We will now apply these conclusions to the theory of the ignition of an
explosive gas-mixture, and in particular to the combustion of "knallgas"
(a mixture of hydrogen and oxygen) to water-vapour. At ordinary
temperatures knallgas undergoes practically no change, and it might be
supposed that the two gases, oxygen and hydrogen, have no affinity for
each other. This conclusion, however, is shown to be incorrect by the
observation that it is only necessary to add some suitable catalyst such
as platinum-black in order to immediately start the reaction. We must
therefore conclude that even at ordinary temperatures strong chemical
affinity is exerted between oxygen and hydrogen, but that at low
temperatures this encounters great frictional resistances, or in other
words that the reaction-velocity is very small. It is a matter of
general experience that the resistances which the chemical forces have
to overcome diminish with rising temperature, i.e. the reaction-velocity
increases with temperature. Therefore, when we warm the knallgas, the
number of collisions of oxygen and hydrogen molecules favourable to the
formation of water becomes greater and greater, until at about 500 deg.
the gradual formation of water is observed, while at still higher
temperatures the reaction-velocity becomes enormous. We are now in a
position to understand what is the result of a strong local heating of
the knallgas, as, for example, by an electric spark. The strongly heated
parts of the knallgas combine to form water-vapour with great velocity
and the evolution of large amounts of heat, whereby the adjacent parts
are brought to a high temperature and into a state of rapid reaction,
i.e. we observe an ignition of the whole mixture. If we suppose the
knallgas to be at a very high temperature, then its combustion will be
no longer complete owing to the dissociation of water-vapour, whilst at
extremely high temperatures it would practically disappear. Hence it is
clear that knallgas appears to be stable at low temperatures only
because the reaction-velocity is very small, but that at very high
temperatures it is really stable, since no chemical forces are then
active, or, in other words, the chemical affinity is very small.
The determination of the question whether the failure of some reaction
is due to an inappreciable reaction-velocity or to absence of chemical
affinity, is of fundamental importance, and only in the first case can
the reaction be hastened by catalysts.
Many chemical compounds behave like knallgas. Acetylene is stable at
ordinary temperatures, inasmuch as it only decomposes slowly; but at the
same time it is explosive, for the decomposition when once started is
rapidly propagated, on account of the heat evolved by the splitting up
of the gas into carbon and hydrogen. At very high temperatures, however,
acetylene acquires real stability, since carbon and hydrogen then react
to form acetylene.
Explosion-waves.
Many researches have shown that the combustion of an inflammable
gas-mixture which is started at a point, e.g. by an electric spark, may
be propagated in two essentially different ways. The characteristic of
the slower combustion consists in this, viz. that the high temperature
of the previously ignited layer spreads by conduction, thereby bringing
the adjacent layers to the ignition-temperature; the velocity of the
propagation is therefore conditioned in the first place by the magnitude
of the conductivity for heat, and more particularly, in the second
place, by the velocity with which a moderately heated layer begins to
react chemically, and so to rise gradually in temperature, i.e.
essentially by the change of reaction-velocity with temperature. A
second entirely independent mode of propagation of the combustion lies
at the basis of the phenomenon that an explosive gas-mixture can be
ignited by strong compression or--more correctly--by the rise of
temperature thereby produced. The increase of the concentrations of the
reacting substances consequent upon this increase of pressure raises the
reaction-velocity in accordance with the law of chemical mass-action,
and so enormously favours the rapid evolution of the heat of combustion.
It is therefore clear that such a powerful compression-wave can not only
initiate the combustion, but also propagate it with extremely high
velocity. Indeed a compression-wave of this kind passes through the
gas-mixture, heated by the combustion to a very high temperature. It
must, however, be propagated considerably faster than an ordinary
compression-wave, for the result of ignition in the compressed (still
unburnt) layer is the production of a very high pressure, which must in
accordance with the principles of wave-motion increase the velocity of
propagation. The absolute velocity of the explosion-wave would seem, in
the light of these considerations, to be susceptible of accurate
calculation. It is at least clear that it must be considerably higher
than the velocity of sound in the mass of gas strongly heated by the
explosion, and this is confirmed by actual measurements (see below)
which show that the velocity of the explosion-wave is from one and a
half times to double that of sound-waves at the combustion temperature.
We are now in a position to form the following picture of the processes
which follow upon the ignition of a combustible gas-mixture contained in
a long tube. First we have the condition of slow combustion; the heat is
conveyed by conduction to the adjacent layers, and there follows a
velocity of propagation of a few metres per second. But since the
combustion is accompanied by a high increase of pressure, the adjacent,
still unburnt layers are simultaneously compressed, whereby the
reaction-velocity increases, and the ignition proceeds faster. This
involves still greater compression of the next layers, and so if the
mixture be capable of sufficiently rapid combustion, the velocity of
propagation of the ignition must continually increase. As soon as the
compression in the still unburnt layers becomes so great that
spontaneous ignition results, the now much more pronounced
compression-waves excited with simultaneous combustion must be
propagated with very great velocity, i.e. we have spontaneous
development of an "explosion-wave." M.P.E. Berthelot, who discovered the
presence of such explosion-waves, proved their velocity of propagation
to be independent of the pressure, the cross-section of the tubes in
which the explosive gas-mixture is contained, as well as of the material
of which these are made, and concluded that this velocity is a constant,
characteristic of the particular mixture. The determination of this
velocity is naturally of the highest interest.
In the following table Berthelot's results are given along with the
later (1891) concordant ones of H.B. Dixon, the velocities of
propagation of explosions being given in metres per second.
+-------------------------------------+---------------------+
| | Velocity of Wave in |
| Reacting Mixture. | Metres per second. |
| +-----------+---------+
| | Berthelot.| Dixon. |
+-------------------------------------+-----------+---------+
|Hydrogen and oxygen, H2+O | 2810 | 2821 |
|Hydrogen and nitrous oxide, H2+N2O | 2284 | 2305 |
|Methane and oxygen, CH4+4O | 2287 | 2322 |
|Ethylene " " C2H4+6O | 2210 | 2364 |
|Acetylene " " C2H2+5O | 2482 | 2391 |
|Cyanogen " " C2N2+4O | 2195 | 2321 |
|Hydrogen and chlorine, H2+Cl2 | .. | 1730 |
| " " " 2H2+Cl2 | .. | 1849 |
+-------------------------------------+-----------+---------+
The maximum pressure of the explosion-wave possesses very high values;
it appears that a compression of from 1 to 30-40 atmospheres is
necessary to produce spontaneous ignition of mixtures of oxygen and
hydrogen. But since the heat evolved in the path of the explosion causes
a rise of temperature of 2000 deg.-3000 deg., i.e. a rise of absolute
temperature about four times that directly following upon the initial
compression, we are here concerned with pressures amounting to
considerably more than 100 atmospheres. Both the magnitude of this
pressure and the circumstance that it so suddenly arises are peculiar to
the very powerful forces which distinguish the explosion-wave from the
slow combustion-wave.
_Nascent State._--The great reactive power of freshly formed or nascent
substances (_status nascens_)may be very simply referred to the
principles of mass-action. As is well known, this phenomenon is
specially striking in the case of hydrogen, which may therefore be taken
as a typical example. The law of mass-action affirms the action of a
substance to be the greater the higher its concentration, or, for a gas,
the higher its partial-pressure. Now experience teaches that those
metals which liberate hydrogen from acids are able to supply the latter
under extremely high pressure, and we may therefore assume that the
hydrogen which results, for example, from the action of zinc upon
sulphuric acid is initially under very high pressures which are then
afterwards relieved. Hence the hydrogen during liberation exhibits much
more active powers of reduction than the ordinary gas.
A deeper insight into the relations prevailing here is offered from the
atomistic point of view. From this we are bound to conclude that the
hydrogen is in the first instance evolved in the form of free atoms, and
since the velocity of the reaction H + H = H2 at ordinary temperatures,
though doubtless very great, is not practically instantaneous, the
freshly generated hydrogen will contain a remnant of free atoms, which
are able to react both more actively and more rapidly. Similar
considerations are of course applicable to other cases.
_Ion-reactions._--The application of the law of chemical mass action is
much simplified in the case in which the reaction-velocity is enormously
great, when practically an instantaneous adjustment of the equilibrium
results. Only in this case can the state of the system, which pertains
after mixing the different components, be determined merely from
knowledge of the equilibrium-constant. This case is realized in the
reactions between gases at very high temperatures, which have, however,
been little investigated, and especially by the reactions between
electrolytes, the so-called ion-reactions. In this latter case, which
has been thoroughly studied on account of its fundamental importance for
inorganic qualitative and quantitative analysis, the degrees of
dissociation of the various electrolytes (acids, bases and salts) are
for the most part easily determined by the aid of the freezing-point
apparatus, or of measurements of the electric conductivity; and from
these data the equilibrium-constant K may be calculated. Moreover, it
can be shown that the state of the system can be determined when the
equilibrium constants of all the electrolytes which are present in the
common solution are known. If this be coupled with the law that the
solubility of solid substances, as with vapour-pressures, is independent
of the presence of other electrolytes, it is sufficient to know the
solubilities of the electrolytes in question, in order to be able to
determine which substances must participate in the equilibrium in the
solid state, i.e. we arrive at the theory of the formation and solution
of precipitates.
Strength of acids and bases.
As an illustration of the application of these principles, we shall deal
with a problem of the doctrine of affinity, namely, that of the relative
strengths of acids and bases. It was quite an early and often repeated
observation that the various acids and bases take part with very varying
intensity or avidity in those reactions in which their acid or basic
nature comes into play. No success attended the early attempts at giving
numerical expression to the strengths of acids and bases, i.e. of
finding a numerical coefficient for each acid and base, which should be
the quantitative expression of the degree of its participation in those
specific reactions characteristic of acids and bases respectively.
Julius Thomsen and W. Ostwald attacked the problem in a far-seeing and
comprehensive manner, and arrived at indisputable proof that the
property of acids and bases of exerting their effects according to
definite numerical coefficients finds expression not only in
salt-formation but also in a large number of other, and indeed very
miscellaneous, reactions.
When Ostwald compared the order of the strengths of acids deduced from
their competition for the same base, as determined by Thomsen's
thermo-chemical or his own volumetric method, with that order in which
the acids arrange themselves according to their capacity to bring
calcium oxalate into solution, or to convert acetamide into ammonium
acetate, or to split up methyl acetate into methyl alcohol and acetic
acid catalytically, or to invert cane-sugar, or to accelerate the mutual
action of hydriodic on bromic acid, he found that in all these
well-investigated and very miscellaneous cases the same succession of
acids in the order of their strengths is obtained, whichever one of the
above chemical processes be chosen as measure of these strengths. It is
to be noticed that all these chemical changes cited took place in dilute
aqueous solution, consequently the above order of acids refers only to
the power to react under these circumstances. The order of acids proved
to be fairly independent of temperature. While therefore the above
investigations afforded a definite qualitative solution of the order of
acids according to strengths, the determination of the quantitative
relations offered great difficulties, and the numerical coefficients,
determined from the separate reactions, often displayed great
variations, though occasionally also surprising agreement. Especially
great were the variations of the coefficients with the concentration,
and in those cases in which the concentration of the acid changed
considerably during the reaction, the calculation was naturally quite
uncertain. Similar relations were found in the investigation of bases,
the scope of which, however, was much more limited.
These apparently rather complicated relations were now cleared up at
one stroke, by the application of the law of chemical mass-action on the
lines indicated by S. Arrhenius in 1887, when he put forward the theory
of electrolytic dissociation to explain that peculiar behaviour of
substances in aqueous solution first recognized by van't Hoff in 1885.
The formulae which must be made use of here in the calculation of the
equilibrium-relations follow naturally by simple application of the law
of mass-action to the corresponding ion-concentrations.
The peculiarities which the behaviour of acids and bases presents, and,
according to the theory of Arrhenius, must present--peculiarities which
found expression in the very early distinction between neutral solutions
on the one hand, and acid or basic ones on the other, as well as in the
belief in a polar antithesis between the two last--must now, in the
light of the theory of electrolytic dissociation, be conceived as
follows:--
The reactions characteristic of acids in aqueous solution, which are
common to and can only be brought about by acids, find their explanation
in the fact that this class of bodies gives rise on dissociation to a
common molecular species, namely, the positively charged hydrogen-ion
(+H). The specific chemical actions peculiar to acids are therefore to
be attributed to the hydrogen-ion just as the actions common to all
chlorides are to be regarded as those of the free chlorine-ions. In like
manner, the reactions characteristic of bases in solution are to be
attributed to the negatively charged hydroxyl-ions (-OH), which result
from the dissociation of this class of bodies.
A solution has an acid reaction when it contains an excess of
hydrogen-ions, and a basic reaction when it contains an excess of
hydroxyl-ions. If an acid and an alkaline solution be brought together
mutual neutralization must result, since the positive H-ions and the
negative OH-ions cannot exist together in view of the extremely weak
conductivity of pure water and its consequent slight electrolytic
dissociation, and therefore they must at once combine to form
electrically neutral molecules, in the sense of the equation
[+H] + [-OH] = H2O.
In this lies the simple explanation of the "polar" difference between
acid and basic solutions. This rests essentially upon the fact that the
ion peculiar to acids and the ion peculiar to bases form the two
constituents of water, i.e. of that solvent in which we usually study
the course of the reaction. The idea of the "strength" of an acid or
base at once arises. If we compare equivalent solutions of various
acids, the intensity of those actions characteristic of them will be the
greater the more free hydrogen-ions they contain; this is an immediate
consequence of the law of chemical mass-action. The degree of
electrolytic dissociation determines, therefore, the strength of acids,
and a similar consideration leads to the same result for bases.
Now the degree of electrolytic dissociation changes with concentration
in a regular manner, which is given by the law of mass-action. For if C
denote the concentration of the electrolyte and a its degree of
dissociation, the above law states that
C^2a^2/C(1-a) = Ca^2/(1-a) = K.
At very great dilutions the dissociation is complete, and equivalent
solutions of the most various acids then contain the same number of
hydrogen-ions, or, in other words, are equally strong; and the same is
true of the hydroxyl-ions of bases. The dissociation also decreases with
increasing concentration, but at different rates for different
substances, and the relative "strengths" of acids and bases must hence
change with concentration, as was indeed found experimentally. The
dissociation-constant K is the measure of the variation of the degree of
dissociation with concentration, and must therefore be regarded as the
measure of the strengths of acids and bases. So that in this special
case we are again brought to the result which was stated in general
terms above, viz. that the dissociation-coefficient forms the measure of
the reactivity of a dissolved electrolyte. Ostwald's series of acids,
based upon the investigation of the most various reactions, should
therefore correspond with the order of their dissociation-constants, and
further with the order of their freezing-point depressions in
equivalent solutions, since the depression of the freezing-point
increases with the degree of electrolytic dissociation. Experience
confirms this conclusion completely. The degree of dissociation of an
acid, at a given concentration, for which its molecular conductivity is
A, is shown by the theory of electrolytic dissociation to be a =
A/A[oo]; A[oo], the molecular conductivity at very great dilution in
accordance with the law of Kohlrausch, is u + v, where u and v are the
ionic-mobilities (see CONDUCTION, ELECTRIC). Since u, the ionic-mobility
of the hydrogen ion, is generally more than ten times as great as v, the
ionic-mobility of the negative acid-radical, A[oo] has approximately
the same value (generally within less than 10%) for the different acids,
and the molecular-conductivity of the acids in equivalent concentration
is at least approximately proportional to the degree of electrolytic
dissociation, i.e. to the strength.
In general, therefore, the order of conductivities is identical with
that in which the acids exert their specific powers. This remarkable
parallelism, first perceived by Arrhenius and Ostwald in 1885, was the
happy development which led to the discovery of electrolytic
dissociation (see CONDUCTION, ELECTRIC; and SOLUTION).
_Catalysis._--We have already mentioned the fact, early known to
chemists, that many reactions proceed with a marked increase of velocity
in presence of many foreign substances. With Berzelius we call this
phenomenon "catalysis," by which we understand that general acceleration
of reactions which also progress when left to themselves, in the
presence of certain bodies which do not change in amount (or only
slightly) during the course of the reaction. Acids and bases appear to
act catalytically upon all reactions involving consumption or liberation
of water, and indeed that action is proportional to the concentration of
the hydrogen or hydroxyl-ions. Further, the decomposition of hydrogen
peroxide is "catalysed" by iodine-ions, the condensation of two
molecules of benzaldehyde to benzoin by cyanogen-ions. One of the
earliest known and technically most important instances of catalysis is
that of the oxidation of sulphur dioxide to sulphuric acid by oxygen in
the presence of oxides of nitrogen. Other well-known and remarkable
examples are the catalysis of the combustion of hydrogen and of sulphur
dioxide in oxygen by finely-divided platinum. We may also mention the
interesting work of Dixon and Baker, which led to the discovery that a
large number of gas-reactions, e.g. the combustion of carbon monoxide,
the dissociation of sal-ammoniac vapour, and the action of sulphuretted
hydrogen upon the salts of heavy metals, cease when water-vapour is
absent, or at least proceed with greatly diminished velocity.
"Negative catalysis," i.e. the retardation of a reaction by addition of
some substance, which is occasionally observed, appears to depend upon
the destruction of a "positive catalyte" by the body added.
A catalyte can have no influence, however, upon the affinity of a
process, since that would be contrary to the second law of
thermodynamics, according to which affinity of an isothermal process,
which is measured by the maximum work, only depends upon the initial and
final states. The effect of a catalyte is therefore limited to the
resistances opposing the progress of a reaction, and does not influence
its driving-force or affinity. Since the catalyte takes no part in the
reaction its presence has no effect on the equilibrium-constant. This,
in accordance with the law of mass-action, is the ratio of the separate
reaction-velocities in the two contrary directions. A catalyte must
therefore always accelerate the reverse-reaction. If the velocity of
formation of a body be increased by addition of some substance then its
velocity of decomposition must likewise increase. We have an example of
this in the well-known fact that the formation, and no less the
saponification, of esters, proceeds with increased velocity in the
presence of acids, while the observation that in absence of water-vapour
neither gaseous ammonium chloride dissociates nor dry ammonia combines
with hydrogen chloride becomes clear on the same grounds.
A general theory of catalytic phenomena does not at present exist. The
formation of intermediate products by the action of the reacting
substance upon the catalyte has often been thought to be the cause of
these. These intervening products, whose existence in many cases has
been proved, then split up into the catalyte and the reaction-product.
Thus chemists have sought to ascribe the influence of oxides of nitrogen
on the formation of sulphuric acid to the initial formation of
nitrosyl-sulphuric acid, SO2(OH)(NO2), from the mixture of sulphur
dioxide, oxides of nitrogen and air, which then reacted with water to
form sulphuric and nitrous acids. When the velocity of such intermediate
reactions is greater than that of the total change, such an explanation
may suffice, but a more certain proof of this theory of catalysis has
only been reached in a few cases, though in many others it appears very
plausible. Hence it is hardly possible to interpret all catalytic
processes on these lines.
In regard to catalysis in heterogeneous systems, especially the
hastening of gas-reactions by platinum, it is very probable that it is
closely connected with the solution or absorption of the gases on the
part of the metal. From the experiments of G. Bredig it seems that
colloidal solutions of a metal act like the metal itself. The action of
a colloidal-platinum solution on the decomposition of hydrogen peroxide
is still sensible even at a dilution of 1/70,000,000 grm.-mol. per
litre; indeed the activity of this colloidal-platinum solution calls to
mind in many ways that of organic ferments, hence Bredig has called it
an "inorganic ferment." This analogy is especially striking in the
change of their activity with time and temperature, and in the
possibility, by means of bodies like sulphuretted hydrogen, hydrocyanic
acid, &c., which act as strong poisons upon the latter, of "poisoning"
the former also, i.e. of rendering it inactive. In the case of the
catalytic action of water-vapour upon many processes of combustion
already mentioned, a part of the effect is probably due to the
circumstance, disclosed by numerous experiments, that the union of
hydrogen and oxygen proceeds, between certain temperature limits at
least, after the equation H2 + O2 = H2O2, that is, with the preliminary
formation of hydrogen peroxide, which then breaks down into water and
oxygen, and further, above all, to the fact that this substance results
from oxygen and water at high temperatures with great velocity, though
indeed only in small quantities.
The view now suggests itself, that, for example, in the combustion of
carbon monoxide at moderately high temperatures, the reaction
(I.) 2CO + O2 = 2CO2
advances with imperceptible speed, but that on the contrary the two
stages
(II.) 2H2O + O2 = 2H2O2,
(III.) 2CO + 2H2O2 = 2CO2 + 2H2O,
which together result in (I.), proceed rapidly even at moderate
temperatures.
_Temperature and Reaction-Velocity._--There are few natural constants
which undergo so marked a change with temperature as those of the
velocities of chemical changes. As a rule a rise of temperature of 10
deg. causes a twofold or threefold rise of reaction-velocity.
If the reaction-coefficient k, in the sense of the equation derived
above, viz. k = t^{-1} log [a/(a-x)], be determined for the inversion of
cane-sugar by an acid of given concentration, the following values are
obtained:--
Temperature = 25 deg. 40 deg. 45 deg. 50 deg. 55 deg.
k = 9.7 73 139 268 491;
here a rise of temperature of only 30 deg. suffices to raise the speed of
inversion fifty times.
We possess no adequate explanation of this remarkable temperature
influence; but some account of it is given by the molecular theory,
according to which the energy of that motion of substances in
homogeneous gaseous or liquid systems which constitutes heat increases
with the temperature, and hence also the frequency of collision of the
reacting substances. When we reflect that the velocity of motion of the
molecules of gases, and in all probability those of liquids also, are
proportional to the square root of the absolute temperature, and
therefore rise by only 1/6% per degree at room-temperature, and that we
must assume the number of collisions proportional to the velocity of the
molecules, we cannot regard the actually observed increase of
reaction-velocity, which often amounts to 10 or 12% per degree, as
exclusively due to the quickening of the molecular motion by heat. It is
more probable that the increase of the kinetic energy of the atomic
motions within the molecule itself is of significance here, as the rise
of the specific heat of gases with temperature seems to show. The change
of the reaction-coefficient k with temperature may be represented by the
empirical equation log k = -AT^{-1} + B + CT, where A, B, C are positive
constants. For low temperatures the influence of the last term is as a
rule negligible, whilst for high temperatures the first term on the
right side plays a vanishingly small part.
_Definition of Chemical Affinity._--We have still to discuss the
question of what is to be regarded as the measure of chemical affinity.
Since we are not in a position to measure directly the intensity of
chemical forces, the idea suggests itself to determine the strength of
chemical affinity from the amount of the work which the corresponding
reaction is able to do. To a certain extent the evolution of heat
accompanying the reaction is a measure of this work, and attempts have
been made to measure chemical affinities thermo-chemically, though it
may be easily shown that this definition was not well chosen. For when,
as is clearly most convenient, affinity is so defined that it determines
under all circumstances the direction of chemical change, the above
definition fails in so far as chemical processes often take place with
absorption of heat, that is, contrary to affinities so defined. But even
in those cases in which the course of the reaction at first proceeds in
the sense of the evolution of heat, it is often observed that the
reaction advances not to completion but to a certain equilibrium, or, in
other words, stops before the evolution of heat is complete.
A definition free from this objection is supplied by the second law of
thermodynamics, in accordance with which all processes must take place
in so far as they are able to do external work. When therefore we
identify chemical affinity with the maximum work which can be gained
from the process in question, we reach such a definition that the
direction of the process is under all conditions determined by the
affinity. Further, this definition has proved serviceable in so far as
the maximum work in many cases may be experimentally measured, and
moreover it stands in a simple relation to the equilibrium constant K.
Thermodynamics teaches that the maximum work A may be expressed as A =
RT log K, when R denotes the gas-constant, T the absolute temperature.
In this it is further assumed that both the molecular species produced
as well as those that disappear are present in unit concentration. The
simplest experimental method of directly determining chemical affinity
consists in the measurement of electromotive force. The latter at once
gives us the work which can be gained when the corresponding galvanic
element supplies the electricity, and, since the chemical exchange of
one gram-equivalent from Faraday's law requires 96,540 coulombs, we
obtain from the product of this number and the electromotive force the
work per gram-equivalent in watt-seconds, and this quantity when
multiplied by O.23872 is obtained in terms of the usual unit, the
gram-calorie. Experience teaches that, especially when we have to deal
with strong affinities, the affinity so determined is for the most part
almost the same as the heat-evolution, whilst in the case in which only
solid or liquid substances in the pure state take part in the reaction
at low temperatures, heat-evolution and affinity appear to possess a
practically identical value.
Hence it seems possible to calculate equilibria for low temperatures
from heats of reaction, by the aid of the two equations
A = Q, A = RT log K;
and since the change of A with temperature, as required by the
principles of thermodynamics, follows from the specific heats of the
reacting substances, it seems further possible to calculate chemical
equilibria from heats of reaction and specific heats. The circumstance
that chemical affinity and heat-evolution so nearly coincide at low
temperatures may be derived from the hypothesis that chemical processes
are the result of forces of attraction between the atoms of the
different elements. If we may disregard the kinetic energy of the atoms,
and this is legitimate for low temperatures, it follows that both
heat-evolution and chemical affinity are merely equal to the decrease of
the potential energy of the above-mentioned forces, and it is at once
clear that the evolution of heat during a reaction between only pure
solid or pure liquid substances possesses special importance.
More complicated is the case in which gases or dissolved substances take
part. This is simplified if we first consider the mixing of two mutually
chemically indifferent gases. Thermodynamics teaches that external work
may be gained by the mere mixing of two such gases (see DIFFUSION), and
these amounts of work, which assume very considerable proportions at
high temperatures, naturally affect the value of the maximum work and so
also of the affinity, in that they always come into play when gases or
solutions react. While therefore we regard as chemical affinity in the
strictest sense the decrease of potential energy of the forces acting
between the atoms, it is clear that the quantities here involved exhibit
the simplest relations under the experimental conditions just given, for
when only substances in a pure state take part in a reaction, all mixing
of different kinds of molecules is excluded; moreover, the circumstance
that the respective substances are considered at very low temperatures
reduces the quantities of energy absorbed as kinetic energy by their
molecules to the smallest possible amount.
_Chemical Resistance._--When we know the chemical affinity of a
reaction, we are in a position to decide in which direction the process
must advance, but, unless we know the reaction-velocity also, we can in
many cases say nothing as to whether or not the reaction in question
will progress with a practically inappreciable velocity so that apparent
chemical indifference is the result. This question may be stated in the
light of the law of mass-action briefly as follows:--From a knowledge of
the chemical affinity we can calculate the equilibrium, i.e. the
numerical value of the constant K = k/k'; but to be completely informed
of the process we must know not only the ratio of the two
velocity-constants k and k', but also the separate absolute values of
the same.
In many respects the following view is more comprehensive, though
naturally in harmony with the one just expressed. Since the chemical
equilibrium is periodically attained, it follows that, as in the case of
the motion of a body or of the diffusion of a dissolved substance, it
must be opposed by very great friction. In all these cases the velocity
of the process at every instant is directly proportional to the
driving-force and inversely proportional to the frictional resistance.
We hence arrive at the result that an equation of the form
_reaction-velocity = chemical force/chemical resistance_
must also hold for chemical change; here we have an analogy with Ohm's
law. The "chemical force" at every instant may be calculated from the
maximum work (affinity); as yet little is known about "chemical
resistance," but it is not improbable that it may be directly measured
or theoretically deduced. The problem of the calculation of chemical
reaction-velocity in absolute measure would then be solved; so far we
possess indeed only a few general facts concerning the magnitude of
chemical resistance. It is immeasurably small at ordinary temperatures
for ion-reactions, and, on the other hand, fairly large for nearly all
reactions in which carbon-bonds must be loosened (so-called "inertia of
the carbon-bond") and possesses very high values for most gas-reactions
also. With rising temperature it always strongly diminishes; on the
other hand, at very low temperatures its values are always enormous, and
at the absolute zero of temperature may be infinitely great. Therefore
at that temperature all reactions cease, since the denominator in the
above expression assumes enormous values.
It is a very remarkable phenomenon that the chemical resistance is often
small in the case of precisely those reactions in which the affinity is
also small; to this circumstance is to be traced the fact that in many
chemical changes the most stable condition is not at once reached, but
is preceded by the formation of more or less unstable intermediate
products. Thus the unstable ozone is very often first formed on the
evolution of oxygen, whilst in the reaction between oxygen and hydrogen
water is often not at once formed, but first the unstable hydrogen
peroxide as an intermediate product.