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Gibbs Energy Change and Equilibrium

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Gibbs Energy Change and Equilibrium - Lesson Summary

Spontaneous reactions often have a negative enthalpy, that is, the reaction is accompanied by a decrease in enthalpy.

Spontaneous reactions are accompanied by an increase in entropy, that is, there is increase in randomness, where ΔS>0.

Thus, the spontaneity of a reaction involves two thermodynamic properties - enthalpy and entropy.

Entropy is the measure the degree of randomness or disorder.

In the 1870s, J. Willard Gibbs an American mathematical physicist developed the concept of "free energy" to predict the spontaneity of a process, called as "Gibbs energy".

Gibbs energy is represented as G and is calculated as

G = H - TS

G = Free Energy
H = Enthalpy of System
T = Absolute Temparature
S = Entropy of the System

Thus, change in Gibbs energy,

G = H - TS

Gi = Hi - TSi
Gf = Hf - TSf

Gf - Gi = ( Hf - Hi ) - T(Sf - Si)

This equation is known as Gibbs-Helmoholtz equation or Gibbs energy equation. The total entropy change of a system which is not isolated from the surrounding is calculated as

ΔStotal = ΔSsystem + ΔSsurr

Increase in enthalpy of the surrounding is equal to decrease in the enthalpy of the system.

Thus,

ΔHsurr /T = - ΔHsys /T

Therefore,

ΔStotal = ΔSsys + ΔSsurr

ΔSsurr = ΔHsurr /T = - ΔHsys /T

ΔStotal = ΔSsys + (- ΔHsys /T)

TΔStotal = TΔSsys - ΔHsys

But it is known that,

For spontaneous process
        ΔS > 0
Therefore, TΔSsys - ΔHsys > 0

If,

TΔSsys - ΔHsys > 0

-(ΔHsys - TΔSsys) > 0

     - ΔG > 0
       ΔG > 0
ΔG = ΔHsys - TΔSsys

ΔHsys - TΔSsys < 0

ΔHsys - TΔSsys = - TΔStotal

     - TΔStotal < 0

      T ΔStotal > 0

          ΔG < 0

Therefore it can be concluded (at constant temperature and pressure),

ΔG(T,P) < 0 ← Spontaneous Process
ΔG(T,P) > 0 ← Non Spontaneous Process
ΔG(T,P) = 0 ← Equilibrium Process

A reversible reaction can proceed in either direction simultaneously, so that a dynamic equilibrium is set up.

A + B ↔ C + D

Both the reactions in a reversible reaction proceed with a decrease in free energy which is not possible, and is possible only if free energy is minimum at equilibrium.

If, it is not minimum then the system will spontaneously change to the configuration of lower free energy.

Therefore,

Criterion for Equilibrium

     A + B ↔ C + D is ΔrG = 0
      ΔrG = ΔrH - TΔrS
At equilibrium ΔrG = 0 = ΔrH - TΔrS
    So, ΔrH = TΔrS

If all the reactants and products are in standard state, then

     A + B ↔ C + D
      ΔrG = Δr
ΔrG = ΔrG° + RT ln K
0  =  ΔrG° + RT ln K
or -ΔrG° = RT ln K
or ΔrG° = -2.303 RT ln K

               ΔrG° < 0 ← Spontaneous Process
               ΔrG° > 0 ← Non Spontaneous Process
               ΔrG° = 0 ← Equilibrium Process

Where R is gas constant, T is absolute temperature and K is the equilibrium constant for the reaction.

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