CHEMICAL EQUILIBRIUM Law of Mass Action.—We have referred to the observation of Berthollet that the concentration of the reactants is often sufficient to determine whether a given reaction or its reverse will take place. In this way we may explain why it so often happens that a chemical change fails to become complete, and comes to an apparent halt before the reacting material has been com pletely transformed. Evidently the forward reaction, transform ing reactants A and B into resultants A' and B', is accompanied by a reaction which transforms A' and B' into A and B. Thus each reaction offsets the other, and the chemical change accord ingly remains incomplete. The result is chemical equilibrium, commonly formulated with reversed arrows, thus : The proportions in which the different reactants are present in a mixture of substances which have attained a condition of chemical equilibrium are determined by a principle discovered by C. M. Guldberg and P. Waage in 1867. These investigators showed that the state of equilibrium attained in a reversible re action can be interpreted on the assumption that the equilibrium state is the result of the equality of the speeds of the two opposed reactions, for each of which the velocity v or v' can be expressed in terms of a constant multiplied by the concentrations of the reacting substances, expressed by [A], [B], or [A'], [B']. The velocities of the two opposed reactions are therefore given by v= k [A] • [ B] and v'= k' [A'] • [B'] . At equilibrium these two velocities are equal, hence in which K is the so-called equilibrium constant. If the reaction corresponds with the equilibrium constant may be written The practical importance of a knowledge of equilibrium con stants, calculated as just shown, will be realized when it is re marked that the equilibrium constant for any given reaction at a given temperature is independent of the concentrations in which the reactants are brought together. Thus when the numerical value of the constant has once been determined we may substitute this in the preceding equations, and determine the proportions in which the reactants and resultants will be intermingled when equi librium is reached, starting from any given initial concentrations.
Though the mathematical expressions just given (commonly called mass-action expressions) may be regarded as empirical statements of actual laboratory experience with systems in chem ical equilibrium, nevertheless they may readily be derived from the kinetic theory. (See MOLECULE.) It may be assumed in the simplest case that the interaction of two reactants A and B is the result of collision between the respective molecules. It fol lows that the rate of change should be proportional to the fre quency with which such collisions occur. The frequency with which a given molecule of A collides with molecules of B is pro portional to the number of the latter in unit volume, i.e., the molecular concentration of B ; and in the same way the frequency of the collisions between a given molecule of B and the molecules of A is proportional to the molecular concentration of the latter. The total number of collisions between the molecules of A and B is therefore proportional to the product of the molar concentra tions. Kinetic considerations thus led to v = k [A] [ B] which is the expression for the reaction velocity, embodied in mass-action expressions above. The coefficient k in this formula is called the specific reaction rate, and represents the velocity when the con centrations of the two reacting substances are each equal to unity. It depends on the nature of the reacting substances, the tem perature, and the medium (solvent) in which the reaction occurs. In the case of gaseous reactions there is no solvent to be con sidered, but it may be noted that many apparently gaseous reactions are in reality surface reactions, i.e., reactions which take place largely, if not entirely, on the surface of the walls of the containing vessel. (See ADSORPTION.) Influence of Temperature on Reaction Velocity.—The principal weakness of the explanation which makes chemical change depend solely on collisions between molecules, is that the velocity should be approximately the same for all reactions of the same type under like conditions of temperature and concentra tion. Actually rate of chemical change is a highly specific quantity, which varies widely from one reaction to another. Moreover, if we conceive of reaction rate as depending altogether on the fre quency of collisions between molecules, we find it impossible to account for the extraordinary influence of temperature on reac tion rate. In the simplest cases, an increase of temperature of 1o° C would speed up the molecules sufficiently to make collisions between them several per cent more frequent, whereas reaction velocity in that temperature range is actually increased several hundred per cent. The simplest way of explaining this involves the assumption that molecular collision is not always followed by chemical change. Collision between molecules, when reactants A and B are transformed into resultants A' and B', is a necessary but not sufficient condition for reaction.
We have then to account for the fact that the proportion of the colliding molecules which react grows rapidly larger as the tem perature is increased. We might assume that reaction takes place only when molecules collide that happen to have velocities ex ceeding some stated critical velocity. Yet the proportion of such molecules, calculated from Maxwell's law of distribution of veloci ties (see MOLECULE), does not increase with increasing tem perature in a way that fits the experimental facts. Actually, as was first pointed out by Svante Arrhenius (1889), the specific reaction rate k for many common reactions varies with the tern perature in a way that may be explained by assuming that only a very small proportion of the molecules are in a condition to react on collision. In other words the vast majority of collisions do not result in chemical change but this only takes place when the energy content of the colliding molecules is much greater than the average. The proportion (a) of the effective collisions in creases rapidly with the temperature and if the extra energy (energy of activation) required at the absolute temperature T is represented by q, then the empirical relation of Arrhenius for the connection between reaction velocity and temperature may be put in the form At a given temperature, the value of a thus depends on the magnitude of q and diminishes as q increases. When the concept of active molecules is incorporated in the mass action equation, this becomes in which q represents the extra energy of the impact which is required for the collisions between molecules of A and B to be effective.
This discussion neglects the possibility that even molecules possessed of the requisite supply of energy may not react when they collide unless they happen to be disposed in favourable posi tions with respect to each other at the moment of collision. A collision between molecules of ethyl alcohol and acetic acid, for example, would not be expected to produce a molecule of ethyl acetate unless the hydroxyl and carboxyl groups are favourably placed when collision takes place. Neglecting this difficulty, the coefficient k can be evaluated in terms of specific and general constants and the equation for the bimolecular reaction becomes in which N is the Avogadro number (6 X a- is the mean diameter of the molecules and and are the molecular weights of A and B. This equation, due to W. C. McC. Lewis (1918) does actually enable us to calculate certain reaction rates with an accuracy which is satisfactory in view of the fact that the effective diameter of the colliding molecules is known only very roughly.
Unirnolecular Reactions.—The assumption embodied in the preceding discussion, that chemical change occurs when molecules collide which happen to be possessed of a more-than-average supply of energy, at once meets the difficulty that many reversible reactions are known in which collisions between molecules appear to play no part. Thus when phosphorus pentachloride dissociates, forming phosphorus trichloride and chlorine, according to the equation each molecule of would seem to decompose independently of other molecules in accordance with the ordinary law of chance. By some chemists it has been asserted that such chemical changes (called unimolecular re actions) are not really possible. The fact that they seem to be of frequent occurrence is presumed to be explained by the presence of traces of foreign substances, which, in acting as catalysts, provide the means for interpreting the mechanism on the basis of molecular collisions.
Recent work would, however, seem to have definitely estab lished the occurrence of non-catalysed gaseous reactions which proceed in accordance with the requirements of the unimolecular type of change over a wide range of concentration. An explana tion of these has been sought in the radiation hypothesis, accord ing to which the cause of the reaction is to be found in the selective absorption of radiant energy. The mechanism of the photochemical change would on this view be extended to all types of chemical reaction (see PHOTOCHEMISTRY). The wave-length of the active radiation can be derived from the heat of activation of the molecules by Planck's relation, q=/iv (see QUANTUM THEORY), but in general the reacting substances afford no evi dence of the requisite absorption bands. For this and other reasons the radiation hypothesis cannot be said to be acceptable. For a fuller discussion see Trans. Faraday Soc. (1922).
On the other hand, it seems probable that the apparently uni molecular reactions are primarily due to molecular collisions, for it is only necessary to assume that the molecules activated by collision are for the most part deactivated by further collisions before they have time to reach that particular internal phase which is essential for chemical change to occur and the observed facts can be readily accounted for.
Since the molecules of the reaction products are the result of collisions between active molecules of the reactants and there fore, in general, distinguished by a high energy content, it follows that such "hot" molecules may hand on their excess of energy to other molecules of the reactants leading to a so-called chain reaction. Such chain reactions constitute a type which is illus trated by the combination of hydrogen and chlorine.
In practical applications the attempt is made to calculate activity or effective concentration by multiplying the actual con centration c, for the given substance, by an activity coefficient, f, which is itself a function of the concentration. Then by sub stituting a = f c for c, in the mass-action expressions given above, more nearly constant values for the equilibrium constant are found than would otherwise be obtained. To be fully satisfactory, this method would require that the activity coefficient, f, by means of which actual concentrations are converted into effective concentrations, should be independent of the nature of the reac tion in which the given substance takes part. This has been found not to be the case. Accordingly J. N. Bronsted has introduced the assumption that the interaction of two substances A and B in volves the intermediate formation of a "collision complex" X and this leads to v= f A. f x where is the activity co efficient of the complex. In this connection it may be noted that the activity coefficients of ions depend largely on their charges and on the ionic strength of their environment. (Ionic strength is calculated by taking half the sum of products formed by multi plying the concentration of each cation or anion in the solution by the square of its valence.) In accordance with the theory of P. Debye and E. Hiickel, the relation may be expressed in the form —log f where x is the valence of the ion con cerned and µ is the ionic strength of the solution in which it is present. This relation, when combined with Bronsted's reaction velocity formula, affords results for ionic reactions of varied types which are in accord with experimental observations provided that the solutions are sufficiently dilute.