Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.9 REACTIONEQUILIBRIA 409

If we treat H 2 O as a solvent and Ca^2 Cand HCO 3 as the solute species, then we write the
thermodynamic equilibrium constant as follows:

KD

aCa^2 

aCaCO 3 aCO 2 aH 2 O

Dr

(^) C (^) ^2 mCm^2 =.m/^3

fCO 2 =p

(^) H 2 OxH 2 O

(12.9.2)

The subscriptsCandrefer to the Ca^2 Cand HCO 3 ions, and all quantities are for the
system at reaction equilibrium.ris the proper quotient of pressure factors, given for this
reaction by^15

rD

C^2

CaCO 3 H 2 O

(12.9.3)

Unless the pressure is very high, we can with little error set the value ofrequal to unity.
Equation12.9.2is an example of a “mixed” equilibrium constant—one using more
than one kind of standard state. From the definition of the mean ionic activity coefficient

(Eq.10.3.7), we can replace the product (^) C (^) ^2 by (^) ^3 , where (^) is the mean ionic activity
coefficient of aqueous Ca(HCO 3 ) 2 :
KDr
(^) ^3 mCm^2 =.m/^3

fCO 2 =p

(^) H 2 OxH 2 O

(12.9.4)

Instead of treating the aqueous Ca^2 Cand HCO 3 ions as solute species, we can regard the
dissolved Ca(HCO 3 ) 2 electrolyte as the solute and write

KD

am;B

aCaCO 3 aCO 2 aH 2 O

(12.9.5)

We then obtain Eq.12.9.4by replacingam;Bwith the expression in Table12.2for an elec-
trolyte solute.
The value ofKdepends only onT, and the value ofrdepends only onT andp.
Suppose we dissolve some NaCl in the aqueous phase while maintaining the system at

constantT andp. The increase in the ionic strength will alter (^) and necessarily cause a
compensating change in the solute molarity in order for the system to remain in reaction
equilibrium.
An example of a different kind of reaction equilibrium is the dissociation (ionization)
of a weak monoprotic acid such as acetic acid
HA.aq/ïHC.aq/CA.aq/
for which the thermodynamic equilibrium constant (theacid dissociation constant) is
KaDr
(^) C (^) mCm
(^) m,HAmHAm
Dr
(^) ^2 mCm
(^) m,HAmHAm

(12.9.6)

Suppose the solution is prepared from water and the acid, and HCfrom the dissociation of
H 2 O is negligible compared to HCfrom the acid dissociation. We may then writemCD

(^15) The productC (^2) in the numerator of Eq.12.9.3is the pressure factorm;Bfor the solute Ca(HCO 3 ) 2 (see
Eq.10.3.11on page 292 ).