## Chemical Thermodynamics

# Gibbs Energy Change and Equilibrium

**Gibbs energy (ΔG) :**

G = H − TS

⇒ ΔG = ΔH − TΔS − SΔT

⇒ ΔG_{system} = ΔH_{system} − TΔS_{system}

ΔT = 0

**Relation between ΔG and equilibrium constant**

According to thermodynamics

ΔG = ΔGº + RT ln Q

At equilibrium ΔG = 0

ΔGº = −RT ln k_{equilibrium}

ΔGº = −RT ln k_{eq}

K_{eq} = e^{-\frac{\Delta G}{RT}}

For spontaneous ΔG < 0

**Relation between ΔG and emf cell :**

ΔG = − nFE_{cell}

ΔGº = − nFE_{cell}_{}

for spontaneous

ΔG < 0 , E_{cell} > 0

**Third law of thermodynamics :**

S_{T→ 0} = 0

\Delta S = \frac{q_{rev}}{T} ⇒ \frac{\Delta H}{T} = \frac{C_{P}.\Delta T}{T}

\Delta S = S_{2} - S_{1} = \int_{T_{1}}^{T_{2}} \frac{C_{P} - \Delta T}{T}

### Part1: View the Topic in this Video from 3:08 to 6:58

### Part2: View the Topic in this Video from 32:00 to 47:08

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1. Gibbs Energy or Gibbs Free Energy :

*G = H - TS*2. Change in Gibbs energy during the process is given by Gibbs Helmholtz equation.

(Δ*G* =* G*_{2} - *G*_{1} = Δ*H* - *T*Δ*S*)

- where, ΔG = Gibbs free energy
- H = enthalpy of system
- TS = random energy

3. Δ*G*_{system} = - TΔS_{total}

- The Gibbs energy criterion of spontaneity
- Δ
*G*> 0, process is non-spontaneous - Δ
*G*< 0, process is spontaneous - Δ
*G*= 0, process is in equilibrium state.

4. **Standard Free Energy Change( Δ G^{o}) :** Δ

*G*

^{o}= Δ

*H*

^{o}-

*T*Δ

*S*

^{o}

- ΔG
^{o}= ΣΔ*G*^{o}_{f(Products)}- ΣΔG^{o}_{f(Reactant)} - where, Δ
*G*^{o}_{f}= standard energy of formation

5. **Relation between **Δ**G**^{o}** and EMF of the Cell**

Δ*G*^{o} = - *nFE*^{o}_{cell}

where, *n* = number of electrons lost or gained

*F* = Faraday or 96500 C

*E*^{o}_{cell} = standard electrode potential