only 1% 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 0.23872 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