Joseph William Mellor.

A comprehensive treatise on inorganic and theoretical chemistry (Volume 1) online

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large, the expression reduces to that employed by G. A. Hulett, for S 2 then denotes
the ordinary or normal solubility of the substance. For calcium sulphate, where
Z>=2'33 ; M=136 ; <r=1050 ergs per sq. cm. at 25,

S 2 Ma- >S'j 14-69 X 10- 4

orlog ,s 2 = -&r



SOLUTIONS



509



if D and a- are independent of temperature. On calculating the solubilities of
gypsum for different values of r and T it is found that the solubility curve for r
=50'0/Lt is virtually the same as when r is infinite. The results shown in Fig. 1
represent the solubility curves (milligram-molecules per litre) for r=0'5/z ; rl'Ofi ;
r=3'0fji ; and r=50'0ju.

A solution in equilibrium with fine-grained particles, say 0'5/x, is super-saturated
with respect to coarser-grained particles, say 50/x,. Consequently with a mixture
of coarse and fine grains, the coarse grains will grow at the expense of the fine
grains. In illustration, a fine-grained precipitate, after standing some time in contact
with its solution, becomes coarser-grained, so that the freshly-made precipitate
readily passes through the filter paper, while the older precipitate does not




E. Podszus found that certain oxides alumina, thoria, and zirconia usually not
acted upon by the hydrochloric acid are dissolved by this reagent when they have
been reduced to a fine state of subdivision so that the particles have a diameter of
the order 1/z. The dissolution of the oxides in hydrochloric acid is a phenomenon
different in kind from the solution of, say, gypsum in water. W. Herz calculated
the molecular diameter, d, of liquids from the equation d=2yv/L, where y denotes
the capillary constant, v the specific volume, and L the latent heat of evaporation
per gram. He then examined the relation between this magnitude and the solu-
bility of the liquids in water, and found that in general
the solubility is greater the smaller the diameter. The
rule can be entirely altered by specific chemical properties.
The effect of grain size on solubility recalls the fact
that when drops of liquid are suspended in air or other
gas, the smaller drops of liquid grow smaller and dis-
appear, so that the larger drops grow larger at the expense
of the smaller drops. The vapour pressure of a liquid
depends on the curvature of its surface; the greater the
curvature the greater the vapour pressure, and hence the
vapour from the smaller drops is distilled on to the larger
drops 1. 9, 6. The two phenomena are not strictly
analogous except in this way. The boundary-surface
between a liquid and a solid is the seat of a certain amount
of energy the so-called free surface energy of the liquid.
The greater the curvature of a liquid, the greater the surface energy. The greater
the free surface energy of a substance, the greater the solubility e.g. the allotropic
forms of a substance have different solubilities, the less stable is always the more
soluble. Hence, P. Curie inferred that the greater the free surface energy between
a solid and its solution, the greater the solubility.

Is water in aqueous solutions identical with water alone ? When the absorption
of light by a given layer of an aqueous solution is compared with that of a layer
of water of the same depth, it cannot be assumed that the water in the aqueous
solution absorbs as much light as pure uncombined water ; and that the difference
between the light absorption of the aqueous solution and of pure water is due to
the dissolved substance. The different transparency of the water in a solution as
compared with water alone must be ascribed to a relation between the dissolved
substance and the solvent water ; part, at least, of the water must be different from
water alone, and the most probable hypothesis is that the water is partly de-
polymerized by the solute or that part of the water present in a solution is in com-
bination with the dissolved substance. Of the salts examined by H. C. Jones
(1913) and his co-workers, those which do not form hydrates absorb practically
the same amount of light as a corresponding layer of water. A difference in light
absorptive power is only exhibited by solutions of those substances which form
hydrates ; this is taken to mean that the difference between light absorbing power
of solutions of hydrated salts and the corresponding amount of the solvent is not



Temperatures

FIG. 1. Solubility
Curves of Calcium
Sulphate of Different
Grain-size.



510



INORGANIC AND THEORETICAL CHEMISTRY



fully explained by the depolymerization or the breaking down of associated
molecules of water by the dissolved substance.

The influence of temperature on solubility. The solubility of most substances
increases with the temperature ; the higher the temperature, the greater the
solubility. Graphs obtained by plotting the relation between the solubility of
solids and temperature are called solubility curves. The solubility curve presents
a graphic picture which enables the relation between solubility and temperature
to be seen at a glance. In illustration, the upward left-to-right slope of the
solubility curve of calcium sulphate shows that the solubility of this salt
increases with a rise of temperature up to about 40, and the downward left-to-right
slope over that temperature shows that the solubility then decreases as the tempera-
ture rises. Sodium chloride is but slightly more soluble in hot than in cold water.
The solubilities of a few typical salts at 0, 50, and 100 are as follows :



Solubility of

Potassium hydroxide, KOH
Sodium chloride, NaCl.
Calcium hydroxide, Ca(OH) 2
Calcium chromate, CaCrO 4 .
Cerium sulphate, Ce 2 (SO 4 ) 3 .





97-00

35-63

0-14

4-50

19-09



50

140-00

36-67

0-10

1-12

4-78



100

178-00

39-12

0-06

0-42

0-78



The solubility of a substance depends on so many complex factors that a
satisfactory quantitative theory has not yet been established. E. Clapeyron and
R. Clausius' equation can be written :

d log 8 Q 1 dS Q

I 1 )



dT



SdT



so as to show the relation between the absolute solubility, S t and the temperature
coefficient, dS/dT, of the solubility i.e. approximately the change in solubility
per degree and the reversible heat of solution, Q. The gas constant R is nearly
2 calories. It is usual to represent the observed data between the concentration
$ and the temperature by an empirical formula of the type, 8=ad-+-bd 2
-|-c0 3 -|-. . ., where a, b, c are constants to be evaluated from the measurements
of the solubilities S at temperatures 9 lt 2 > #3> R- T. Hardmann and J. R.
Partington 8 used the empirical expression log S=A BT~ l C log T, which
contains three constants like the simpler relation, S=a-+-bO-\-c6 2 .

Starting from F. M. Raoult's vapour pressure law, G. Bodlander calculated
the solubilities of some very sparingly soluble salts from the heats of formation Q
of an equivalent amount of the salt, and the electrode potentials of their ions E"
for the cation, E' for the anion :



^ i)logS=E - +E '^

where n' and n' respectively denote the valencies of cation and anion, and the
solubility S is expressed in gram-equivalents per litre. It is here assumed that the
free energy of the reaction is equal to the total energy change. F. Dolezalek also
calculated the solubility of gases in liquids on the assumption that Raoult's law is
valid. J. H. Hildebrand deduced the following expression for the solubility N of
a solid at the absolute temperature T :



2V

where n/N denotes the solubility of the compound expressed in terms of the
molecular fraction n representing the number of gram-molecules of the solute in
the solution, and N the total number of gram-molecules of solvent and solute ;
A denotes the heat of fusion per gram-molecule assumed to be independent of the
temperature ; T mt the absolute melting temperature of the solute. It follows



SOLUTIONS 511

from this conclusion that the solubility of a solid is smaller the greater the heat
of fusion, and the higher the melting point over T.

D. Tyrer assumes that the solubility of a given substance depends not only upon the
temperature and nature of the solvent, but also on the mass of the solvent contained in
unit volume of the solution. The solubility of a substance in a given solvent is always
diminished when the solvent is diluted with a liquid in which the given solute is insoluble.
On this assumption he deduces the relation, Sn=a(V/v)n b, which also contains three
constants, n, a, and b. V represents the total volume of the solution and v the specific volume
of the solute. Sufficient data have not been published to establish this relation.

The influence of pressure on solubility. The effect of pressure on solubility in
condensed systems liquids and solids is relatively small one per cent, per
1000 atm. when contrasted with the effect of temperature, and it may be either
positive or negative. Pressure has but a slight influence on binary condensed
systems generally. The most accurate work on the effect of pressure on solubility
is that by E. Cohen and co-workers 9 on the solubility of sodium chloride and
mannite ; when at 24*05, it was found :

Pressure .... 1 250 500 1000 1300 atm.

Solubility . . 26-41 26'60 26'76 27'02 27/20 per cent.

and H. F. Sill's work on sodium chloride and barium hydroxide, Ba(OH) 2 .8H 2 0,
where it was found, for the latter, at 25 :

Pressure 1 25 490 atm.

Solubility . . 8'299 8-790 9*366 per cent.

In 1862, K. Moller stated that that pressure must exercise an influence on the
solubility of a salt ; and in 1863, H. C. Sorby 10 made some remarks on the
subject. The solubility of a salt is increased by pressure if, during solution, a
contraction occurs ; and conversely, the solubility of a salt is decreased by
pressure if an expansion occurs during solution. For example, the percentage
changes in the volumes of solid sodium and ammonium chlorides over their
volumes in a saturated solution are respectively -f-13'57 and 15'78 ; the
percentages changes in solubilities per atmosphere increase of pressure are re-
spectively -fO'00419 and 0'00638, when the -f signs denote increases, and the
- signs decreases. In 1870, C. M. Guldberg deduced a general expression for the
change of solubility S which occurs when the pressure changes by an amount dp.
This is usually expressed in the form :

d log S 8v 1 dS_8^
dp -RT' T 'S'dp~RT

These expressions follow directly from Clapeyron's equation. The observed results
are in agreement with these formulae when 8v denotes the change in volume which
occurs during the solution of the solid, and dS/dp, the pressure coefficient of the
solubility that is, the change of solubility which occurs when the pressure changes
one unit. F. Braun made a special study of the subject in 1870, and this work
has crystallized in the statement : The solubility of a salt will increase with
pressure if the solution occupies a less volume than the sum of the volumes of its
constituent parts ; while the solubility will diminish if the solution occupies a gre'ater
volume than the sum of the volumes of its constituent parts. This is but a
specialized form of the so-called generalization of G. Robin in 1879 : At constant
temperature there is one definite pressure at which a system will be in equilibrium ;
on raising the pressure, the reaction will take place in that direction which is
produced with a decrease in volume ; while if the pressure be reduced, the reaction
will proceed in that direction which has the greater volume. This, again, is a
special case of J. H. van't Hoff's law of mobile equilibrium ; which in turn is a
special case of the principle of least action, foreshadowed in a vague sort of way by



512 INORGANIC AND THEORETICAL CHEMISTRY

Maupertius in 1747 all natural changes take place in such a way that the existing
state of things will suffer the least possible change.

By division of the expression (1) for the relation between the temperature
coefficient of the solubility, dS/dT, and the heat of solution Q by the above expression,
(2) for the relation between the pressure coefficient of solubility, dS/dp, and volume
change dv, it follows that

< 3)

where v 2 v represents the change in volume, in c.c., which occurs when a gram*
molecule of the solid is dissolved at the temperature T in an unlimited quantity of
the saturated solution ; Q represents the heat of solution under these conditions.
The term dp may be taken to represent the increase in pressure necessary to cause
one gram more of the solute to pass into solution and dT the increase in temperature
necessary to produce that result ; or dS/dT, the temperature coefficient of the
solubility represents the change in solubility per degree change of temperature,
and ds/dp the pressure coefficient of the solubility. Values of Q for barium hydroxide
calculated from this equation agree well with the observed.

Since chemical equilibrium n is determined only by the relative concentration
of the different kinds of molecules concerned in the reaction, the equilibrium can
be altered by pressure only by changing the relative concentration of the substance
concerned in the reaction ; but the compressibility of liquids and solids is small, and
differences in the compressibility of the components in a reaction must therefore
be very small. Consequently, the effect produced by changes of pressure on
chemical equilibrium in condensed systems must be small. When one of the
components is a gas, the case is different because gases are highly compressible,
and their reactivity is almost proportional to the pressure. A compound involving
a volatile component will not be formed in a reaction unless the concentration or
partial pressure exceeds a certain limiting value which is mainly dependent on the
temperature. For instance, liquid water will not be formed at 200 if the pressure
is less than 15 atm., and at 300 if the pressure be less than 100 atm. Calcium
hydroxide in an atmosphere of steam at 550 and one atm. pressure, does not
dissociate into water and calcium oxide, but at 750 a pressure of 15 atms. is required
to prevent dissociation.

According to G. Tammann, 12 if a solvent and a solution be subjected to a certain pressure
p,it is sufficient to raise the pressure on the solvent by a certain amount of 8p in order
that it may behave like the solution with respect to volume, temperature, and pressure.
The extra pressure Sp required to make the coefficient of thermal expansion of the solvent,
or the coefficient of compressibility of the solvent, equal to that of the solution under the
standard pressure, depends upon the concentration and nature of the solute. G. Tammann
explains the phenomenon by assuming that internal pressure is raised by the solution of a
substance in the solvent, so that the solvent requires an additional external pressure to
compensate the extra internal pressure of the solution. Under these circumstances the
equations of state of solution and solvent are the same.

Transition temperatures. Some solubility curves exhibit irregularities at
certain temperatures. The solubility curve may change its direction, as calcium
sulphate does at 35, and barium butyrate at 45. The solubility curve
of sodium sulphate is a very trite illustration, but none the less instructive on
that account. It is shown in Fig. 2. 13 The solubility of sodium sulphate, said
J. L. Gay Lussac, follows une marche tres singuli&re for the solubility of the salt,
Na 2 S0 4 .10H 2 0, increases rapidly with rise of temperature, as shown by the slope of
the curve EO, Fig. 2. There is an abrupt change in the direction of the solubility
curve at 32*383, 0, Fig. 2. Above that temperature the solubility decreases
with rise of temperature. This, said J. L. Gay Lussac in 1819, is the second
example of a body whose solubility decreases with a rise of temperature, for
J. Dalton had previously shown that lime behaves in a similar manner.



SOLUTIONS



513



The break point de rebroussement in the solubility curve of sodium sulphate,
the first of its kind, was discovered by J. L. Gay Lussac in 1819, and in 1839 he recog-
nized that the breaks in the solubility curves of some substances can be accounted
for by assuming that at this point it is no longer the same substance which dissolves
further. In 1840, H. Kopp showed that the solubility curves above and below
the point de rebroussement are two distinct curves representing the solubility of two
different substances. The one curve below the transition point can be represented
by the formula /S^ =5*02 +0*305940 0*0004100 2 +0*00099770 3 ; and the other
by S 2 ^58*50-0*277830+0*00069000 2 +0*000<X)4980203. At the transition
point S 1 =S 2 , and 6 then becomes 32*93. The observed value is a little lower than
this, viz. 32*383. At the transition temperature, adds H. Kopp, the crystallized
sodium sulphate passes into the anhydrous salt. Consequently, the curve of
increasing solubility of temperature below 32 '383 represents the solubility of
curve of the decahydrate, Na 2 S0 4 .10H 2 ; and the curve of decreasing solubility
with rise of temperature represents the solubility curve of the anhydrous salt,
Na 2 S0 4 . The decahydrate, at 32*383, is transformed into the anhydrous salt.
The decahydrate is not stable above 32*383 ; the
anhydrous salt is not stable below 33. This tem-
perature is called the transition temperature or
transition point, and the change is symbolized :

32-383

Na 2 S0 4 .10H 2 O^Na 2 S0 4 +10H 2

The solubility curves, it will be observed, represent
the conditions of equilibrium between the solvent and
salt. It makes no difference whether we start with the
anhydrous sulphate or the decahydrate. When in
equilibrium, the solution in contact with the solid will
contain the amounts of sodium sulphate Na 2 S0 4
indicated by the solubility curves, Fig. 2. The
saturated solutions, when in equilibrium, have the
same concentration and are identical in every way.
We cannot continue the observation of the solubility
of the decahydrate beyond 32*383, because it im-
mediatelysvKts up either into a less hydrated form-
e.g. Na 2 S0 4 .7H 2 or the anhydrous form, Na 2 S0 4 .
The solubility curve of the heptahydrate meets the
solubility curve of the anhydrous sulphate in the region of instability ; the
transition point from the heptahydrate to the anhydrous salt is 34




SKt

Curve of
Sodium Sulphate.



or



34 C



Na 2 S0 4 .7H 2 O^Na 2 S0 4 +7H 2

The so-called eutectic points E and E 2 will be discussed later, but since the trans-
formation of the anhydrous salt into the hydrate takes an appreciable time, it is
possible to measure the approximate solubility of the anhydrous salt below 32*8.
This is indicated by the dotted line in the diagram. In saturated solutions of
hydrates, a definite hydrate is in dynamic equilibrium with the solution ; if the
hydrate changes as shown by E. Demargay's study (1883) of the hydrates of thorium
sulphate, the maximum amount of a salt which can enter into solution depends
on its temperature and on its state of hydration ; the solubilities of the different
hydrates of a salt are different, and at the transition temperature, there is a break
in the continuity of the solubility curve. H. W. B. Roozebooin's studies of the
hydrates of a number of salts show that the solubility curves of the different
hydrates of a salt indicate the limits of their stability.

The solubilities of the two sodium sulphates anhydrous and decahydrate
are quite different. If the solid decahydrate were in contact with a saturated
VOL. i. 2 L



514 INOKGANIC AND THEOKETICAL CHEMISTRY

solution at 20, and some of the anhydrous sulphate were added to the solution,
some of the latter would dissolve and be deposited later as the decahydrate.
The final result would be a transformation, through the medium of the solution,
of the anhydrous salt into the decahydrate. Although 100 c.c. of water at
can only dissolve about 5*0 grams of the decahydrate, the same quantity of
water can dissolve much more of the anhydrous sulphate. The general result of
a multitude of experiments is to show that salts which crystallize in two or more
different forms with different amounts of combined water, have different solubilities ;
and at certain temperatures a solution may be saturated with either of two different
hydrates, e.g. Na 2 S04.10H 2 0, or Na 2 S0 4 .7H 2 ; it is therefore necessary to specify
which sodium sulphate is in question when reference is made to a saturated solution
of sodium sulphate. Of two hydrates that containing the less water is usually the
more soluble at any temperature below the transition temperature H. le Chatelier's
rule. For instance, sodium sulphate forms the hydrates, Na 2 S04.7H 2 and
Na 2 S0 4 .10H 2 0, and 100 grams of a saturated solution of the former at 10 has 23'1
grams of the former and 8*3 grams of the latter. The rule is not general ; the
hydrates of manganous sulphate do not fit the rule.

The solubility curve of anhydrous rhombic sodium sulphate progresses from
3 into the metastable region. The solubility curve is at first retrograde
decreasing with rise of temperature and it then becomes normal increasing
with rise of temperature. A. Smits explains the retrograde solubility curve of
rhombic sodium sulphate by assuming a retrogression of the degree of hydration
of the salt in solution with a rising temperature. At the transition point, 234,
the rhombic crystals of sodium sulphate pass into the monoclinic form :

234
Na 2 S0 4r hombic Na 2 SO 4mon oclmic

The solubility of anhydrous monoclinic sodium sulphate is wholly retrograde, and
at the critical temperature (365) the concentration of the solution is so small that
the critical temperature is virtually the same as that of water. A. Smits assumes
that the strongly retrograde solubility of monoclinic sodium sulphate indicates that
the latent heat of liquefaction of this salt is much less than that of the rhombic
salt. In the diagram, the concentration near the point C is on a much enlarged
scale in order to make the relations clear, for the curve up to C represents the
solubility of sodium sulphate in the vapour phase, and hence this curve virtually
coincides with the H 2 axis. At the critical temperature of the solution, the
liquid and vapour perhaps have the same composition, and the two curves join up
with one another.

Is a heterogeneous solution to be regarded as a phase ? -In heterogeneous
solutions there are an infinite number of phases because every different degree of
concentration can be regarded as a phase. The phase rule is concerned with con-
ditions of equilibrium, and a heterogeneous solution is not in equilibrium because
there is a tendency to diffusion. Hence, the phase rule is not needed to determine
if such a solution is in equilibrium. If sulphur be placed in contact with iron,
it might be said that, neglecting vapour, there are two components, and two phases,
and therefore the system is univariant. Hence, sulphur and iron will not interact
when heated. It will be noticed, however, that the mixture of sulphur and iron is
not a system in equilibrium ; the two elements are not phases of a prior system, or
molten ferrous sulphide, FeS, on cooling would separate into particles of free sulphur
and free iron. Consequently, the phase rule does not apply.

Is a solution to be regarded as a one-phase or as a two-phase system ? The
decrease in the solubility of a substance with rise of temperature is due to the
solute changing its nature thus, the diminishing solubility of sodium sulphate,
Na 2 S0 4 .10H 2 0, above 33 is referred to the passage of the decahydrate into the
anhydrous salt, Na 2 S0 4 ; with calcium hydroxide, Ca(OH) 2 , too, the change is
usually attributed to the transformation of some hydroxide into oxide, CaO. In



SOLUTIONS 515

general, a turning point in the solubility curve shows that the solid phase in the
saturated solution is changing. From this it follows that the molecules of a substance
in solution may retain their individuality and that they can undergo changes in
the solution similar to those they suffer when heated alone. H. C. Jones and
J. S. Guy 14 showed that water which is combined with salts in solution is far more
transparent than pure water ; and J. E. L. Holmes and H. C. Jones, that the rate
of saponification of methyl acetate or formate is likewise faster with combined than
it is with free water.

While a solution in equilibrium can be said to have the same composition in
all its parts, so that it cannot be separated by mechanical or physical operations
into different individual parts, yet, according to the molecular theory, there must



Online LibraryJoseph William MellorA comprehensive treatise on inorganic and theoretical chemistry (Volume 1) → online text (page 87 of 177)