Free Enthalpy

The free function enthalpy G was introduced by Willard Gibbs. It is associated with the Second principle of thermodynamics, principle of evolution of the physicochemical systems.

The second principle stipulates that any real transformation is carried out with creation of Entropie, i.e. the entropic assessment ΔS (system) + ΔS (external) > 0 .

The function entropy can be used for the study of the evolution of a thermodynamic Système. Indeed for a system isolated the entropy by a maximum to balance thus any evolution passes must go in this direction.

In general, intuitively it is thought that a balance is reached when energy is minimal. It is the case of the potential energy (gravitation, electromagnetism…). Moreover in the case of the entropy it is necessary to study in addition to the system, the evolution of the entropy of the external medium.

Gibbs defined a new function which takes into account these two remarks.

The free enthalpy G behaves indeed like a potential function and integrates the behavior of the external medium. Moreover it is the function of state the most adapted to study chemical balances realized at the temperature T and constant pressure what is the batch of many reactions carried out with the free air, with the atmospheric pressure.

Definition

Let us consider a chemical reaction carried out at the temperature T and with pressure constant p. the work is only with the compressive forces (not of electrochemical assembly giving of electric work). That is to say Q_P the heat concerned by the reactional system. Like p = constant, concerned heat is equal to the variation of Enthalpie of the system: ΔH (syst) = Q_P .

Let us apply the second principle:

ΔS (created) = ΔS (syst) + ΔS (ext.) > 0

However the heat provided by the system is received by the external medium, therefore its sign changes (rule of the signs): - Q_P = - ΔH (syst) .

The variation of entropy of the external medium becomes: ΔS (ext.) = - Q_P/T = - ΔH (syst)/T .

The entropic assessment is written: ΔS (syst) - ΔH (syst)/T > 0 .

Let us multiply the two members of this inequality by (- T), one obtains:

ΔH (syst) - TΔS (syst) < 0 .

One obtains the new function of state G = H - TS

With temperature and constant pressure ΔG_{T, P} (syst) = ΔH (syst) - TΔS (syst) < 0

the reaction can occur only in the direction corresponding to the reduction in the G_{T function, P} (syst); balance being reached for the minimum of G_{T, P} (syst).

Differential of G

G = H - TS

dG = dH - TdS - SdT

however H = U + statement

dH = of + pdV + Vdp

dG = of + pdV + Vdp - TdS - SdT

First principle: = δQ + δW = δQ - pdV + δW'

Work corresponds either to the compressive forces (- pdV) or to electric work in an assembly of pile (δW').

dG = δQ - pdV + δW' + pdV + Vdp - TdS - SdT = δQ + δW' + Vdp - TdS - SdT

Let us apply the second principle: dS (syst) = δQ (rév)/T from where δQ (rév) = TdS dG = TdS + δW' (rév) + Vdp - TdS - SdT = δW' (rév) + Vdp - SdT

dG = Vdp - SdT + δW' (rév)

Case of a reversible pile which functions with T and p constants

A Battery is a particular device which makes it possible to convert the chemical energy concerned during a reaction of Oxydo-réduction, in electrical energy provided to the external medium: W'. If the pile outputs under weak a tension one can consider that the reaction occurs in a way close to the Réversibilité and that thus, at every moment, the state of the pile is close to a state of balance. This operating process can be carried out while introducing into the external circuit against close tension, except for a ε, of the electromotive Force of the pile.

Under these conditions, with T and P constants:

dG = δW' (rév) and for a finished transformation: ΔG_{T, P} (syst) = W' (rév)

the free variation of enthalpy in a reversible pile corresponds to the electric work provided to the external medium.

If the pile is not reversible like any real pile, the second principle applies by the inequality of Clausius (see Entropie): dS (syst) > δQ (irrév)/T. By taking again calculations, one leads to the following inequality:

ΔG_{T, P} (syst) < W' (irrév)

From where W' (rév) < W' (irrév) and as the work provided by the electrochemical system is negative according to the rule of the signs: | W' (rév) | > | W' (irrév) |

the electric work provided by the pile is more important if the pile approaches a reversible operation, i.e. with a low imbalance of tension. The irreversibility appears here by Joule effect.

Case of a chemical reaction with T and p constants, irreversible by nature

If there is no assembly of pile, there is no electric work, δW' = 0.

The chemical reaction is irreversible and the second principle applies by the inequality of Clausius (see Entropie): dS (syst) > δQ (irrév)/T

If one takes again calculations of the differential dG, one obtains the inequality then:

dG < Vdp - SdT

However here T and p are constant

dG_{T, P} (syst) < 0 and for a reaction ΔG_{T, P} (syst) < 0

One can express the free variation of enthalpy according to the entropy created:

ΔS (created) = ΔS (syst) + ΔS (ext.) > 0

ΔS (created) = ΔS (syst) - ΔH (syst)/T, let us multiply by - T

- TΔS (created) = - TΔS (syst) + ΔH (syst)

from where ΔG_{T, P} (syst) = - TΔS (created) < 0

Consequently any chemical reaction can progress only if the free enthalpy of the reactional system decreases. When this function reaches a minimum, the system is with balance.

the function G_{T, P} (syst) thus makes it possible to define the direction of the reaction and its positioning in balance. It is the most important function for the study of chemical balances.

Note:: a physical Changement of state can be regarded as a particular chemical reaction which can be carried out while approaching the Réversibilité. For example the fusion of the ice can be carried out with O^°C + ε . In this case the entropy created is close to zero. It follows that ΔG_{T, P} (syst) ≈ 0 . This is why one speaks then about balance of change of state.

See too

chemical Entropy
Balance

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