where C', C" are the concentrations of the saturated solution
corresponding to the temperatures [theta]' and [theta]". This
equation may be employed to calculate the latent heat of solution Q
from two observations of the solubility. It follows from these
equations that Q is of the same sign as dC/d[theta], that is to say,
the solubility increases with rise of temperature if heat is absorbed
in the formation of the saturated solution, which is the usual case.
If, on the other hand, heat is liberated on solution, as in the case
of caustic potash or sulphate of calcium, the solubility diminishes
with rise of temperature.
(b) In the case of a solution saturated with respect to ice (curve
AC), if one gramme of water having a volume v is separated by
freezing, we obtain a precisely similar equation to (5), but with L
the latent heat of fusion of water instead of Q, and v instead of V.
If the solution is dilute, we may neglect the external work Pv in
comparison with L, and also the heat of dilution, and may write P/t
for dP/d[theta], where t is the depression of the F.P. below that of
the pure solvent. Substituting for P in terms of V from equation (4),
we obtain
t = 2[theta]^2v / LVM = 2[theta]^2w / LWM, (8)
where W is the weight of water and w that of salt in a given volume of
solution. If M grammes of salt are dissolved in 100 of water, w = M
and W = 100. The depression of the F.P. in this case is called by van
't Hoff the "Molecular Depression of the F.P." and is given by the
simple formula
t = .02[theta]^2 / L. (9)
Equation (8) may be used to calculate L or M, if either is known, from
observations of t, [theta] and w/W. The results obtained are
sufficiently approximate to be of use in many cases in spite of the
rather liberal assumptions and approximations effected in the course
of the reasoning. In any case the equations give a simple theoretical
basis with which to compare experimental data in order to estimate the
order of error involved in the assumptions. We may thus estimate the
variation of the osmotic pressure from the value given by the gaseous
equation, as the concentration of the solution or the molecular
dissociation changes. The most uncertain factor in the formula is the
molecular weight M, since the molecule in solution may be quite
different from that denoted by the chemical formula of the solid. In
many cases the molecule of a metal in dilute solution in another metal
is either monatomic, or forms a compound molecule with the solvent
containing one atom of the dissolved metal, in which case the
molecular depression is given by putting the atomic weight for M. In
other cases, as Cu, Hg, Zn, in solution in cadmium, the depression of
the F.P. per atom, according to Heycock and Neville, is only half as
great, which would imply a diatomic molecule. Similarly As and Au in
Cd appear to be triatomic, and Sn in Pb tetratomic. Intermediate cases
may occur in which different molecules exist together in equilibrium
in proportions which vary according to the temperature and
concentration. The most familiar case is that of an electrolyte, in
which the molecule of the dissolved substance is partly dissociated
into ions. In such cases the degree of dissociation may be estimated
by observing the depression of the F.P., but the results obtained
cannot always be reconciled with those deduced by other methods, such
as measurement of electrical conductivity, and there are many
difficulties which await satisfactory interpretation.
Exactly similar relations to (8) and (9) apply to changes of boiling
point or vapour pressure produced by substances in solution (see
VAPORIZATION), the laws of which are very closely connected with the
corresponding phenomena of fusion; but the consideration of the vapour
phase may generally be omitted in dealing with the fusion of mixtures
where the vapour pressure of either constituent is small.
[Illustration: FIG. 3.--Solubility Curves of Hydrates.]
8. _Hydrates._--The simple case of a freezing point curve, illustrated
in fig. 1, is generally modified by the occurrence of compounds of a
character analogous to hydrates of soluble salts, in which the dissolved
substance combines with one or more molecules of the solvent. These
hydrates may exist as compound molecules in the solution, but their
composition cannot be demonstrated unless they can be separated in the
solid state. Corresponding to each crystalline hydrate there is
generally a separate branch of the solubility curve along which the
crystals of the hydrate are in equilibrium with the saturated solution.
At any given temperature the hydrate possessing the least solubility is
the most stable. If two are present in contact with the same solution,
the more soluble will dissolve, and the less soluble will be formed at
its expense until the conversion is complete. The two hydrates cannot be
in equilibrium with the same solution except at the temperature at which
their solubilities are equal, i.e. at the point where the corresponding
curves of solubility intersect. This temperature is called the
"Transition Point." In the case of ZnSO4, as shown in fig. 3, the
heptahydrate, with seven molecules of water, is the least soluble
hydrate at ordinary temperatures, and is generally deposited from
saturated solutions. Above 39 deg. C., however, the hexahydrate, with six
molecules, is less soluble, and a rapid conversion of the hepta- into
the hexahydrate occurs if the former is heated above the transition
point. The solubility of the hexahydrate is greater than that of the
heptahydrate below 39 deg., but increases more slowly with rise of
temperature. At about 80 deg. C. the hexahydrate gives place to the
monohydrate, which dissolves in water with evolution of heat, and
diminishes in solubility with rise of temperature. Intermediate hydrates
exist, but they are more soluble, and cannot be readily isolated. Both
the mono- and hexahydrates are capable of existing in equilibrium with
saturated solutions at temperatures far below their transition points,
provided that the less soluble hydrate is not present in the crystalline
form. The solubility curves can therefore be traced, as in fig. 3, over
an extended range of temperature. The equilibrium of each hydrate with
the solvent, considered separately, would present a diagram of two
branches similar to fig. 1, but as a rule only a small portion of each
curve can be realized, and the complete solubility curve, as
experimentally determined, is composed of a number of separate pieces
corresponding to the ranges of minimum solubility of different hydrates.
Failure to recognize this, coupled with the fact that in strong and
viscous solutions the state of equilibrium is but slowly attained, is
the probable explanation of the remarkable discrepancies existing in
many recorded data of solubility.
_Transition Points of Hydrates._
Na2CrO4.10H2O 19.9 deg. NaBr.2H20 50.7 deg.
Na2SO4.10H2O 32.4 deg. MnCl2.4H2O 57.8 deg.
Na2CO3.10H2O 35.1 deg. Na3PO4.12H2O 73.4 deg.
Na2S2O3.5H2O 48.0 deg. Ba(OH)2.8H2O 77.9 deg.
The transition points of the hydrates given in the above list (Richards,
_Proc. Amer. Acad._, 1899, 34, p. 277) afford well-marked constant
temperatures which can be utilized as fixed points for experimental
purposes.
9. _Formation of Mixed Crystals._--An important exception to the general
type already described, in which the addition of a dissolved substance
lowers the F.P. of the solvent, is presented by the formation of mixed
crystals, or "solid solutions," in which the solvent and solute occur
mixed in varying proportions. This isomorphous replacement of one
substance by another, in the same crystal with little or no change of
form, has long been known and studied in the case of minerals and salts,
but the relations between composition and melting-point have seldom been
investigated, and much still remains obscure. In this case the process
of freezing does not necessitate the performance of work of separation
of the constituents of the solution, the F.P. is not necessarily
depressed, and the effect cannot be calculated by the usual formula for
dilute solutions. One of the simplest types of F.P. curve which may
result from the occurrence of mixed crystals is illustrated by the case
of alloys of gold and silver, or gold and platinum, in which the F.P.
curve is nearly a straight line joining the freezing-points of the
constituents. The equilibrium between the solid and liquid, in both of
which the two metals are capable of mixing in all proportions, bears in
this case an obvious and close analogy to the equilibrium between a
mixed liquid (e.g. alcohol and water) and its vapour. In the latter
case, as is well known, the vapour will contain a larger proportion of
the more volatile constituent. Similarly in the case of the formation of
mixed crystals, the liquid should contain a larger proportion of the
more fusible constituent than the solid with which it is in equilibrium.
The composition of the crystals which are being deposited at any moment
will, therefore, necessarily change as solidification proceeds,
following the change in the composition of the liquid, and the
temperature will fall until the last portions of the liquid to solidify
will consist chiefly of the more fusible constituent, at the F.P. of
which the solidification will be complete. If, however, as seems to be
frequently the case, the composition of the solid and liquid phases do
not greatly differ from each other, the greater part of the
solidification will occur within a comparatively small range of
temperature, and the initial F.P. of the alloy will be well marked. It
is possible in this case to draw a second curve representing the
composition of the _solid_ phase which is in equilibrium with the liquid
at any temperature. This curve will not represent the average
composition of the crystals, but that of the outer coating only which is
in equilibrium with the liquid at the moment. H.W.B. Roozeboom (_Zeit.
Phys. Chem._ xxx. p. 385) has attempted to classify some of the possible
cases which may occur in the formation of mixed crystals on the basis of
J.W. Gibbs's thermodynamic potential, the general properties of which
may be qualitatively deduced from a consideration of observed phenomena.
But although this method may enable us to classify different types, and
even to predict results in a qualitative manner, it does not admit of
numerical calculation similar to equation (8), as the Gibbs's function
itself is of a purely abstract nature and its form is unknown. There is
no doubt that the formation of mixed crystals may explain many apparent
anomalies in the study of F.P. curves. The whole subject has been most
fruitful of results in recent years, and appears full of promise for the
future.
For further details in this particular branch the reader may consult a
report by Neville (_Brit. Assoc. Rep._, 1900), which contains numerous
references to original papers by Roberts-Austen, Le Chatelier,
Roozeboom and others. For the properties of solutions see SOLUTION.
(H. L. C.)
FUSSEN, a town of Germany, in the kingdom of Bavaria, at the foot of the
Alps (Tirol), on the Lech, 2500 ft. above the sea, with a branch line to
Oberdorf on the railway to Augsburg. Pop. 4000. It has six Roman
Catholic churches, a Franciscan monastery and a castle. Rope-making is
an important industry. The castle, lying on a rocky eminence, is
remarkable for the peace signed here on the 22nd of April 1745 between
the elector Maximilian III., Joseph of Bavaria and Maria Theresa. Two
miles to the S.E., immediately on the Austrian frontier, romantically
situated on a rock overlooking the Schwanensee, is the magnificent
castle of Hohenschwangau, and a little to the north, on the site of an
old castle, that of Neuschwanstein, built by Louis II. of Bavaria.
See H. Feistle, _Fussen und Umgebung_ (1898).
FUST, JOHANN ( ?-1466), early German printer, belonged to a rich and
respectable burgher family of Mainz, which is known to have flourished
from 1423, and to have held many civil and religious offices. The name
was always written Fust, but in 1506 Johann Schoffer, in dedicating the
German translation of Livy to the emperor Maximilian, called his
grandfather Faust, and thenceforward the family assumed this name, and
the Fausts of Aschaffenburg, an old and quite distinct family, placed
Johann Fust in their pedigree. Johann's brother Jacob, a goldsmith, was
one of the burgomasters in 1462, when Mainz was stormed and sacked by
the troops of Count Adolf of Nassau, on which occasion he seems to have
perished (see a document, dated May 8, 1463, published by Wyss in
_Quartalbl. des hist. Vereins fur Hessen_, 1879, p. 24). There is no
evidence that, as is commonly asserted, Johann Fust was a goldsmith, but
he appears to have been a money-lender or banker. On account of his
connexion with Gutenberg (q.v.), he has been represented by some as the
inventor of printing, and the instructor as well as the partner of
Gutenberg, by others as his patron and benefactor, who saw the value of
his discovery and supplied him with means to carry it out, whereas
others paint him as a greedy and crafty speculator, who took advantage
of Gutenberg's necessity and robbed him of the fruits of his invention.
However this may be, the Helmasperger document of November 6, 1455,
shows that Fust advanced money to Gutenberg (apparently 800 guilders in
1450, and another 800 in 1452) for carrying on his work, and that Fust,
in 1455, brought a suit against Gutenberg to recover the money he had
lent, claiming 2020 (more correctly 2026) guilders for principal and
interest. It appears that he had not paid in the 300 guilders a year
which he had undertaken to furnish for expenses, wages, &c., and,
according to Gutenberg, had said that he had no intention of claiming
interest. The suit was apparently decided in Fust's favour, November 6,
1455, in the refectory of the Barefooted Friars of Mainz, when Fust made
oath that he himself had borrowed 1550 guilders and given them to
Gutenberg. There is no evidence that Fust, as is usually supposed,
removed the portion of the printing materials covered by his mortgage to
his own house, and carried on printing there with the aid of Peter
Schoffer, of Gernsheim (who is known to have been a scriptor at Paris in
1449), to whom, probably about 1455,[1] he gave his only daughter Dyna
or Christina in marriage. Their first publication was the Psalter,
August 14, 1457, a folio of 350 pages, the first printed book with a
complete date, and remarkable for the beauty of the large initials
printed each in two colours, red and blue, from types made in two
pieces.[2] The Psalter was reprinted with the same types, 1459 (August
29), 1490, 1502 (Schoffer's last publication) and 1516. Fust and
Schoffer's other works are given below.[3] In 1464 Adolf of Nassau
appointed for the parish of St Quintin three _Baumeisters_
(master-builders) who were to choose twelve chief parishioners as
assistants for life. One of the first of these "Vervaren," who were
named on May-day 1464, was Johannes Fust, and in 1467 Adam von Hochheim
was chosen instead of "the late" (_selig_) Johannes Fust. Fust is said
to have gone to Paris in 1466 and to have died of the plague, which
raged there in August and September. He certainly was in Paris on the
4th of July, when he gave Louis de Lavernade of the province of Forez,
then chancellor of the duke of Bourbon and first president of the
parliament of Toulouse, a copy of his second edition of Cicero, as
appears from a note in Lavernade's own hand at the end of the book,
which is now in the library of Geneva. But nothing further is known than
that on the 30th of October, probably in 1471, an annual mass was
instituted for him by Peter Schoffer, Conrad Henlif (for Henekes, or
Henckis, Schoffer's partner? who married Fust's widow about 1468[4]) and
Johann Fust (the son), in the abbey-church of St Victor of Paris, where
he was buried; and that Peter Schoffer founded a similar memorial
service for Fust in 1473 in the church of the Dominicans at Mainz
(Bockenheimer, _Gesch. der Stadt Mainz_, iv. 15).
Fust was formerly often confused with the famous magician Dr Johann
Faust, who, though an historical figure, had nothing to do with him (see
FAUST).