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Free Energy
Free energy is a property provided a convenient measure of the driving force of a reaction.

The entropy change that must be considered if the direction of a chemical reaction is to be deduced is that of the universe of the reaction. This reaction change is the sum of that occurring in the system and that occurring in the thermal surroundings. Both contributions can be calculated from changes in the properties of the system.

Consider a chemical system in which a reaction occurs at constant temperature and constant pressure. The entropy change in the system is represented by ΔS.

The entropy change in the thermal surroundings is calculated from the change in these surroundings. If we are dealing with an “ordinary” chemical reaction in which no mechanical energy, other than P dv type of energy is involved, then the energy change of the thermal surroundings is equal to - ∆H/T.

The entropy change of the universe of the reaction system is given by:

∆Suniv = T∆S - ∆H

Then, recognizing that T∆S is equated to an expression involving properties of the system, we introduce a new system property term, the free energy, with symbol G. changes in this free energy in the enthalpy minus the product of the temperature and the change in the entropy.

Thus, the change in the free energy of a system, for any constant temperature process, is equal to the property of free energy changes of which are given by the following equation is defined by

G = H – TS

Since H and S are properties of the system, so is G.

Free energy and spontaneity: T∆Suniv = -∆G

Now we can draw these general conclusions:

If ∆G is negative, the reaction can proceed spontaneously.

If ∆G is positive, the reverse reaction would proceed spontaneously.

If ∆G is zero, the reaction would proceed reversibly, or at a state of balance.

Free energy and mechanical energy: now consider a reaction system like that occurring in the electrochemical cell, which can supply energy and above any P dV energy to the mechanical surroundings. Again we think of a process occurs at some fixed temperature and fixed pressure.

The conservation of energy principle of the first law lets us write:

dU = dUtherm – dUmech

We can explicitly distinguish the P dV type of energy of the mechanical surroundings from other non-P dV type of energy that is delivered to the mechanical surroundings by writing dUmech = dUmech + P dV. Then eq. becomes:

dU = -dUtherm – dU’therm – dU’mech – P dV

The corresponding enthalpy expression, obtained from dH = dU + P dV for constant pressure processes is:

dH = -dUtherm – dU’mech – P dV + P dV

= -dUtherm – dU’mech

The enthalpy expression can be used to see how free energy changes are related to energy changes in the surroundings. The change in G for an infinitesimal change in the properties t which free energy has been related is:

dG = dH – T dS

with this eq. we have:

dG = -dUtherm –dU’mech – TdS

if the reaction can be made to proceed in a balanced, reversible way, as is often possible with reactions in electrochemical cells, then the entropy of the universe of the process is constant. Then:

dS + dStherm = dS +dUtherm/T = 0 or dUtherm + T dS = 0 (reversible)

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