Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.8 THETHERMODYNAMICEQUILIBRIUMCONSTANT 355

as reactants or products, these values correctly giveÅrSusing Eq.11.8.22, orÅrGusing
Eq.11.8.24.

The relation of Eq.11.8.23does not apply to an ion, because we cannot write a for-

mation reaction for a single ion. Instead, the relation betweenÅfG,ÅfHandSmis

more complicated.

Consider first a hypothetical reaction in which hydrogen ions and one or more

elements form H 2 and a cation MzCwith charge numberzC:

zCHC(aq)Celements!.zC=2/H 2 (g)CMzC(aq)

For this reaction, using the convention thatÅfH,Sm, andÅfGare zero for the

aqueous HCion and the fact thatÅfHandÅfGare zero for the elements, we can

write the following expressions for standard molar reaction quantities:

ÅrHDÅfH.MzC/ (11.8.25)

ÅrSD.zC=2/Sm.H 2 /CSm.MzC/

X

elements

Si (11.8.26)

ÅrGDÅfG.MzC/ (11.8.27)

Then, fromÅrGDÅrHTÅrS, we find

ÅfG.MzC/DÅfH.MzC/

T

"

Sm.MzC/

X

elements

SiC.zC=2/Sm.H 2 /

#

(11.8.28)

For example, the standard molar Gibbs energy of the aqueous mercury(I) ion is found

from

ÅfG.Hg 22 C/DÅfH.Hg 22 C/TSm.Hg 22 C/

C2TSm.Hg/^22 TSm.H 2 / (11.8.29)

For an anion Xzwith negative charge numberz, using the hypothetical reaction

jz=2jH 2 (g)Celements! jzjHC(aq)CXz(aq)

we find by the same method

ÅfG.Xz/DÅfH.Xz/

T

"

Sm.Xz/

X

elements

Sijz=2jSm.H 2 /

#

(11.8.30)

For example, the calculation for the nitrate ion is

ÅfG.NO 3 /DÅfH.NO 3 /TSm.NO 3 /

C^12 TSm.N 2 /C^32 TSm.O 2 /C^12 TSm.H 2 / (11.8.31)