# Gibb’s Energy and Chemical Equilibrium:

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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 ΔSTotal be the total enthalpy of the system and ΔGT,P is Gibb’s energy at constant temperature and pressure.
• If ΔSTotal > 0 (positive) or ΔGT,P < 0 (negative), the process will be spontaneous and proceeds in a backward direction. It nears to completion. (K > 1)
• If ΔSTotal < 0 (negative) or ΔGT,P > 0 (positive), the process will be non-spontaneous. and favoured in backward direction. (K < 1)
• If ΔSTotal = 0 or ΔGT,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 ΔGis given by

ΔG = ΔGo  + RT ln Q

Where      R = Universal gas constant

T = Absolute temperature of the system

Q = Concentration coefficient

At equilibrium ΔG = 0 and Q = Kc

∴   0 = ΔGo  + RT ln Kc

∴    ΔGo  = – RT ln Kc

∴    ΔGo  = – 2.303 RT log 10 Kc

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

In exponential form, the expression can be written as Science > You are Here