# Chemical equilibrium

The chemical equilibrium is a state in which the overall reaction appears to be static when viewed from the outside, i.e. no changes on the macroscopic level are discernible. The externally observable reaction rate is zero. In spite of this, the chemical reactions ("forward" and "backward" reactions) continue to run, and in both directions at the same speed.

It is therefore not a static equilibrium as it appears from the outside, but a dynamic equilibrium , i.e. This means that both directions of the reaction take place with the same frequency, which is why the concentrations remain the same.

## The state of equilibrium

While the system moves from the initial state to the equilibrium state, its composition changes and with it its entropy . It changes its composition voluntarily in the direction in which the entropy increases ( Second Law of Thermodynamics ). The state of equilibrium is reached at the composition at which the total entropy of the system and the environment assumes the greatest possible value. For the (mostly present) case that the reaction takes place at constant temperature ( isothermal ) and constant pressure ( isobaric ) and the system does no work except possibly volume change work, the condition of maximum entropy of the system and the environment is equivalent to the condition of minimum Gibbs -Energy of the system . The equilibrium composition can thus be determined by looking for the composition with the lowest Gibbs energy.

In the state of equilibrium, the quotient of the product of the concentrations of the products and the product of the concentrations of the starting materials is constant. The concentration of the reactants in equilibrium is called the equilibrium concentration. ${\ displaystyle K_ {c}}$

The value of this equilibrium constant is temperature-dependent and characteristic of every reaction. In the case of homogeneous reactions in solutions, however, it also depends on the solvent in which the reaction takes place.

Although back and forth reactions take place continuously, i.e. starting materials are converted into products and these are in turn converted into starting materials, the concentrations of the starting materials and products do not change in equilibrium. This is due to the fact that in equilibrium the speed of the back and forth reaction is exactly the same, that is, as much educt reacts to product per period of time as product is consumed by educt.

The state of equilibrium should not be confused with a dormant chemical reaction. In this case, too, the concentration of educt and product practically does not change, but the chemical reaction continues to run much more slowly.

## The law of mass action

Main article: Law of mass action

The law of mass action is used, for example, for the reaction (with sufficiently small particle interactions)

${\ displaystyle \ mathrm {\ alpha \, A + \ beta \, B \ \ rightleftharpoons \ \ gamma \, C + \ delta \, D}}$

formulated as follows:

${\ displaystyle K_ {c} = {\ frac {c ^ {\ mathrm {\ gamma}} (\ mathrm {C}) \ cdot c ^ {\ mathrm {\ delta}} (\ mathrm {D})} { c ^ {\ mathrm {\ alpha}} (\ mathrm {A}) \ cdot c ^ {\ mathrm {\ beta}} (\ mathrm {B})}}}$.

Note that the concentration-based equilibrium constant is considered here , which can carry a dimension. The dimensionless equilibrium constant , on the other hand, is simply a number without a unit. ${\ displaystyle K_ {c}}$${\ displaystyle K = \ exp {\ biggl (} - {\ frac {\ Delta G ^ {\ circ}} {k _ {\ mathrm {B}} T}} {\ biggr)}}$

### Equilibrium position

The position of an equilibrium - and thus the equilibrium constant - is determined by the reaction conditions of temperature, pressure and molar concentration:

• If the equilibrium constant is very large , there are high concentrations of products in equilibrium . One then says: “The balance is on the side of the products”.${\ displaystyle (K_ {c} \ gg 1)}$
• If the equilibrium constant is very small , there are high concentrations of educts in equilibrium . One then says: “The equilibrium is on the side of the educts”.${\ displaystyle (K_ {c} \ ll 1)}$

The equilibrium constant says something about which side of the chemical equation the equilibrium is on: An increase in the equilibrium constant means that the equilibrium is shifted to the side of the products, a decrease in means a shift of the equilibrium toward the side of the educts. ${\ displaystyle K_ {c}}$${\ displaystyle K_ {c}}$

### Free enthalpy

In equilibrium with the difference, the larger the standard: applies Gibbs ( ) between reactants and products, the more the equilibrium is on the side with the lower free energy (Note: see. Default state ) ${\ displaystyle {\ ce {\ Delta G = 0}}}$${\ displaystyle \ Delta G ^ {\ circ}}$${\ displaystyle \ Delta G ^ {\ circ} \ neq \ Delta G}$

${\ displaystyle \ Delta G ^ {\ circ} = - {\ text {R}} T \ cdot \ ln K}$

With

R = gas constant = 8.31447 J K −1 mol −1
K = dimensionless equilibrium constant (defined with relative activities)
T = temperature in Kelvin

## Influence of a catalyst

A catalyst accelerates or slows down the back and forth reaction in the same way. It does not change the equilibrium concentrations of the educts and products, but has the effect that the state of equilibrium is established more quickly. The function of a catalyst is based on the opening of a new reaction path that takes place via different elementary reactions than the uncatalyzed reaction. The catalyst itself is involved in these elementary reactions, but leaves the process (chemically) unchanged. The influence of a catalyst can be seen when looking at the reaction profile. It lowers the activation energy .

## Disturbance of the balance - principle of Le Chatelier

If a chemical equilibrium is disturbed, the reaction that reverses this disturbance accelerates. This is why this is also called the “principle of the smallest constraint” ( Le Chatelier's principle ): the “constraint” imposed on the balance by the disturbance is compensated for by the accelerated reaction.

Disturbances are:

• Changes in concentration or changes in the amount of substance (by adding or removing one of the substances involved in the equilibrium)
• Supply or withdrawal of heat or temperature changes
• Change of pressure
• Change in volume in gas reactions

## Entropy in reactions

Whether a reaction proceeds from the educts in the direction of the products (and how far) depends on whether the entropy increases. This is e.g. B. is already the case when a gaseous product can spread over a larger space . But it is not only the change in entropy of the reacting components that counts . In the course of a reaction, heat (enthalpy of reaction ) is usually exchanged with the environment and this also causes a change in entropy there: The equation is divided ${\ displaystyle \ Delta S}$${\ displaystyle \ Delta H}$

${\ displaystyle \ Delta G = \ Delta HT \ cdot \ Delta S}$

by the absolute temperature , then one obtains a connection between three quantities with the dimension of an entropy (J / K): ${\ displaystyle T}$

${\ displaystyle {\ frac {\ Delta G} {T}} = {\ frac {\ Delta H} {T}} - \ Delta S}$

This only refers to one step along the sales variable . is the amount of the change in entropy of the environment that has absorbed or given off the heat of reaction . The fact that a negative corresponds to a net increase in total entropy is due to the signs that are based on the reacting system. B. from heat, the calculation is negative and the contribution to is also negative. (But in the surrounding area the entropy increases by the same, positive amount.) If the entropy change of the reacting system is also positive, then the minus sign in the equation gives another negative contribution. The reaction continues as long as decreases or is negative. In the minimum of the Gibbs energy / free enthalpy there are then back and forth reactions in equilibrium. ${\ displaystyle \ Delta}$${\ displaystyle {\ tfrac {\ Delta H} {T}}}$${\ displaystyle \; \ Delta H}$${\ displaystyle {\ tfrac {\ Delta G} {T}}}$${\ displaystyle \ Delta H}$${\ displaystyle {\ tfrac {\ Delta G} {T}}}$${\ displaystyle \ Delta S}$${\ displaystyle G}$${\ displaystyle \ Delta G}$ ${\ displaystyle G}$

## Extension to electrochemical equilibria

For redox reactions (in which a voltage is applied between electrodes), the electrochemical equilibrium describes the material composition of the cell, which depends on the applied voltage. The following relationship applies:

${\ displaystyle \ Delta G ^ {\ circ} = (\ varepsilon _ {\ text {I}} ^ {\ circ} - \ varepsilon _ {\ text {II}} ^ {\ circ}) \ cdot z {\ text {F}}}$

With

z = number of electrons exchanged
F = Faraday constant = 96,485.3399 C mol −1
ε 0 = normal potential of a redox partial reaction

For an electrochemical redox reaction, the free enthalpy results from the converted amount of substance n (usually given in mol ), the Faraday constant F and the potential difference. Energy is supplied until the electrochemical equilibrium is reached:

${\ displaystyle \ Delta G = -n \ cdot F \ cdot \ Delta E}$

## Individual evidence

1. ^ AF Holleman , E. Wiberg , N. Wiberg : Textbook of Inorganic Chemistry . 101st edition. Walter de Gruyter, Berlin 1995, ISBN 3-11-012641-9 , p. 186.
2. ^ PW Atkins: Physical Chemistry. 2nd reprint d. 1st edition. VCH, Weinheim 1990, ISBN 3-527-25913-9 , p. 115.