## What is the Law of Mass Action?

The law of mass action states that the rate of a reaction is proportional to the product of the concentrations of each reactant. This law can be used to explain the behaviour exhibited by solutions in dynamic equilibria. The law of mass action also suggests that the ratio of the reactant concentration and the product concentration is constant at a state of chemical equilibrium.

### The Equilibrium Constant (K_{c})

The concentration of reactants and products, at equilibrium, are constant at a given temperature. Consider the following simple reversible reaction where A & B are the reactants whereas C & D are the products.

**A + B â‡Œ C + D**

A mixture of products and reactants in a state of chemical equilibrium is known as an equilibrium mixture. There exists a relation between the concentration of products and the concentration of reactants for an equilibrium mixture. This relation can be equated as follows.

\(K_c\) = \(\frac{[C][D]}{[A][B]}\)

Here, K_{cÂ }is called the equilibrium constant. In this equation, the concentration of A at equilibrium is represented as [A] (similarly for B, C, and D), and the stoichiometric coefficients of the reactants and products are 1. It has been experimentally observed that the equilibrium constant is also dependant on the stoichiometric coefficients of the reactants and products.

Therefore, the law of mass action dictates that the equilibrium constant, at a given constant temperature, is equal to the product of the concentration of products raised to the respective stoichiometric coefficients divided by the product of the reactant concentrations, each raised to the corresponding stoichiometric coefficient.

This is also known as the equilibrium law or the law of chemical equilibrium.

## Representation of the Equilibrium Constant

For a balanced reaction of the type,

**aA + bB â‡ŒÂ cC + dD**

According to the law of mass action, the constant value obtained by relating equilibrium concentrations of reactants and products is called the equilibrium constant. For the forward reaction, this is given by

\(K_c\) = \(\frac{[C]^c[D]^d}{[A]^a[B]^b}\)

The equilibrium constant for the reverse reaction is the inverse of the forward reaction and is given by:

\(K’_c\) = \(\frac{1}{K_c}\) = \(\frac{[A]^a[B]^b}{[C]^c[D]^d}\)

If the coefficients of the chemical equation are multiplied by a factor â€˜nâ€™ then the equilibrium constant is raised by the power â€˜nâ€™ i.e. the constant becomes \(K_c^n\).

Equilibrium Constant Representation |
Expressed in terms of |
Expressed as |

K_{c} |
Concentrations of reactants and products | \(\frac{[C]^c[D]^d}{[A]^a[B]^b}\) |

K_{p} |
Partial pressures of reactants and products. (only for the substances which are in gaseous state) | \(\frac{p_{C}^{c}p_{D}^{d}}{p_{A}^{a}p_{B}^{b}}\) |

K_{x} |
Mole fractions of reactants and products | \(\frac{[X_C]^c[X_D]^d}{[X_A]^a[X_B]^b}\) |

### Relation between K_{c}, K_{p }and K_{x}

\(K_p\) = \( K_c (RT)^{âˆ†n_g}\)

\(K_x\) = \( K_p (RT)^{âˆ†n_g} \)

Where,

\(âˆ†n_g\) = moles of gaseous products â€“ moles of gaseous reactants.

K_{c} is the equilibrium constant expressed in terms of the concentration of the reactants/products. Similarly, K_{p} is the constant in terms of the partial pressures of the substances and K _{x} is expressed in terms of the mole fraction.

## Applications of the Law of Mass Action

This law is also applicable to semiconductors and, therefore, has several important implications in the fields of electronics and semiconductor physics. Here, the law of mass action provides a relationship between the concentrations of electron holes and free electrons when the semiconductor system is in a state of thermal equilibrium.

The law of mass action also has applications in the following fields:

- Mathematical ecology
- Sociophysics (social physics)
- Mathematical epidemiology

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