole
apparatus is left at rest for some time, so that the tube _e_,
and the gas in it, may attain the same temperature as that of
the surrounding water, which is marked by a thermometer _k_
tied to the tube _e_. The interior tube is then again closed by
turning it in the nut, the cover _p_ again shut, and the whole
apparatus is shaken in order that the gas in the tube _e_ may
entirely saturate the water. After several shakings, the tube
_e_ is again opened by turning it in the nut, and the apparatus
is left at rest for a certain time; it is then closed and again
shaken, and so on until the volume of gas does not diminish after
a fresh shaking--that is, until saturation ensues. Observations
are then made of the temperature, the height of the mercury in
the interior tube, and the level of the water in it, and also
of the level of the mercury and water in the exterior tube. All
these data are necessary in order to calculate the pressure under
which the solution of the gas takes place, and what volume of gas
remains undissolved, and also the quantity of water which serves
as the solvent. By varying the temperature of the surrounding
water, the amount of gas dissolved at various temperatures may
be determined. Bunsen, Carius, and many others determined the
solution of various gases in water, alcohol, and certain other
liquids, by means of this apparatus. If in a determination of
this kind it is found that _n_ cubic centimetres of water at
a pressure _h_ dissolve _m_ cubic centimetres of a given gas,
measured at 0° and 760 mm., when the temperature under which
solution took place was _t_°, then it follows that at the
temperature _t the co-efficient of solubility of the gas_ in 1
volume of the liquid will be equal to _m_/_n_ × 760/_h_.
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] [Illustration: FIG. 17.--Curves expressing the contraction,
quantity of heat, and rises of temperature produced by mixing
sulphuric acid with water. Percentage of H_{2}SO_{4} is given
along the axis of abscissae.]
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.
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.