Page 912 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Appendix H: Dissolved Gases 867

alternative. This results in Equations H.30 through H.32, that Note that p(atm, 1524 m) was from Equation H.6; r w
correspond to H.28, H.29, and H.107, respectively, i.e., was obtained from Figure H.2 and Equation H.6; g
was from Table QR.1.
3. Substituting, the preceding calculated values for
C i
S
H < (H:30) 3
i H CH 4 (308C) and for P CH 4 (bubbles) in (H.32).
p i
mg CH =LH 2 O
S * ¼ 19:04 4
H p i < C i (H:31) C CH 4 1:32 atm CH 4
i
atm CH 4
S * mg CH 4
H p i [bubbles] ¼ C i (H:32) ¼ 25:1
i
LH 2 O
*
where C i is the concentration of dissolved gas i in equilib- 4. For carbon dioxide the procedure is the same and
rium with gas bubbles at pressure, p i (bubbles) (mg i=LH 2 O= the data are the same except that
atm i)
mg CO =LH 2 O
Equations H.30 through H.32, which are really the vari- H S (30 C) ¼ 1257 2

CO 2
ations of a single equation, may be easier to use than any of atm CO 2
S
the others because the units are common and H is found which results in,
i
directly in Table H.5. Equation H.31 says that when the
S
aqueous gas concentration of i exceeds the product, H p i ,or mg CO 2
*
i C CO 2 ¼ 1659
*
C i , then gas precipitation will occur. LH 2 O
Examples will help to illustrate the utility of the criterion of
Comments
Equations H.31 or H.32. The concentrations of dissolved gases in the benthic zone
* , and
of the lake will not exceed the levels given by C CH 3
* . Note that methane has a much lower solubility than
Example H.12 Gas Precipitation in Benthic Mud’s C CO 2
carbon dioxide. The calculations assume that the gases
precipitate independently. It is likely that some of the
A lake at elevation 1524 m (5000 ft) has accumulated bubbles will coalesce before reaching the water surface.
organic matter in its benthic zone and during the summer
months, gas bubbles are observed breaking the surface of
the lake. The lake is 5.0 m (16.4 ft) deep and the tempera- PROBLEMS
ture is 308C. Explain the situation with respect to dissolved
gases. H.1 Bubbles in Water
When a glass of cold water is permitted to warm to room
Analysis
The benthic zone is most probably anaerobic, which temperature, bubbles are observed. Explain.
means that methane and carbon dioxide are the products H.2 Boiling Water
of the decomposition of the organic matter. These reaction Explain why water boils as its temperature is elevated.
products will be generated and accumulate in the dis- Solution
solved state until the criterion of Equation H.31 is satisfied An everyday illustration of gas precipitation is seen in
at which time gas precipitation will occur.
boiling water. For water, [H 2 O] ¼ 1000 mg=L. Now, as
Solution the temperature rises, the Henry’s law coefficient rises
1. Apply Equation H.32 for methane first and then also, which is the ratio of vapor pressure to concentra-
carbon dioxide, i.e., tion of water, which is 1000 mg=L. Finally, as the
temperature reaches 1008C, the vapor pressure of water
*
H S p CH 4 [bubbles] ¼ C CH 4 (H:32) is 1.0 atm, and so we can say,
CH 4
S
2. First H S (30 C) and p CH4 (bubbles) must be deter- H [H 2 O, 1008C] ¼ 1000 mg=L=1.0 atm

CH 4
mined,
S
The H P product is,
mg CH =LH 2 O
S
H S (30 C) ¼ 19:04 4 (Table H:5) H [H 2 O, 1008C] P(local pressure ¼ 1 atm]

CH 4
atm CH 4
¼ 1000 mg=L=atm 1.0 atm
and ¼ 1000 mg=L
Thus, since [H 2 O] actual ¼ 1000 mg=L, the criterion for gas
(bubbles) ¼ p(atm, 1524 m) þ g h
p CH 4 w
precipitation is satisfied and gas bubbles form. While
kg m
¼ 84:31 kPa þ 996 3 9:806 65 2 5:0m boiling water is explained merely by the fact that boiling
m s occurs when the vapor pressure of the water increases to
¼ 84:31 kPa þ 48:84 kPa
the local atmospheric pressure, the Henry’s law explan-
¼ 133:15 kPa
ation shows the parallel with precipitation of any gas
¼ 1:32 atm species.