Relation between ∆G and ∆Stotal

Derive the relation between ∆G and ∆S_total

soln:-

          Gibb’s free energy G is defined as

                            G = H - TS

Where H= enthalpy of system

            S= entropy of system

            T= absorbed temp

G is state function because H, T, S are state functions and extensive property.

          The change in Gibb’s energy ∆G depends upon the initial and final state and does not depend upon path

Therefore the change on Gibb’s energy at const temp and pressure defined as

                                       ∆G = ∆H - T∆S

Free energy change = Total enthalpy change - Temp X (Total entropy change)

 Definition:-

          It is the energy which is measure of work that can be obtained from a system at const temp and pressure.

Unit; - The SI unit of ∆G is J or KJ (or J/mol/or KJ/mole)

            The C.G.S unit of ∆G is cal or Kcal (Cal/mol or Kcal/mole)

 Gibb’s Energy and Spontaneity:-

            The total entropy change for a system and its surrounding for the process is given by.

            ∆Stotal = ∆Ssystem + ∆S surr.

            ∆S total = ∆S + ∆S (surr)

By second law of thermodynamics’ for spontaneous process

            ∆S total > 0

            If + ∆H is the entropy increases for the process or reaction at const. temp (T) and pressure then enthalpy decreases for surrounding will be -∆H

            ∆S (surr) = - ∆H /T

            ∆S = ∆S system + ∆S surr

            ∆S total = ∆S system - ∆H /T

T ∆S total = T ∆S system - ∆H

-T ∆S total = ∆H  - T ∆S system -------------  1

By Gibb’s equation

            ∆G = ∆H - T∆S total -------------------2

Comparing above two equation

∆G = -T ∆S total

This equation indicate that ∆G and ∆S total are have opposite signs because T is always positive.

∆G increases and ∆S total decreases

 Signification of ∆G

i)      ∆G < 0 process is spontaneous

ii)    ∆G > 0 process is non - spontaneous

iii)   ∆G =  0 process is at equilibrium