LAW OF MASS ACTION: APPLICATIONS, EXAMPLES - CHEMISTRY - 2024

The law of mass action establishes the relationship between the active masses of reactants and that of products, under equilibrium conditions and in homogeneous systems (solutions or gas phases). It was formulated by the Norwegian scientists CM Guldberg and P. Waage, who recognized that equilibrium is dynamic and not static.

Why dynamic? Because the rates of the forward and reverse reactions are equal. Active masses are usually expressed mol / L (molarity). Such a reaction can be written like this: aA + bB <=> cC + dD. For the equilibrium cited in this example, the relationship between reactants and products is illustrated in the equation in the image below.

K is always constant, regardless of the initial concentrations of the substances, as long as the temperature does not vary. Here A, B, C and D are the reactants and products; while a, b, c and d are their stoichiometric coefficients.

The numerical value of K is a characteristic constant for each reaction at a given temperature. So, K is what is called the equilibrium constant.

The notation means that in the mathematical expression the concentrations appear in units of mol / L, raised to a power equal to the reaction coefficient.

What is the law of mass action?

As previously mentioned, the law of mass action expresses that the speed of a given reaction is directly proportional to the product of the concentrations of the reactant species, where the concentration of each species is elevated to a power equal to its coefficient stoichiometric in the chemical equation.

In this sense, it can be better explained by having a reversible reaction, the general equation of which is illustrated below:

aA + bB ↔ cC + dD

Where A and B represent the reactants and the substances named C and D represent the products of the reaction. Likewise the values ​​of a, b, c and d represent the stoichiometric coefficients of A, B, C and D, respectively.

Starting from the previous equation, the equilibrium constant mentioned previously is obtained, which is illustrated as:

K = ^{c d} / ^{a b}

Where the equilibrium constant K is equal to a quotient, in which the numerator is made up of the multiplication of the concentrations of the products (in the equilibrium state) raised to their coefficient in the balanced equation and the denominator consists of a similar multiplication but among the reactants elevated to the coefficient that accompanies them.

Meaning of the equilibrium constant

It should be noted that the equilibrium concentrations of the species must be used in the equation to calculate the equilibrium constant, as long as there are no modifications to these or to the temperature of the system.

In the same way, the value of the equilibrium constant provides information about the direction that is favored in a reaction at equilibrium, that is, it reveals whether the reaction is favorable towards the reactants or the products.

In the event that the magnitude of this constant is much greater than unity (K »1), the equilibrium will shift to the right and favor products; Whereas if the magnitude of this constant is much smaller than unity (K «1), the equilibrium will shift to the left and favor the reactants.

Also, although by convention it is indicated that the substances on the left side of the arrow are the reactants and those on the right side are the products, it can become a bit confusing the fact that the reactants that come from the reaction in direct sense become the products in the reaction in reverse and vice versa.

Chemical balance

Reactions often reach an equilibrium between the amounts of initial substances and those of the products that are formed. This balance can additionally shift favoring the increase or decrease of one of the substances that participate in the reaction.

An analogous fact occurs in the dissociation of a dissolved substance: during a reaction the disappearance of the initial substances and the formation of the products can be observed experimentally with a variable speed.

The rate of a reaction is highly dependent on temperature and to varying degrees on the concentration of the reactants. In fact, these factors are studied especially by chemical kinetics.

However, this equilibrium is not static, but comes from the coexistence of a direct and an inverse reaction.

In the direct reaction (->) the products are formed, while in the inverse reaction (<-) they re-originate the initial substances.

This constitutes what is known as dynamic equilibrium, mentioned above.

Equilibrium in heterogeneous systems

In heterogeneous systems -that is, in those formed by several phases- the concentrations of the solids can be considered constant, omitting from the mathematical expression for K.

CaCO ₃ (s) <=> CaO (s) + CO ₂ (g)

Thus, in the decomposition equilibrium of calcium carbonate, its concentration and that of the resulting oxide can be considered constant regardless of its mass.

Balance shifts

The numerical value of the equilibrium constant determines whether or not a reaction favors the formation of products. When K is greater than 1, the equilibrium system will have a higher concentration of products than of reactants, and if K is less than 1, the opposite occurs: in equilibrium there will be a greater concentration of reactants than products.

Le Chatelier Principle

The influence of variations in concentration, temperature and pressure can alter the rate of a reaction.

For example, if gaseous products are formed in a reaction, an increase in pressure over the system causes the reaction to run in the opposite direction (towards the reactants).

In general, the inorganic reactions that take place between ions are very fast, while the organic ones have much lower speeds.

If heat is produced in a reaction, an increase in the outside temperature tends to orient it in the opposite direction, since the reverse reaction is endothermic (absorbs heat).

Likewise, if an excess is caused in one of the reactants within a system in equilibrium, the other substances will form products to neutralize said modification to the maximum.

As a result, the equilibrium shifts favoring one way or the other by increasing the reaction rate, in such a way that the value of K remains constant.

All of these external influences and the balance response to counteract them is what is known as the Le Chatelier principle.

Applications

Despite its enormous utility, when this law was proposed it did not have the desired impact or relevance in the scientific community.

However, from the twentieth century it was gaining notoriety thanks to the fact that British scientists William Esson and Vernon Harcourt took it up again several decades after its promulgation.

The law of mass action has had many applications over time, some of which are listed below:

• As it is formulated in terms of activities rather than concentrations, it is useful for determining deviations from the ideal behavior of reactants in a solution, as long as it is consistent with thermodynamics.
• As a reaction approaches equilibrium, the relationship between the net rate of the reaction and the instantaneous Gibbs free energy of a reaction can be predicted.
• When combined with the detailed equilibrium principle, in general terms this law provides for the resulting values, according to thermodynamics, of the activities and the constant in the equilibrium state, as well as the relationship between these and the resulting velocity constants of reactions in the forward and reverse directions.
• When the reactions are of the elementary type, applying this law is obtained the appropriate equilibrium equation for a given chemical reaction and the expressions of its speed.

Examples of the law of mass action

-When studying an irreversible reaction between ions found in solution, the general expression of this law leads to the Brönsted-Bjerrum formulation, which establishes the relationship between the ionic strength of the species and the rate constant.

-When analyzing the reactions that are carried out in dilute ideal solutions or in a state of gaseous aggregation, the general expression of the original law (decade of the 80's) is obtained.

-As it has universal characteristics, the general expression of this law can be used as part of kinetics instead of seeing it as part of thermodynamics.

-When used in electronics, this law is used to determine that the multiplication between the densities of the holes and the electrons of a given surface has a constant magnitude in the equilibrium state, even independently of the doping that is supplied to the material.

-The use of this law to describe the dynamics between predators and prey is widely known, assuming that the predation relationship on the prey presents a certain proportion with the relationship between predators and prey.

-In the field of health studies, this law can even be applied to describe certain factors of human behavior, from the political and social points of view.

The Law of Mass Action in Pharmacology

Assuming that D is the drug and R is the receptor on which it acts, both react to originate the DR complex, responsible for the pharmacological effect:

K = /

K is the dissociation constant. There is a direct reaction in which the drug acts on the receptor, and another where the DR complex dissociates into the original compounds. Each reaction has its own speed, equaling itself only at equilibrium, with K. being satisfied.

Interpreting the mass law to the letter, the higher the concentration of D, the higher the concentration of the DR complex formed.

However, total receivers Rt have a physical limit, so there is no unlimited amount of R for all available D. Likewise, experimentally studies in the area of ​​pharmacology have found the following limitations to the mass law in this field:

- It assumes that the RD link is reversible, when in most cases it really is not.

- The RD bond can structurally alter one of the two components (the drug or the receptor), a circumstance that is not considered by mass law.

- Furthermore, the mass law pales in the face of reactions where multiple intermediaries intervene in the formation of RD.

Limitations

The law of mass action assumes that every chemical reaction is elemental; in other words, that the molecularity is the same as the respective reaction order for each species involved.

Here the stoichiometric coefficients a, b, c, and d are considered as the number of molecules involved in the reaction mechanism. However, in a global reaction these do not necessarily match your order.

For example, for the reaction aA + bB <=> cC + dD:

The velocity expression for the direct and inverse reactions are:

This only applies to elementary reactions, since for global ones, although the stoichiometric coefficients are correct, they are not always the reaction orders. In the case of the direct reaction, the latter could be:

In this expression w and z would be the true reaction orders for species A and B.

References

1. Jeffrey Aronson. (2015, November 19). The Laws of Life: Guldberg and Waage's Law of Mass Action. Retrieved on May 10, 2018, from: cebm.net
2. ScienceHQ. (2018). Law of mass action. Retrieved on May 10, 2018, from: sciencehq.com
3. askiitans. (2018). Law of Mass Action and Equilibrium Constant. Retrieved on May 10, 2018, from: askiitians.com
4. Salvat Encyclopedia of Sciences. (1968). Chemistry. Volume 9, Salvat SA of ediciones Pamplona, ​​Spain. P 13-16.
5. Walter J. Moore. (1963). Physical Chemistry. In Thermodynamics and chemical equilibrium. (Fourth ed.). Longmans. P 169.
6. Alex Yartsev. (2018). The Law of Mass Action in Pharmacodynamics. Retrieved on May 10, 2018, from: derangedphysiology.com