This appears to have been an unfortunate concession to the views of
others on the part of Berzelius, for the barred symbols were not
generally adopted, partly on account of difficulties in printing, and
the great achievement in theory made by him was lost sight of for a long
period of time.
_The Law of Atomic Heats._—In 1819, Dulong and Petit of France, from
experiments upon the specific heats of a number of solid elementary
substances, came to the conclusion that the atoms of simple substances
have equal capacities for heat, or in other words, that the specific
heats of elements multiplied by their atomic weights give a constant
called the atomic heat. For instance, the specific heats of sulphur,
iron, and gold have been given as 0·2026, 0·110, and 0·0324, while their
atomic weights are about 32, 56, and 197, respectively; hence the atomic
heats obtained by multiplication are 6·483, 6·116, and 6·383.
Further investigations showed that the atomic heats display a
considerable variation. Those of carbon, boron, beryllium, and silicon
are very low at ordinary temperatures, although they increase and
approach the usual values at higher temperatures. More recent work has
shown, however, that the specific heats of other elements vary greatly
with the temperature, almost disappearing at the temperature of liquid
hydrogen, and hence possibly disappearing entirely at the absolute zero,
where the electrical resistance of the metals appears to vanish
likewise.
It has been found that most of the solid elements near ordinary
temperatures give atomic heats that are approximately 6·4. Berzelius
applied the law in fixing a number of atomic weights, and its importance
for this purpose is still recognized.
It may be mentioned here that two well-known Yale men, W. O. Mixter and
E. S. Dana, while students in Bunsen’s laboratory at Heidelberg in 1873,
made determinations of the specific heats of boron, silicon, and
zirconium. This was the first determination of this constant for
zirconium, and it was consequently important in establishing the atomic
weight of that element.
_Isomorphism and Polymorphism._—Mitscherlich observed in 1818 that
certain phosphates and arsenates have the same crystalline form, and
afterwards he reached the conclusion that identity in form indicates
similarity in composition in connection with the number of atoms and
their arrangement. This law of isomorphism was of much assistance in the
establishment of correct formulas and consequently of atomic weights.
For instance, since the carbonates of barium, strontium, and lead
crystallize in the same form, the oxides of these metals must have
analogous formulas. From such considerations Berzelius was able to make
several improvements in his atomic weight table of 1826.
Mitscherlich was the first to observe two forms of sulphur crystals, and
from this and other cases of dimorphism or of polymorphism it became
evident that analogous compounds were not necessarily always
isomorphous, a circumstance which has restricted the application of the
law to some extent.
Besides its application in fixing analogous formulas, the law of
isomorphism has come to be of much practical use in the understanding
and simplification of the formulas for minerals, for these natural
crystals very often contain several isomorphous compounds in varying
proportions, and an understanding of this “isomorphous replacement,” as
it is called, makes it possible to deduce simple general formulas for
them.
In some cases isomorphism takes place to a greater or less extent
between substances which are not chemically similar, and this brings
about a variation in composition which at times has caused confusion.
For instance, the mineral pyrrhotite has a composition which usually
varies between Fe_{7}S_{8} and Fe_{11}S_{12}, and both these formulas
have been assigned to it. It was recently shown by Allen, Crenshaw and
Johnston in the Journal (=33=, 169, 1912) that this is a case where the
compound FeS is capable of taking up various amounts of sulphur
isomorphously.
The idea of solid solution was advanced by van’t Hoff to explain the
crystallization of mixtures, including cases of evident isomorphism.
This view has been widely accepted, and it has been particularly useful
in cases where isomorphism is not evident. Solid solution between metals
has been found to be exceedingly common, many alloys being of this
character. A case of this kind was observed by Cooke and described in
the Journal (=20=, 222, 1855). He prepared two well-crystallized
compounds of zinc and antimony to which he gave the formulas Zn_{3}Sb
and Zn_{2}Sb, but he observed that excellent crystals of each could be
obtained which varied largely in composition from these formulas. As the
two compounds were dissimilar in their formulas and crystalline forms,
Cooke assumed that isomorphism was impossible and concluded “that it is
due to an actual perturbation of the law of definite proportions,
produced by the influence of mass.” We should now regard this as a case
of solid solution.
_A Lack of Confidence in Avogadro’s Principle._—One reason why chemists
were so slow in arriving at the correct atomic weights and formulas was
a partial loss of confidence in Avogadro’s principle. About 1826 the
young French chemist Dumas devised an excellent method for the
determination of vapor densities at high temperatures, and his results
and those of others showed some discrepancies in the expected densities.
For example, the vapor density of sulphur was found to be about three
times too great, that of phosphorus twice too great, that of mercury
vapor and that of ammonium chloride only about half large enough to
correspond to the values expected from analogy and other considerations.
Thus, one volume of oxygen with two volumes of hydrogen make two volumes
of steam, but only one third of a volume of sulphur vapor was found to
unite with two volumes of hydrogen to make two volumes of hydrogen
sulphide. Berzelius saw clearly that the results pointed to the
existence of such molecules as S_{6}, P_{4}, and Hg_{1}, but it was not
generally realized in those days that Avogadro’s rule is fundamentally
reliable, and Berzelius himself appears to have lost confidence in it on
account of these complications, for he did not apply Avogadro’s
principle to decisions about atomic weights, except in the cases of
substances gaseous at ordinary temperatures.
_Electro-chemical Theories._—The observation was made by Nicholson and
Carlisle in 1800 that water was decomposed into its constituent gases by
the electric current. Then in 1803 Berzelius and Hisinger found that
salts were decomposed into their bases and acids by the same agency, and
in 1807 Davy isolated potassium, sodium, and other metals afterwards, by
a similar decomposition. Since those early times a vast amount of
attention has been paid to the relation of electricity to chemical
changes, a relation that is evidently of great importance from the fact
that while electric currents decompose chemical compounds, these
currents, on the other hand, are produced by chemical reactions.
Berzelius was particularly prominent in this direction, and in 1819 he
published an elaborate electro-chemical theory. He believed that atoms
were electrically polarized, and that this was the cause of their
combination with one another. He extended this idea to groups of atoms,
particularly to oxides, and regarded these groups as positive or
negative, according to the excess of positive or negative electricity
derived from their constituent atoms and remaining free. He thus arrived
at his dualistic theory of chemical compounds, which attained great
prominence and prevailed for a long time in chemical theory. According
to this idea, each compound was supposed to be made up of a positive and
a negative atom or group of atoms. For example, the formulas for
potassium nitrate, calcium carbonate, and sulphuric acid corresponded to
K_{2}O.N_{2}O_{5}, CaO.CO_{2} and H_{2}O.SO_{3} where we now write
KNO_{3}, CaCO_{3} and H_{2}SO_{4}, and the theory was extended to
embrace organic compounds also.
The eminent English chemist and physicist Faraday announced the
important law of electro-chemical equivalents in 1834. This law shows
that the quantities of elements set free by the passage of a given
quantity of electricity through their solutions correspond to the
chemical equivalents of those elements. Faraday made a table of the
equivalents of a number of elements, regarding them important in
connection with atomic weights, but at that time no sharp distinction
was usually made between equivalents and atomic weights, and it was not
fully realized that one atom of a given element may be the electrical
equivalent of several atoms of another.
Faraday’s law, which is still regarded as fundamentally exact, has been
of much practical use in the measurement of electric currents and in
calculations connected with electro-chemical processes. In discussing
his experiments, Faraday made use of several new terms, such as
“electrolyte” for a substance which conducts electricity when in
solution, and is thus “electrolyzed,” “electrode,” “anode,” and
“cathode,” terms that have come into general use, and finally “ions” for
the particles that were supposed to “wander” towards the electrodes to
be set free there.
This term “ion” remained in comparative obscurity for more than half a
century, when it was brought into great prominence among chemists by
Arrhenius in connection with the ionic theory.
_Cannizzaro’s Ideas._—Up to about 1869 chaos reigned among the formulas
used by different chemists. Various compound radicals and numerous
type-formulas were employed, dualistic and unitary formulas of several
kinds were in use, but the worst feature of the situation was the fact
that more than one system of atomic weights was in vogue, so that water
might be written