Page 320 - Water and wastewater engineering

LIME–SODA SOFTENING 7-37

From Table 7-5 at a temperature of 10 C and a TDS of 320 mg/L, the correction factor
is 2.56 and the LSI is
LSI pH pH 995. 3 16 2 77 2 56) 9 95 849 1146
.
.
.
(
.
.
.
s
As expected, this water is unstable and CaCO 3 will precipitate.
b. To achieve stability, the pH must be lowered to pH s . Using the second dissociation of

2
carbonic acid ( Equation 7-32 ), solve for the ratio [CO ]/[HCO ] with [H ] pH s in
3 3
moles/L:
[H ][CO 2 3 ]
K a2
[HCO ]
3
[CO 2 ] K a2
3

[HCO 3 ] [H ]
Correcting K a 2 for temperature using Equation 7-34 ,
.
K a2 10 6 498 2909 39 . . /T 0 02379T

/
.
.
(
.
K 10 6 498 29909 39283 002379 283)
a2
3 05 10 11
.
2 11
[CO 3 ] 3 05 10 0 0094
.
.
.
[HCO ] 10 849
3
and
[CO 2 ] 0 0094. [HCO ]
3 3
The total alkalinity will not change. Only the form of alkalinity will change. The total
3
3

2
alkalinity is 0.50 10 equiv/L of CO 1.20 10 equiv/L of HCO . In moles/L
3 3
these are
(0 50 10 3 equiv/L of CO 2 )(30 g/equiv )
.
3 2 50. 10 4 moles/L
60 gg/mole
3
.
120 10 equiv/L oof HCO )(61 g/equiv) . 120 10 3 mooles/L
3
61 g/mole
Thus
2 4 3
3
[CO 3 ] [HCO ] 2.50 10 moles /L 1.20 10 m moles
1.45 10 3 moles /L

This provides two simultaneous equations. Solving for [HCO 3 ],

.
.
0 0094 HCO[ ] [ HCO ] 1 45 10 3 moles/L
3
3