# Gibbs Energy Change and Equilibrium

Gibbs energy (ΔG) :
G = H − TS
⇒ ΔG = ΔH − TΔS − SΔT
⇒ ΔGsystem = ΔHsystem − TΔSsystem
ΔT = 0

Relation between ΔG and equilibrium constant
According to thermodynamics
ΔG = ΔGº + RT ln Q
At equilibrium ΔG = 0
ΔGº = −RT ln kequilibrium
ΔGº = −RT ln keq
K_{eq} = e^{-\frac{\Delta G}{RT}}
For spontaneous ΔG < 0

Relation between ΔG and emf cell :
ΔG = − nFEcell
ΔGº = − nFEcell
for spontaneous
ΔG < 0 , Ecell > 0

Third law of thermodynamics :
ST→ 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}

### 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.

(ΔG = G2 - G1 = ΔH - TΔS)

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

3. ΔGsystem = - TΔStotal

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

4. Standard Free Energy Change( ΔGo) : ΔGo = ΔHo - TΔSo

• ΔGo = ΣΔGof(Products) - ΣΔGof(Reactant)
• where, ΔGof = standard energy of formation

5. Relation between ΔGo and EMF of the Cell

ΔGo = - nFEocell

where, n = number of electrons lost or gained

F = Faraday or 96500 C

Eocell = standard electrode potential