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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

G_{i} = H_{i} - TS_{i}

G_{f} = H_{f} - TS_{f}

G_{f }- G_{i} = ( H_{f} - H_{i} ) - T(S_{f} - S_{i})

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

ΔS_{total} = ΔS_{system} + ΔS_{surr}

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

Thus,

ΔH_{surr /}T = - ΔH_{sys /}T

Therefore,

ΔS_{total} = ΔS_{sys} + ΔS_{surr}

ΔS_{surr }= ΔH_{surr /}T = - ΔH_{sys /}T

ΔS_{total} = ΔS_{sys} + (- ΔH_{sys /}T)

TΔS_{total} = TΔS_{sys} - ΔHsys

But it is known that,

For spontaneous process

ΔS > 0

Therefore, TΔS_{sys} - ΔHsys > 0

If,

TΔS_{sys} - ΔHsys > 0

-(ΔHsys - TΔS_{sys}) > 0

- ΔG > 0

ΔG > 0

ΔG = ΔHsys - TΔS_{sys}

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 Δ_{r}G = 0

Δ_{r}G = Δ_{r}H - TΔ_{r}S

At equilibrium Δ_{r}G = 0 = Δ_{r}H - TΔ_{r}S

So, Δ_{r}H = TΔ_{r}S

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

A + B ↔ C + D

Δ_{r}G = Δ_{r}G°

Δ_{r}G = Δ_{r}G° + RT ln K

0 = Δ_{r}G° + RT ln K

or -Δ_{r}G° = RT ln K

or Δ_{r}G° = -2.303 RT ln K

Δ_{r}G° < 0 ← Spontaneous Process

Δ_{r}G° > 0 ← Non Spontaneous Process

Δ_{r}G° = 0 ← Equilibrium Process

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

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

G_{i} = H_{i} - TS_{i}

G_{f} = H_{f} - TS_{f}

G_{f }- G_{i} = ( H_{f} - H_{i} ) - T(S_{f} - S_{i})

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

ΔS_{total} = ΔS_{system} + ΔS_{surr}

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

Thus,

ΔH_{surr /}T = - ΔH_{sys /}T

Therefore,

ΔS_{total} = ΔS_{sys} + ΔS_{surr}

ΔS_{surr }= ΔH_{surr /}T = - ΔH_{sys /}T

ΔS_{total} = ΔS_{sys} + (- ΔH_{sys /}T)

TΔS_{total} = TΔS_{sys} - ΔHsys

But it is known that,

For spontaneous process

ΔS > 0

Therefore, TΔS_{sys} - ΔHsys > 0

If,

TΔS_{sys} - ΔHsys > 0

-(ΔHsys - TΔS_{sys}) > 0

- ΔG > 0

ΔG > 0

ΔG = ΔHsys - TΔS_{sys}

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 Δ_{r}G = 0

Δ_{r}G = Δ_{r}H - TΔ_{r}S

At equilibrium Δ_{r}G = 0 = Δ_{r}H - TΔ_{r}S

So, Δ_{r}H = TΔ_{r}S

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

A + B ↔ C + D

Δ_{r}G = Δ_{r}G°

Δ_{r}G = Δ_{r}G° + RT ln K

0 = Δ_{r}G° + RT ln K

or -Δ_{r}G° = RT ln K

or Δ_{r}G° = -2.303 RT ln K

Δ_{r}G° < 0 ← Spontaneous Process

Δ_{r}G° > 0 ← Non Spontaneous Process

Δ_{r}G° = 0 ← Equilibrium Process

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