 # 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

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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