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**Gibb’s Energy or Free Energy: **

- Gibb’s energy or free energy is a thermodynamic function which helps us in the development of a criterion of spontaneity or a feasibility of a process. It refers to the capacity of the system to do useful work.
- Gibb’s energy is defined as the amount of energy available from a system at given set of conditions that can be put into useful work.

Mathematically, G = U + PV – TS

Where G = Gibb’s energy

U = Internal energy of the system

P = Pressure of the system

V = Volume of the system

T = Absolute temperature of the system

S = Entropy of the system

The absolute value of Gibb’s energy cannot be calculated. But the change in it can be calculated as

ΔG = ΔU + Δ(PV) – Δ(TS)

For constant pressure and constant temperature process

ΔG = ΔU + PΔV – TΔS

But ΔU + PΔV = ΔH

∴ ΔG = ΔH – TΔS

This relation is known as Gibb’s Helmholtz equation.

Where, ΔG = Change in Gibb’s energy

ΔH = Change in enthalpy of the system

T = Absolute temperature of the system

ΔS = Change in entropy of the system

**The spontaneity of a Reaction w.r.t. Gibb’s Energy and Total Entropy:**

- Let ΔS
_{Total}be the total enthalpy of the system and ΔG_{T,P}is Gibb’s energy at constant temperature and pressure. - If ΔS
_{Total}> 0 (positive) or ΔG_{T,P}< 0 (negative), the process will be spontaneous and proceeds in a backward direction. It nears to completion. (K > 1) - If ΔS
_{Total}< 0 (negative) or ΔG_{T,P}> 0 (positive), the process will be non-spontaneous. and favoured in backward direction. (K < 1) - If ΔS
_{Total}= 0 or ΔG_{T,P}= 0, the process will be in equilibrium state. (K = 1)

**Relation Between Gibb’s Energy and Chemical Equilibrium:**

- For spontaneous process Gibb’s energy is negative.
- For a reversible reaction, there is a decrease in the Gibb’s energy during the course of reaction whether we start from reactants or products.

Let us consider a hypothetical reaction

A ⇌ B

- A graph is drawn by taking Gibb’s energy on the y-axis and the change in the composition of the reacting mixture with time on the x-axis. The graph is as follows.

- The minima in the curve correspond to the composition of the reaction mixture at the equilibrium state at which Gibb’s energy is minimum.
- From graph following points should be noted.
- In reaching the equilibrium state whether from A or from B, the ΔG is negative.
- At equilibrium state, there is no change in Gibb’s energy. i.e. ΔG at equilibrium = 0.
- If minima of the curve lie very close to the products, then it means that the equilibrium composition strongly favours the products and hence K >> 1. i.e. reaction will proceed to completion.
- If minima of the curve lie very close to the reactants, then it means that the equilibrium composition strongly favours the reactants and hence K < 1. i.e. the reaction hardly proceeds.

**Relation Between Standard Gibb’s Energy change and Equilibrium Constant:**

Let us consider a hypothetical reaction

A + B ⇌ C + D

- The relation between Gibb’s energy change (ΔG)and standard Gibb’s energy change ΔG
^{o }is given by

ΔG = ΔG^{o} + RT ln Q

Where R = Universal gas constant

T = Absolute temperature of the system

Q = Concentration coefficient

At equilibrium ΔG = 0 and Q = K_{c}

∴ 0 = ΔG^{o} + RT ln K_{c}

∴ ΔG^{o} = – RT ln K_{c}

∴ ΔG^{o} = – 2.303 RT log _{10} K_{c}

This is the relation between standard Gibb’s energy change and equilibrium constant.

In exponential form, the expression can be written as

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