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# Gibbs free energy 'G' and Standard free energy (G°)

For this purpose, "a free energy function" has been introduced by II law of thermodynamics. The free energy function, called the Gibbs free energy function, denoted by the symbol 'G' is mathematically defined as, G = H - TS

Gibbs free energy 'G'

According to II law of thermodynamics, inorder to predict the spontaneity of a process entropy of universe is considered. DSuniverse is the sum of DSsystemand DSsurroundings. It is difficult to determine DSsurroundings in most of the physical and chemical processes. Therefore a thermodynamic function which reformulates the spontaneity criterion considering only the system under study is required.

For this purpose, "a free energy function" has been introduced by II law of thermodynamics. The free energy function, called the Gibbs free energy function, denoted by the symbol 'G' is mathematically defined as,

G = H - TS

where H = enthalpy or heat content of the system, T = Temperature in Kelvin and S = entropy

This expression is valid for constant temperature and pressure processes.

In an isothermal process, if DH and DS are the changes in enthalpy and entropy of the system, then free energy change DG is given by,

DG = DH - TDS

If 1 and 2 refer to the initial and final states of the system during the isothermal process, then

DG = (G2-G1) = (H2-H1) - T(S2-S1)

from I law of thermodynamics

DH = DE + PDV

Therefore DG = DE + PDV - TDS.

For a spontaneous process, the enthalpy change at constant pressure will be negative. This is because in an exothermic process, the enthalpy of the final state (H2) is lower than the enthalpy of the initial state (H1) so that (H2-H1) is negative and the process take place spontaneously to attain the lower enthalpy state. Similarly, the entropy change (DS) increases in a spontaneous process since entropy of the final state S2 will be greater than the initial state S1 so that (S2-S1) = DS, is positive. Combining negative DH and positive DS, in the expression for free energy change DG, at constant temperature, the overall

magnitude of DG becomes negative for a spontaneous process. Here, DH and DS terms refer only to the system.

DG = DH - TDS

Hence, criterion for the prediction of feasibility of a reaction (or) the prediction of thermodynamic spontaneity of a process based on the free energy change (DG) of the process is given as : when at constant temperature and pressure of  the system, if,

DG < 0,   DG is -ve, the process is spontaneous and feasible

i.e.      DG = 0,   the process is in equilibrium

i.e.      DG < 0,   DG is +ve, the process is non spontaneous and non feasible.

In chemical thermodynamics, spontaneous processes are also known as

irreversible (or) feasible processes while non spontaneous processes are known as non feasible processes since time factor of the process is not considered here.

All reversible processes are considered as equilibrium processes.

Thermodynamic conditions for spontaneity and equilibrium

Spontaneous (irreversible) at constant P and T

DG < 0

DH < 0

DS > 0

Equilibrium (reversible)

DG = 0

DH = 0

DS = 0

Non spontaneous (nonfeasible)

DG > 0

DH > 0

DS < 0

Characteristics of Free energy 'G'

i) G is defined as (H-TS) where H and S are the enthalpy and entropy of the system respectively. T = temperature. Since H and S are state functions, G is a state function.

i) G is an extensive property while DG = (G2-G1) which is the free energy change between the initial (1) and final (2) states of the system becomes the intensive property when mass remains constant between initial and final states (or) when the system is a closed system.

iii)    G has a single value for the thermodynamic state of the system.

iv) G and DG values correspond to the system only. There are three cases of DG in predicting the nature of the process. When, DG<0 (negative), the  process is spontaneous and feasible; DG = 0. The process is in equilibrium and DG > 0 (positive), the process is nonspontaneous and not feasible.

v) DG = DH - TDS. But according to I law of thermodynamics,

DH = DE + PDV and DE = q - w.

DG = q - w + PDV - TDS

But DS = q/T  and TDS = q = heat involved in the process.

DG = q - w + PDV - q = -w + PDV

(or) -DG = w - PDV = network.

The decrease in free energy -DG, accompanying a process taking place at constant temperature and pressure is equal to the maximum obtainable work  from the system other than work of expansion.

This quantity is called as the "net work" of the system and it is equal to (w - PDV).

Net work = -DG = w - PDV.

-DG represents all others forms of work obtainable from the system such  as electrical, chemical or surface work etc other than P-V work.

Standard free energy (G o )

Like standard enthalpy of formation of substances, standard enthalpy change of a reaction, standard free energy of formation of substances and standard free energy change of reactions are considered. The standard free energy value (G o ) of all substances either elements or compounds may be calculated from H o and S o values at standard conditions of temperature (298 K) and pressure (1 atm) and the substance being present in the standard state.

i.e        G o = H o - TS o

Standard free energies of formation of elements are taken as zero. Hence, standard free energy change of a reaction which is stoichiometrically balanced, is equal to the difference between the total sum of the standard free energies of products and the total sum of the standard free energies of reactants, at standard conditions.

DG o reaction = SG o product - SG o reactants

DG o reaction can also be calculated from DH o reaction and DS o reaction values. DH o reaction  and DS o reaction can be calculated from H o f and S o values of respective product and reactant molecules at the constant temperature and pressure.

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11th 12th std standard Class Organic Inorganic Physical Chemistry Higher secondary school College Notes : Gibbs free energy 'G' and Standard free energy (G°) |