Concise Physical Chemistry

c06 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

FREE ENERGIES OF FORMATION 85

This equation implies constantpby the use ofHand constantTat thermal equilibrium.

Multiplication ofSbyTis also consistent with the definition of entropy asdS=

dq/T, whereqis a reversible thermal energy or enthalpy. The infinitesimal and small

finite expressionsdGand
Gare also implied:

dG=dH−TdS

and

G=
H−T
S

The Gibbs function is the algebraic sum of a thermodynamic state functionHand

a constant times a thermodynamic function –TS, hence it is a thermodynamic state

function as well.

The termsGibbs state function, Gibbs free energy, andchemical potentialare all

used for the thermodynamic propertyG.Usually the first term is used to stress the

mathematical properties of the function, the second is used in general descriptions,

and the third is used to stress the intensive nature of themolarfree energyμ=G/n.

We shall use these terms more or less synonymously, relying on context to make the

meaning clear or reminding the reader, from time to time, of the distinction between

the molar Gibbs free energyGand the extensive Gibbs functionG. The term chemical

potential, for the molar (or partial molar) quantityμ, depicts well the property of

chemical systems to flow down a gradient toward a minimum that we refer to as an

equilibrium point.

6.2 FREE ENERGIES OF FORMATION

At this point, we are able to determine the enthalpy change of a chemical reaction by

direct or indirect calorimetric measurement of
fHof the participants in the reaction

and we can find the corresponding entropy change by integration of heat capacity data

for each of the participants. These results permit us to calculateGibbs free energies

of formation. Suppose that we select combustion of C(graphite) in O 2 (g) to form

CO 2 (g) as the illustrative case and that we have determined the standard entropies

of these three species to be 5.74, 205.138, and 213.74 J K−^1 mol−^1 , respectively. We

apply the general formula

Sr^298 =

∑

S(products)−

∑

S(reactants)

to the reaction

C(gr)+O 2 (g)→CO 2 (g)