Environmental Engineering Reference
In-Depth Information
where [ B ] eq is the concentration of B at equilibrium. If the pH of a sample of
water is 5.7, then [ H + ]=[ C ] eq = 2 × 10 6 mol/L. By stoichiometry [ HCO 3 ] eq =
[ B ] eq =[ C ] eq = 2 × 10 6 mol/L. If the closed system considered has an initial CO 2 of
5 × 10 5 mol/L, then [ A ] 0 =[ CO 2 ( aq ) ]= 5 × 10 5 mol/L. Then we have [ B ]= 2 ×
10 6
0.96 ) ] and [ A ]=[ A ] 0 −[ B ]= 5 × 10 5
[ ( e 1.5 t
1 )/( e 1.5 t
−[ B ] . If the equi-
librium pH is 5, then [ B ] eq = 1 × 10 5 mol/L, and hence [ B ]= 1 × 10 5
[ ( e 0.27 t
1 )/( e 0.27 t
0.8 ) ] and [ A ]= 5 × 10 5
−[ B ] . Figure 5.7 gives the concentration of
aqueous CO 2 with time as it is being converted to HCO 3 in the system. The func-
tional dependence on pH is shown. Equilibrium values of CO 2 (aq) is pH dependent
and reaches 48 μ Min 0.7 s at a pH of 5.7 and 40 μ Min 14satapHof5.Ifthe
final equilibrium pH is to increase, more CO 2 (aq) has to be consumed and hence the
concentration falls to a lower equilibrium value.
In the case of SO 2 solution in water, we have
k f
k b
HSO 3 ( aq ) + H + ( aq ) ,
SO 2 ( aq ) + H 2 O
(5.55)
where k f = 3.4 × 10 6 s 1 and k b = 2 × 10 8 mol/L/s. Notice first of all that k f in this
case is much larger than for CO 2 , and hence a virtually instantaneous reaction can be
expected. Let the initial SO 2 concentration be 5 × 10 5 mol/L. A similar analysis as
above for CO 2 can be carried out to determine the approach to equilibrium for SO 2 .
Figure 5.8 displays the result at two pH values of 5.7 and 5.0. The striking differences
in time to equilibrium from those for CO 2 dissolution reactions are evident. At a pH of
5.7 the equilibrium value is reached in 6 ns, whereas at a pH of 5.0 the characteristic
time is 0.1 μ s.
5.2 10 -5
5 10 -5
4.8 10 -5
4.6 10 -5
pH = 5.7
pH = 5.0
4.4 10 -5
4.2 10 -5
4 10 -5
0
5
10
15
20
25
t /s
FIGURE 5.7 Kinetics of solution of CO 2 in water at different pH values.
continued
 
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