Page 299 - Water and wastewater engineering

7-16 WATER AND WASTEWATER ENGINEERING

2
[H ][CO ]
Ka2 3 p Ka2 10 33 at 25 C (7-32)

3
.
[HCO3 ]
where [ ] concentration in moles/L.
For water temperatures other than 25 C, the dissociation constants may be estimated as
(Rossum and Merrill, 1983)

.
0 032786T
.
K a1 10 14 8453 3404 71/T .
(7-33)
.
K 10 6 498 2909 39 . . /T 0 02379T
a2 (7-34)
where T absolute temperature, K.

When the pH is less than 8.3, HCO 3 is the dominant form of alkalinity, and total alkalinity is

nominally taken to be equal to the concentration of HCO 3 (Figure 6-8). For most natural waters
this is a reasonable assumption. Thus, we can ignore the dissociation of bicarbonate to form car-
bonate. With this assumption, the procedure to solve the problem is:

a. Calculate the [H ] from the pH.
b. Correct the K a value for temperature.

c. Calculate the [HCO 3 ] from the alkalinity.
d. Solve the first equilibrium expression of the carbonic acid dissociation for [H 2 CO 3 ].
e. Use the assumption that [CO 2 ] [H 2 CO 3 ] to estimate the CO 2 concentration.

Example 7-3 illustrates a simple case where one of the forms of alkalinity predominates.

Example 7-3. What is the estimated CO 2 concentration of a water with a pH of 7.65 and a total
alkalinity of 310 mg/L as CaCO 3 ? Assume the water temperature is 25 C.

Solution. When the raw water pH is less than 8.3, we can assume that the alkalinity is pre-

dominately HCO 3 . Thus, we can ignore the dissociation of bicarbonate to form carbonate.

a. The [H ] concentration is
.
.
[H ] 10 765 2 24 10 8 moles/L
b. Because the alkalinity is reported as mg/L as CaCO 3 , it must be converted to mg/L as the
species using Equation 6-7 before the molar concentration may be calculated. The ratio

61/50 is the ratio of the equivalent weight of HCO 3 to the equivalent weight of CaCO 3 .

The [HCO 3 ] concentration is
⎛ 61 mg/meq⎞ ⎛ 1 ⎞

[HCO 3 (310 mg/L ) ⎜ ⎝ 50 mg/meq⎠ (61 g/mole )(10 mg/g )⎠ ⎟
]
⎟ ⎜
3
( ⎝
.
620 10 3 moles/L
s