surface energy is manifested by the fact that it is necessary to
expend a certain amount of work & to increase the separating sur-
face of the two liquids by a quantity As, and experiment shows that
&
the ratio As~^
is a constant, at a given temperature, for two definite liquids.
This coefficient Y is what is ordinarily called the surface tension
of the two liquids. Its value for a liquid and its vapor, for example,
is easily determined by means of a special apparatus devised by
Ramsay and Shields, by measuring the height to which the liquid
rises in a capillary tube containing the vapor of the liquid and by
employing the known formula
Y = X g r h (p - - 8)
in which g is the acceleration of gravity, r is the radius of the capil-
lary tube, h is the height the liquid ascends in the capillary tube, p
and 8 are the densities of the liquid and vapor, respectively, at the
temperature of the experiment.
The experiments show that, in the case of a liquid and its own
vapor, y decreases with an increase in the temperature, becoming
zero at the critical point ; and it is the same with the surface energy
*W. Ramsay, I'Energie de surface pour determiner la complexite molecu-
laire des liquides (Lectures before la Societe Chimique de Paris, 1893 to 1900,
p. 27).
BASED UPON CHEMICAL REACTIONS
129
ys (produced from y by the surface s separating the liquid and its
vapor), if we take s constant. If then we express as ordinates the
temperature and as abscissas the value of the surface energy, we
will obtain, for a given liquid a curve expressing this energy as a
function of the temperature.
The experiment shows that, for all liquids whose critical point
has been determined, the curve has the form as represented in
Figure V.
FIG. V
From A (critical point where ys = ) to B (at a few degrees
below the critical point) it presents a curvilinear form; then it takes
the form of a straight line BC. Leaving out of consideration the
curved portion, the surface energy is represented for certain tem-
peratures below the critical temperature, by the linear equation:
(i) ys = k(t 0)
in which k is a constant, t the variable temperature counted from
the critical temperature down, and a constant equal to AA'.
We can express comparison between two liquids: For that pur-
pose, we can, just as is done for gases, consider equimolecular sur-
faces of these liquids, that is, plane surfaces containing the same
9
130 METHODS OF ANALYTICAL CHEMISTRY
number of assumed molecules distributed at an equal distance from
one another, and compare the equations (i) relative to each of these
liquids, in which s is an equimolecular surface. If we designate, by
v, the volume of the unit mass of a liquid, by M the mass of its
molecular weight, the product Mv represents for all the liquids,
volumes containing the same number of molecules, assuming that
the molecules are simple and not polymerised.
The two-thirds power of the products Mv will then represent
equimolecular surfaces for each of these liquids and equation (i)
becomes :
(2)
an equation analogous to that of the perfect gases
p(Mv)=k(t-r),
where p represents the pressure and r an interval of temperature
analogous to the interval 0.
Ramsay and Shields, by comparing the established equation (2)
for a certain number of liquids at their known critical temperatures,
have ascertained that k is a constant whose average value is 2.12.
The following are, in fact, the values of k for a few organic liquids :
LIQUID
k
Efthyl Ether
Methyl Formate
Ethyl Acetate
Carbon Tetrachloride
Benzene
Chlorbenzene
2.1716
2.0419
2.2256
2.1052
2.1043
2.0770
In most cases the critical temperature is not known, but the
value of k can then be determined by measuring the surface tension
at two different temperatures, which permits the elimination of
between the two corresponding equations (2) and results in the
relation
(3) * =
in which all of the terms are known, t f being equal to the inter-
val of temperature of the two experiments. This relation is exactly
the same as that given by the Mariotte-Gay Lussac law for perfect
gases :
BASED UPON CHEMICAL REACTIONS 131
pMv p'Mi/
~t=r
If, then, for a given liquid, it is found that k differs notably from
the average value, 2.12, it is because just as for dissociated gases,
the hypothesis from which we started (the invariability of the num-
ber of the molecules in the molecular weight, whatever may be the
liquid) was not legitimate. We must conclude from it that M was
badly chosen and that it is necessary to multiply it by a coefficient
x in such a manner that the equation
(5) (*Ms;)K=2.i2 (t0)
be verified, absolutely, as in the case of dissociated gases (ammo-
nium chloride, iodine vapor, sulphur vapor, etc) . It is necessary to
multiply M by a certain factor in equation (4) in order to obtain
the constant R. In these cases, the coefficient x may be considered
as being the number of simple molecules which are associated to
form a complex liquid molecule. It is easily calculated by means of
the equation (5).
Ramsay and Shields have thus found by determining y at differ-
ent temperatures, that x varies for alcohol from 1.64 at 20 to 1.06
at 210, for water from 1.71 at o to 1.29 at 140, etc. As the
value of k is a little uncertain, x is determined only within about
15 per cent for water. For example, if, however, the degree of
association is not known with a great accuracy, the principle itself
of this association, or polymerisation, is placed beyond a doubt by
the method of Ramsay and Shields. Their experiments, made upon
a great number of liquids, have shown that most bodies possess in
the liquid state the same molecular size as in the gaseous state, but,
in general, compounds containing the OH group are an exception
to this rule, particularly, water, alcohol, acetic acid, etc. So that
water, for example, should be considered as containing in the state
of equilibrium simple and condensed molecules, the equilibrium de-
pending upon the absolute temperature, just as for the vapors of
sulphur and iodine.
H. Crompton's Theories of Coefficient i. The analogy of the
conclusions of Ramsay and Shields with those of Van't Hoff, re-
sulting in the equation PV = tRT of the law of osmotic pressure,
for salt solution is striking. The coefficient x plays in the equation
132 METHODS OF ANALYTICAL CHEMISTRY
of Ramsay and Shields the same role as the coefficient i in Van't
Hoff's equation.
Guided by the analogy, Professor Holland Crompton introduced
this new notion of the polymerization of liquids, which he extended
equally to dissolved bodies, into the demonstrations given by
Arrhenius and Van't HofT upon the laws of osmotic pressure and
of the lowering of the freezing points. He has been able thus to
demonstrate in an exact manner that the anomalies of the aqueous
solutions of metallic salts in comparison to organic solutions spring
necessarily from the relation which exists between the state of aggre-
gation of the solvent and that of the dissolved substance, which
varies with the concentration. It is sufficient to assume that this
tends towards the non-molecular state in infinite dilutions in order
to explain and obtain the coefficient i just as easily as with the
hypothesis of electrolytic dissociation.*
The gwcm-constancy of the heat of neutralization of the acids
AH by the bases BOH comes according to Crompton's theory from
the immediate polymerization of the water HOH, resulting from
this neutralization, and the absence of the evolution of heat in reac-
tions among salts (thermoneutrality) depends upon the fact, in this
case, that there is no formation of water, and consequently no
modification in the state of association of the solvent.
Reychler's Hypothesis. Along the same theoretical lines, the
chemist Reychlerf starting from the principle that hydrolysis is the
fundamental phenomenon accompanying the solution of metallic
salts in water, assumes that a salt MA gives a reversible reaction
either with the simple molecules of water, or with its associated
molecules :
M-A+H-OH < M-OH+H-A,
M-A+ (H-OH)w ** M-OH+H-A,
and this would be the continuous displacement of the constituent
parts of salt in ephemeral combination with the H-OH of the sol-
vent, or mobile ions, which would explain, according to him, the
formation of electric currents, the law of thermoneutrality, the
gMO^-constancy of the heats of neutralization and the sharpness of
analytical reactions.
* For these demonstrations see the original articles of Holland Crompton,
Jour. Chem. Soc., Ixxi, 925, 946 and 951 (1897).
t Reychler, Journal de chimie physique, ii, 307 (1904) Geneve.
BASED UPON CHEMICAL REACTIONS 133
Without following this author so far as the electrical conse-
quences which he believes it is his duty to deduce from the hypothe-
sis of mobile ions, we assume with him that the phenomena of
hydrolysis suffice to explain the mechanism of reactions between
aqueous salt solutions, and that the two parts into which a salt dis-
solved in water ought necessarily to separate in order to produce
a double decomposition are not hypothetical electrical ions, but a
real base and acid coming from the chemical action of water upon
the salt in solution.
Conclusion. The great number of facts in contradiction to the
electrolytic theory leads us then to renounce the hypothesis of ions
and its consequences in explaining the constitution of salt solutions
and the double chemical decompositions which they cause.
The electrical conductivity of electrolytes ought to be classified
provisionally in the category of specific properties analogous to the
electrical conductivity of the solid bodies which we observe among
metals and which does not exist in other substances, without our
being able to explain the difference.
It does not follow that everything is to be rejected in the
Arrhenius-Ostwald theories, for it seems indeed that there is in this
conception a sort of reflection of a limiting-law analogous to that
of perfect gases. But as Kahlenberg* points out, while this limiting-
law of perfect gases might have been extended by Van der Waals
in an uninterrupted manner to gases more and more condensed, by
means of coefficients which, decreasing little by little, finally termi-
nate in the theoretical law, it is not the same in the case of the
electrolytic theory, whose conceptions, perhaps valuable for infinite
dilutions, show formal contradictions when one tries to apply them
to solutions more and more concentrated.
These contradictions depend upon the fact that the formulation
of Arrhenius includes phenomena too dissimilar and leaves out of
consideration an important phenomenon : the chemical action of the
solvent upon the dissolved substance, which action plays precisely
so important a role in hydrolysis, the very phenomena in which is
manifested most clearly the inadequacy of the electrolytic theory.
A salt which is dissolved in water diffuses throughout the same in a
manner similar to that of a gas in a vacuum, but only upon the con-
dition that we leave out of consideration the liquid; for, in reality,
the salt does not diffuse into the liquid by virtue of its elastic
*Loc. cit.
134 METHODS OF ANALYTICAL CHEMISTRY
strength as a gas, but by reason of a special affinity which is indi-
cated by osmotic, cryoscopic phenomena, etc. This affinity con-
nected with the state of aggregation of the molecules of the solvent
and of the dissolved substance suffices to explain, as we have just
seen, the anomalies of salt solutions in comparison to solutions of
substances not salts. The difference between the phenomenon of
expansion of gases and that of solubility is again shown by this
fact that while all gases mix (in all proportions) solids do not
dissolve in the same way in all liquids (Kahlenberg).
We are going to depend, in studying methods of analytical
chemistry based upon double decompositions of salts, exclusively
upon principles deduced from our calorimetric theory to which the
new conceptions of the polymerization of solvents and solutes are
not only not contradictory, but rather add a greater strength by
clearing up the general law of equilibrium.
CHAPTER VI
GENERAL PROCESSES OF ANALYSIS BASED UPON
DOUBLE DECOMPOSITIONS OF SALTS
i. Methods of Producing as Complete Precipitation as Possible
Influence of an Excess of the Reagent. Until the middle of the
nineteenth century, chemists, in view of the production of insoluble
precipitates, assumed implicitly that the reaction is effected in a
complete manner in conformity to the equation of reaction, and their
dominating thought was to place themselves within the exact con-
ditions of the equation. That is to say, to introduce into the liquid
the equivalent of the reagent exactly necessary to make the double
decomposition with the salt containing the constituent to be pre-
cipitated. This is what results, for example, in conditions recom-
mended by Rivot for the precipitation of barium sulphate with the
object of determining the sulphuric acid in a sulphate: "By avoid-
ing an excess of the reagent," he says,* "we have the advantage of
obtaining barium sulphate almost pure and very easy to wash." It
is very true that the manipulation indicated by Rivot necessarily
implies the addition of a slight excess of the reagent: "We dilute
with considerable water, add a little hydrochloric acid and pour in a
solution of barium chloride until a precipitate begins to form."
What the author seeks especially in this case, is evidently to limit as
much as possible the carrying down of the barium chloride by the
sulphate which, as we know, retains the chloride firmly.
In the case of other reactions, nevertheless, we see appear Rivot's
ideas of adding an excess of the reagent when the precipitate is
considered somewhat soluble in the mother liquor. This is true for
the precipitation of phosphoric acid in the form of magnesium
ammonium phosphate. Rivot indicates that the precipitation is more
complete when one employs an excess of the reagent. To keep,
however, the precipitate from retaining a considerable quantity of
magnesium sulphate in spite of the washings, he recommends the
use of only a small excess, without moreover otherwise indicating
the proportion.
* Rivot, Dotimasie, 2d edition, T. 234.
135
136 METHODS OF ANALYTICAL CHEMISTRY
The work of H. Rose, of Mulder, of Fresenius, of A. Carnot,
etc., in establishing the best conditions of insolubility of a large
number of precipitates employed in analytical chemistry, have shown
that, in most cases, the insolubility of the precipitate is increased
by the addition of a greater or smaller excess of the precipitating
reagent: of lead sulphate, by the addition of a slight excess of sul-
phuric acid (H. Rose) ; of ammonium phosphomolybdate, by a
large excess of a nitric acid solution of molybdic acid (Sonnen-
schein) ; of silver chloride, by a small excess of silver nitrate, if it
is a question of the precipitation of chlorine ; or by the excess of
sodium chloride, if one desires to determine the silver (Mulder),
etc.
It is the early work of Mulder upon the determination of silver*
which appears first to have clearly shown the role of an excess of
the reagent. Silver chloride is completely insoluble in pure water
or in water slightly acidified with nitric acid. However, on investi-
gating whether one equivalent of sodium chloride dissolved in water
precipitates exactly and completely one equivalent of silver dis-
solved in nitric acid, we find that this does not happen. The clear
supernatant liquid in contact with the precipitate, gives a cloudiness
when a little of the solution of sodium chloride is added as well as
when silver nitrate solution is introduced. As Mulder has demon-
strated perfectly, if into a silver solution, for example, a standard
sodium chloride solution has been introduced until there is no longer
formed any precipitate of silver chloride, an excess, necessarily, of
sodium chloride has been added beyond the quantity required by the
equation
AgNO 3 +NaCl = AgCl+NaNO 3 ,
and it is only due to this excess of sodium chloride that all of the
silver has been precipitated.
A hundredth normal solution of silver then added to the clear
filtrate gives a precipitate of silver chloride, and Mulder showed
that it was necessary to add one cubic centimeter of the hundredth
normal silver solution to have no further precipitate. If to this new
liquid, which contains silver nitrate in excess, we add a hundredth
*G. J. Mulder, Scheikundige Verhandelingen en Onderzoeking, 1857.
Fresenius (p. 255 of the 6th French edition) has presented a resume of the
observations of Mulder: (see Cohn's translation of the 6th German edition
of Fresenius, Vol. I, p. 344-345. Editors' Note).
BASED UPON CHEMICAL REACTIONS 137
normal solution of sodium chloride there is required exactly one
N
cubic centimeter of this solution in order to no longer have a
precipitate of silver chloride.
If we were to add only one half a cubic centimeter we would
have what Mulder calls the point of neutrality; i.e., the point for
which it is necessary to have the same quantities of a hundredth
normal solution of silver nitrate and of sodium chloride, to no longer
have any precipitate of silver chloride, that is, 0.5 c.c. of either
liquid. Since one cubic centimeter of a hundredth normal solution
corresponds to one milligram of silver, it is seen that according as
one titrates the standard silver solution with sodium chloride or one
titrates in the reverse order with a hundredth normal silver solution,
results are obtained which differ by one milligram of silver or one-
thousandth of the weight of the silver, if one employs one gram,
which is the usual amount in silver determinations.
Thus, in a double decomposition of salts giving a substance as
completely insoluble as silver chloride we see that, if we employ the
exact quantity of reagent necessary according to the equation of
the reaction, we may introduce an error amounting to one thousandth
by the fact that the reaction is limited by reverse double decomposi-
tion. An equilibrium is established between the three soluble salts,
silver nitrate, sodium chloride and sodium nitrate, an equilibrium
which is disturbed by the addition of either silver nitrate or sodium
chloride, and the work of Mulder has clearly shown that the pre-
cipitation of chlorine or of silver is complete only with an excess
of the precipitating reagent.
With salts more soluble than silver chloride, the effect of the
excess of the reagent is even more pronounced. This is true, in the
precipitation of lithium by ammonium fluoride, used by A. Carnot*
in his method for the determination of lithium, the author showed
that the solubility of lithium fluoride either in pure water or in
ammoniacal water is reduced about one half by a slight excess of
ammonium fluoride.
This influence of the excess of the reagent is well known at
present and very generally applied in making the precipitation more
complete, and is derived directly from the law of equilibrium in
double decomposition of salts. We shall demonstrate it by an
* A. Carnot, C. R., cvii, 237, 336 (1888).
138 METHODS OF ANALYTICAL CHEMISTRY
example very frequently employed in analytical chemistry, the pre-
cipitation of sulphuric acid by barium chloride :
BaCl 2 +H 2 S0 4 = BaS0 4 +2HCl.
Barium sulphate is very slightly soluble, but its solubility in pure
water (one part in 400,000 parts of water or 2 mg. in 5 liters) is far
from being negligible. If there is then added to the sulphuric acid
just the quantity of barium chloride corresponding to the preceding
equation, there will remain in solution a small quantity of barium
chloride, sulphuric acid and barium sulphate conforming to the
isothermal equation of equilibrium
>'
L BaS0 4
and consequently, a little sulphuric acid will remain unprecipitated.
Let us now add an excess of barium chloride which increases
Cg a Q 2 . In order that the equilibrium be maintained, it is necessary
that CH 2 S0 4 diminish, or that C H *C1 increase, since C^sO*
cannot increase, the solution being saturated with barium sulphate.
Now, in order that the concentration of sulphuric acid should dimin-
ish or that the concentration of hydrochloric acid should increase,
it is necessary that a new quantity of barium sulphate should pre-
cipitate. Thus the excess of the reagent, barium chloride, will ren-
der the precipitation of the sulphuric acid more complete. Likewise,
if we wish to precipitate all the barium contained in a solution, it
will be necessary for the same reason, to add an excess of sulphuric
acid.
If, to simplify the discussion, we reduce the equilibrium equa-
C-C
tion to^^-^=k f it is clear that in order to diminish C one half,
it will suffice to double C, assuming that the denominator varies only
a little ; which is clearly true, since the concentration C" of barium
sulphate, being at the point of saturation, may be regarded as con-
stant, and since C'", the concentration of hydrochloric acid, is rela-
tively very slightly increased by the conversion of the last traces of
free sulphuric acid into barium sulphate, giving an equivalent
quantity of free hydrochloric acid. As the double decomposition
between sulphuric acid and barium chloride, taken in equivalent
quantities, leaves really only very small quantities of free sulphuric
BASED UPON CHEMICAL REACTIONS 139
acid and barium chloride in solution, we see that there will necessar-
ily be required a few milligrams of barium chloride per liter in
excess to reduce to negligible traces the initial quantity of non-
precipitated sulphuric acid. The more soluble the precipitate the
larger must be the excess of the precipitating reagent in order to
render the precipitation more complete.
The role of the excess of the reagent, however, does not stop
with this. It has been known for a long time, in general, that a salt
becomes less soluble in water when there is added to it a certain pro-
portion of the acid or base of the salt. Hence the alkali chlorides
in saturated solutions are precipitated by the addition of hydro-
chloric acid or of the alkali of the salt; similarly lead nitrate
by nitric acid; barium chloride, by hydrochloric acid; etc. More-
over, it is not always necessary that the acid or the base added be
free in order to diminish the solubility of the dissolved salt. They
produce an effect in the same direction, although less energetic,
added in the form of the salt of another metal, if it is a question of
the acid, or of another acid, if it is a question of the base. To bring
out, in this case, the diminution of solubility of the dissolved salt, it
is necessary to discuss slightly soluble salts. As I have shown, a
saturated solution of lead chloride (soluble in 135 parts of cold
water) precipitates immediately upon the addition of a few drops
of lead acetate or lead nitrate, or of sodium chloride. Likewise, a
saturated solution of lead iodide (soluble in 1235 parts of water)
precipitates by a few drops of lead acetate or of potassium iodide,
while the addition of other salts differing from the salt in solution
by acid and by base, produces no precipitation.
The excess of reagent: Introducing into the liquid, either in the
free state or in the form of a salt, an excess of the acid or of the
base contained in the precipitate, has then, in general, the effect of
diminishing still more the solubility of the precipitate. If we rely on
the preceding equilibrium equation, we see that Cjj 2 S04 diminishes
with the excess of BaCl 2 , not only by virtue of the law of equilib-
rium, but also because the value of Cg a so 4 itself decreases, which
brings about a diminution of Cfj 2 $o 4 m order that the equilibrium
may subsist.
This additional influence of the excess of reagent is easily ex-
plained by hydrolysis.
Let us consider, in fact, a saturated solution of a salt AB, in
contact with an excess of the same solid salt. We have present in
140 METHODS OF ANALYTICAL CHEMISTRY
the solution, the non-hydrolyzed dissolved salt in equilibrium with
the free acid A and base B coming from the dissociated portion.
Free acid -f- free base <- non-hydrolyzed dissolved salt
Let us apply to this equilibrium the general law, assuming the
coefficients i equal and the coefficients n = i, to simplify the reason-
ing. We have
r r kc
H** ^B ^AB
Introduce into the solution, without modifying its volume, a
little of the acid or base of the free salt or in the form of another