Concise Physical Chemistry

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

86 THE GIBBS FREE ENERGY

to get

Sr^298 = 213. 74 − 5. 74 − 205. 138 = 2 .862 J K−^1 mol−^1

as the change in standard entropy of the reacting system.

Theenthalpyof formation of CO 2 (g) has been measured and found to be−393.51

kJ mol−^1 (Section 4.2), so from the fundamental equation for a finite change (
G)

G=
H−T
S

we get

Gf=
Hf−T
Sf=− 393. 51 −298(2. 862 × 10 −^3 )

=− 393. 51 − 0. 852 =− 394 .36 kJ mol−^1

which is the Gibbs function of formation at 298 K of CO 2 (g).

Comparable calculations yield the Gibbs functions of many direct formation reac-

tions of elements to their compounds. Armed with these Gibbs functions of formation,

we can manipulate them to find the Gibbs functions of compounds not cleanly formed

from their elements in the same way as we did for the enthalpies of formation.

6.3 SOME FUNDAMENTAL THERMODYNAMIC IDENTITIES

For a reversible change doing onlypVwork, the first law gives

dU=dq−dw=TdS−pdV

whence, knowing thatU=f(S,V),dU=(∂U/∂S)VdS+(∂U/∂V)SdV, we find

that

(

∂U

∂S

)

V

=T and

(

∂U

∂V

)

S

=−p

Also,G=f(p,T),dG=

(

∂G

∂p

)

T

dp+

(

∂G

∂T

)

p

dT, and

dG=Vdp−SdT

with the results that

(

∂G

∂p

)

T

=V and

(

∂G

∂T

)

p

=−S