Applications of Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 135

and hence the apparent air-water partition constant is

K aw

K aw = 1

H + ] l .

(4.30)

+ (K a1 /K w ) [

From the above equation, it is clear that as [H + ] l decreases (or the solution becomes
more alkaline), the apparent air-water partition constant increases. The value of K a1
is 1.709 × 10 − 5 M (Seinfeld and Pandis, 1998).
The effect of pH on the ratio of air-water partition constants for the three species
CO 2 ,SO 2 , and NH 3 is shown in Figure 4.4.

E XAMPLE 4.8 CO 2 E QUILIBRIUM BETWEEN A IR AND W ATER IN A C LOSED
S YSTEM
Consider a 1 mM solution of sodium bicarbonate in an aqueous phase in a closed vessel
of total volume 1 L at 298 K. Let the ratio of gas to aqueous volume be 1:100. If the
pH of the solution is 8.5, what is the equilibrium concentration of CO 2 in the gas
phase? To solve this problem, the primary relationship we need is the equilibrium
between air and water for CO 2 given by Henry's law. K aw = 31.6 atm/mol/L at 298 K.
Hence,

K aw
RT = 1.29.

[ CO 2 ] g

] w =

(4.31)

[ CO 2 · H 2 O

CO 2 in the gas phase is generated from the sodium bicarbonate in solution and follows
the reaction equilibria mentioned earlier in this chapter. The total CO 2 in the aqueous
phase is given by

HCO 3 w + CO 2 3 w .

CO 2 T,w = CO 2 · H 2 O w +

(4.32)

Using the expressions for K c1 and K c2 given in the text, we can show that [CO 2 ·
H 2 O] w = α 0 [CO 2 ] T,w , where

1
1 + K c1 H + l +

K c1 K c2 H + l

α 0 = (4.33)

is the aqueous-phase mole fraction of [CO 2 · H 2 O] w species. Similar expressions can
be derived for the other species [HCO 3 ] w and [CO 2 3 ] w also (see Stumm and Morgan,
1996). Since pH = 8.5, [ H + ]= 3.2 × 10 − 9 M. Using K c1 = 4.3 × 10 − 7 M and K c2 =
4.7 × 10 − 11 M, we then have α o = 7.3 × 10 − 3 . Hence we have [CO 2 .H 2 O] w = 7.3 ×
10 − 3 [CO 2 ] T,w . A total mass balance requires that in the given closed system, the total
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