Free energy change and net useful work



Work other than pressure volume work (PΔV) is net useful work. So, total work of a process is,

W = Wnet + PΔV

Wnet = W – PΔV

From Gibb’s helmuntz equation,

 ΔG = H – TΔS      ……………. (i)

We have,

 H = E +   PΔV

 S = Q /T

 TΔS = Q

Putting the values of   H and TS  in eqn (i), we get

 ΔG = ΔE   + PΔV – Q

From first law of thermodynamics

 Q = ΔE + W

Putting the value of Q in above enq we get,

  G =  Δ E + PΔV – ΔE – W

  G = PΔV – W

  G = – (W – PΔV)

  G = – Wnet

 Wnet is – ΔG

Thus the net useful work is the amount of decrease in free energy of a system under constant temperature and pressure.

 

Relation between free energy change and cell potential

The net work done by galvanic cell in carrying charge is

W = charge × potential difference = nf Ecell

We have,

 ΔG = -Wnet

 ΔG = -nfEcell

 Relation between G and equilibrium constant

The variation of G is given by Nernst equation as,

 G =    ΔG + RT in Q

Where, Q = reaction quotient

  free energy

Where, the reaction is at equilibrium

 g = k (equilibrium constant)

 ΔG = O

 O = G° + RT in k

 Δ = -RT InK

 ΔG = -2.303 RT logK

 The overall reaction for corrosion of iron by oxygen is,

4Fe (s) + 3O2 (g)            →        2Fe2O3 (s) Rust

Calculate the free energy change and equilibrium constant for this reaction at 250°c.

Given,

 Δ and    Δ = -543 JK-1 and -1652 KJ mol-1

 = -1652000 Jmol-1

 Δ  =   Δ  – TΔ

 = 1652000 – 298 × (-543)

 = -1490186 J

Again,

 Δ = -RTInK

 = -2.303 RTlogK

 1490186 = – 2.303 × 8.314 × 298 × log K

 logK = 261.17

 K = 10261.17

 K = 1.48 × 10261.17

 

 

 

Calculate the free energy at standard condition for galvanic cell having following cell reaction.

2Al (s) + 3 Cu ++ (aq)            →            2Al+++ (aq) + 3Cu (s)

E° Cu++/Cu = 0.34 V           →             E° Al+++/A1 = -1.66V

So, the standard cell potential,

 E°cell = E°cathode – E°anode

 = E°cu++/cu – E°Al+++/A1

 = 0.4 – (-1.66)

 = 2V

Again,  Δ G = -nfEcell

 = – 6 × 96500 × 2

 

 = 1.158 × 106J

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