Page 910 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Appendix H: Dissolved Gases 865

3. Calculate H D from the statement of thermo- precipitation is desired and is engineered to occur (as in
CO 2
dynamic equilibrium. dissolved-air-flotation), in other cases the effect is disruptive
(as in filters), and in some cases the effect is expected (as in
DG ¼ RT ln H D

R i opening a bottle of soda). Other examples include floating
sludge in a primary settling basin due to carbon dioxide and
8350 J=mol ¼ (8:314510 J=mol K) (298:15 K)
methane precipitating as bubbles; in an anaerobic lagoon, gas
ln H D
CO 2 bubbles are an index that methane and carbon dioxide are
being produced, a desired result; the ‘‘bends’’ in divers who
3:368 ¼ ln H D
CO 2 rise too quickly; the ‘‘bends’’ in migrating salmon, swimming
atm CO 2 LH 2 O below a dam where nitrogen gas may be ‘‘supersaturated’’ due
H D (298 K) ¼ 29:02
CO 2 to a plunging nappe that entrains air bubbles.
mol CO 2
3
atm CO 2 m H 2 O
¼ 0:029 H.3.1 CRITERION FOR GAS PRECIPITATION
mol CO 2
3
This compares with 0.022 atm CO 2 m H 2 O=mol CO 2 in In searching for an established criterion for the occurrence of
Yaws (1999, p. 407). Converted to H S , gas precipitation, the literature provides little direct guidance.
A probable explanation would be that the problem has not
CO 2
1 come to the attention of the physical chemists, who deal
H S
CO 2 (298 K) ¼ mostly with fundamentals as opposed to applied problems.
atm CO 2 LH 2 O mol CO 2
29:02 Neither has it been articulated well for engineers and oper-
mol CO 2 44,000 mg
ators. To explain gas precipitation, theory provides a means
mg CO for a coherent explanation. To interpret with a common-sense
¼ 1,516 2
LH 2 O atm CO 2 rationale then it can follow a theoretical understanding.
Comments H.3.1.1 Nutshell Explanation for Gas Precipitation
This value for H S compares with 1449 mg CO 2 =L
CO 2 In-a-nutshell, the gas precipitation may be explained first by
H 2 O=atm CO 2 in Table H.5. Comparing with Yaws
(1999, p. 407), the 0.22 value converts to 2000 mg a dissolved gas occurring at a ‘‘supersaturated’’ concentration
CO 2 =LH 2 O=atm CO 2 (which is on the high end of values in a given local environment. The gas may be transferred from
found in the literature). a higher pressure region or could be generated. If the dis-
solved gas concentration exceeds that which could exist in
equilibrium at the pseudo pressure of the pure gas at the
H.3 GAS PRECIPITATION pressure of the local environment, then the gas will come
out of the solution as bubbles. For example, one may observe
In many situations, a dissolved gas will occur in a ‘‘supersat-
gas bubbles around a bloom of algae in stagnant water. From
urated’’ state with respect to the local pressure. When such
Table H.5, C(O 2 ,20C) ¼ 43.39 mg O 2 =L water, which will
condition occurs, the dissolved gas will ‘‘precipitate’’ forming
occur if p(O 2 ) ¼ 1.00 atm O 2 . If oxygen is generated by the
bubbles of the pure gas. The local pressure is whatever occurs
algae through photosynthesis at sea level at zero depth, when
in the water (at any given elevation and at any given depth of
dissolved oxygen concentration exceeds 43.39 mg O 2 =L
water) irrespective of whether a gas–water interface is present.
water, then bubbles of pure oxygen will form. This can be
An everyday example of gas precipitation is observed when a
confirmed by taking a water sample; usually about 30–35 mg
bottle of carbonated beverage is opened; the pressure is
O 2 =L can be measured by a Winkler titration.
released and bubbles appear spontaneously. Another example
is boiling water, which is characterized by the spontaneous
H.3.1.2 Chemical Potential Criterion for Equilibrium
appearance of water vapor bubbles; boiling occurs when the
The chemical potential (see, for example, Eisenberg and
vapor pressure of water equals atmospheric pressure. This
Crothers, 1979, pp. 271–290), can be defined for the dissolved
occurs at lower temperatures as elevation increases, since
state as
atmospheric pressure declines with elevation.
Examples of gas precipitation include when (1) a bottle of
m (aq) ¼ m (aq) þ RT ln [i] (H:18)

soda is opened, carbon dioxide bubbles appear spontaneously i i
within the bottle, (2) dissolved air flotation is due to a sudden
and for the gas state as,
reduction in pressure after supersaturated water reaches the
flotation tank at which time the dissolved gas precipitates and (H:19)
m (g) ¼ m (g) þ RT ln p i
i
i
forms bubbles, (3) oxygen dissolves continuously by photo-
synthesis up to a limit at which gas bubbles may be observed, where
(4) carbon dioxide and methane are produced in anaerobic m i (aq) is the chemical potential of species i in dissolved
environments and each form bubbles when saturation levels is aqueous state (J=mol)
reached, (5) air binding occurs in filters due to supersatur- m (aq) is the standard-state chemical potential of species i

i
ation, negative pressures, or both. Thus, in some cases gas in aqueous state (J=mol)