Gibbs free energy

The Gibbs free energy G, named after the American physicist Josiah Willard Gibbs, is a thermodynamic potential with the natural independent variables temperature T, pressure p and amount of substance n or, alternatively, particle number N. In the German-speaking area, the Gibbs energy is usually as Free enthalpy referred to; in use are also Gibbs free energy or thermodynamic potential. These names should be no longer used in the chemical after a recommendation of the IUPAC. The Gibbs free energy is an extensive quantity.

The change in Gibbs free energy during a chemical reaction is the decisive criterion for determining whether, under what conditions and to what extent the implementation of the substances involved is actually going on:

  • : Exergonic reaction under the given conditions (concentrations) occurs voluntary;
  • : Equilibrium situation, no reaction;
  • : Endergonic reaction, whose effectiveness would require in the direction indicated power supply.
  • 2.1 Chemistry 2.1.1 Standard Conditions
  • 2.1.2 balance
  • 2.1.3 Temperature dependence
  • 2.1.4 conjunction with standard formation

Definition

The Gibbs free energy is defined by

With

  • The internal energy U
  • The volume V and
  • The entropy S.

Because

Also applies

With the enthalpy H. Thus, the free energy of the Legendre transform of the enthalpy with respect to the entropy.

Often one uses the total differential of the Gibbs free energy for a pure substance:

With the chemical potential μ.

For a mixture of different fabrics i apply accordingly:

This equation is crucial for chemical reactions, as they are frequently coupled to a pressure and temperature reservoir.

The unity of the Gibbs energy is Joule,

In practice,

As long as the number of particles N is constant ( dN = 0) is, in practice, often with the molar Gibbs free energy Gm ( unit joules / mole) is worked; i.e., the Gibbs free energy is related to the amount of substance n:

With

  • Molar entropy
  • Molar volume.

To simplify both the word molar and the corresponding indices m are often omitted from the symbols. Then it can be seen only on the units to which definition is, strictly speaking, be.

Application

Chemistry

For the change in the Gibbs free energy is:

With

  • The change in the Gibbs free energy in the course of the reaction under standard conditions, called standard free; This is a reaction specific constant ( Caution: If the considered reaction does not proceed under standard conditions, is. )
  • The universal gas constant = 8.314472 (15) J mol -1 K-1
  • Is the absolute temperature in K
  • The activity of the corresponding reactants
  • The stoichiometric coefficient.

Standard conditions

If all the reactants ( reactants and products ), the activity 1 have (this is part of the standard chemical conditions! )

It follows

And thus

From the sign of that is the (hypothetical) reaction direction can be read under standard conditions:

  • Wherein the reaction takes place under standard conditions, in the direction of the products
  • In the reaction proceeds under standard conditions in the direction of the starting materials;

In specific applications, it may happen that the reaction still proceeds in the reverse direction, namely, when the activities of the use case (which ia of the standard activity 1 differ ) the sign of different precipitates as the sign of.

Balance

The equilibrium of the reaction follows the criterion of minimum Gibbs energy (). In equilibrium, by definition, no longer changes:

From which it follows:

At equilibrium, the product is referred to as thermodynamic equilibrium constant. Thus, the following applies:

Temperature dependence

Only interested in the temperature dependency of a chemical reaction, it is often used following simplified equation:

However, this allows only a statement as to whether a chemical reaction in the given direction can take place voluntarily. Sometimes, however, even in catalytic reactions are inhibited influence (e.g., the formation of ammonia from hydrogen and nitrogen ) so that conclusions about the reaction rate are not possible.

After formation and integration of the differential, the temperature dependence of the Gibbs equation yields the Van 't Hoff equation, which also approximately using the RGT can be estimated generally.

Connection with standard formation

Consider the following general chemical reaction:

Where A, B, C, stoichiometric ratios, and A, B, C, D, d, the chemical compounds or elements.

From this general chemical reaction can be understood with knowledge of the standard enthalpies, , ... of the compounds ( generally expressed as, with f as engl formation. ) Calculate the standard free a chemical reaction:

For the investigation of special thermodynamic problems that the free energy of the Gibbs equation can be differentiated and then integrated. The following thermodynamic problems are particularly important:

  • The pressure dependence in the response of ideal gases:
  • The activity dependence in solutions:

Biochemistry

In biochemistry, the standard free is defined by:

With

  • As gas constant
  • As an absolute temperature, and
  • An equilibrium constant for the reaction.

Here illustrates the superscript zero at G, the reaction - in this case biochemical - Standard conditions takes place, that, unlike the chemical standard temperature of 0 ° C ( = 273.15 K), in this case at 25 ° C ( = 298.15 K). As far as pressure and chemical activity of the reactants, however, the conditions are like in the rest of chemistry: p = 1 atm and ai = 1

The underscore before the superscript zero indicates, moreover, that in the conditions of water a further exception is made, the activity of hydrogen ions so exceptionally not to be 1: As the standard concentration are exactly 10-7 mol / l rather determine what pH a value of 7 ( = neutral / physiological) and a concentration of the water molecules of 55.5 mol / l corresponds to.

This yields for the actual change in the free energy:

Here, the fraction of the actual activities of the reactants is formed, so it is usually not the balance and does not remain in the course of the reaction.

Electrochemistry

In electrochemistry (see Electrochemical series ), the work done useful work of a voluntary conversion of chemical substances can be determined (for example, a fuel cell ) by the relation:

With

  • - Molar free enthalpy of reaction
  • - Number of electrons transferred in the reaction under consideration
  • - Faraday: 96485.3399 ( 24) A s / mol
  • - Equilibrium cell voltage
Legendre-Transformation Product (chemistry) Chemical kinetics Chemical element Standard electrode potential (data page) Gibbs–Helmholtz equation Law of mass action Reduction potential Digital Object Identifier
264777
de