In chemistry, the law of mass action is the proposition that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants.
Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and products is constant.
Both aspects stem from the research performed by Cato M. Guldberg and Peter Waage between 1864 and 1879 in which equilibrium constants were derived by using kinetic data and the rate equation which they had proposed.
The expression of the rate equations was rediscovered independently by Jacobus Henricus van 't Hoff.
[3] Two chemists generally expressed the composition of a mixture in terms of numerical values relating the amount of the product to describe the equilibrium state.
Cato Maximilian Guldberg and Peter Waage, building on Claude Louis Berthollet's ideas[4][5] about reversible chemical reactions, proposed the law of mass action in 1864.
Thus the law of mass action was first stated as follows: In this context a substitution reaction was one such as
[10] The chemical force was assumed to be directly proportional to the product of the active masses of the reactants.
Turning to the kinetic aspect, it was suggested that the velocity of reaction, v, is proportional to the sum of chemical affinities (forces).
By making certain simplifying approximations to those more complicated expressions, the rate equation could be integrated and hence the equilibrium quantity
The extensive calculations in the 1867 paper gave support to the simplified concept, namely, This is an alternative statement of the law of mass action.
The equilibrium constant, K, was derived by setting the rates of forward and backward reactions to be equal.
Nevertheless, Guldberg and Waage were on the right track when they suggested that the driving force for both forward and backward reactions is equal when the mixture is at equilibrium.
Today the expression for the equilibrium constant is derived by setting the chemical potential of forward and backward reactions to be equal.
The generalisation of the law of mass action, in terms of affinity, to equilibria of arbitrary stoichiometry was a bold and correct conjecture.
Guldberg and Waage were fortunate in that reactions such as ester formation and hydrolysis, on which they originally based their theory, do indeed follow this rate expression.
In biochemistry, there has been significant interest in the appropriate mathematical model for chemical reactions occurring in the intracellular medium.
This is in contrast to the initial work done on chemical kinetics, which was in simplified systems where reactants were in a relatively dilute, pH-buffered, aqueous solution.
In more complex environments, where bound particles may be prevented from disassociation by their surroundings, or diffusion is slow or anomalous, the model of mass action does not always describe the behavior of the reaction kinetics accurately.
Several attempts have been made to modify the mass action model, but consensus has yet to be reached.
As an alternative to these mathematical constructs, one school of thought is that the mass action model can be valid in intracellular environments under certain conditions, but with different rates than would be found in a dilute, simple environment [citation needed].
The fact that Guldberg and Waage developed their concepts in steps from 1864 to 1867 and 1879 has resulted in much confusion in the literature as to which equation the law of mass action refers.
[15] Thus, today the "law of mass action" sometimes refers to the (correct) equilibrium constant formula,[16][17][18][19][20][21][22][23][24][25] and at other times to the (usually incorrect)
: Yakov Frenkel represented diffusion process in condensed matter as an ensemble of elementary jumps and quasichemical interactions of particles and defects.
Henry Eyring applied his theory of absolute reaction rates to this quasichemical representation of diffusion.
The law of mass action forms the basis of the compartmental model of disease spread in mathematical epidemiology, in which a population of humans, animals or other individuals is divided into categories of susceptible, infected, and recovered (immune).
The principle of mass action is at the heart of the transmission term of compartmental models in epidemiology, which provide a useful abstraction of disease dynamics.
[29] The law of mass action formulation of the SIR model corresponds to the following "quasichemical" system of elementary reactions: A rich system of law of mass action models was developed in mathematical epidemiology by adding components and elementary reactions.
Individuals in human or animal populations – unlike molecules in an ideal solution – do not mix homogeneously.
There are some disease examples in which this non-homogeneity is great enough such that the outputs of the classical SIR model and their simple generalizations like SIS or SEIR, are invalid.