Page 375 - Water and wastewater engineering

9-14 WATER AND WASTEWATER ENGINEERING

d. Solving for [H ],

3 moles/L ][1 16 10 12 moles/L] ]
[9 52
10
.
.
[H ]
495 10 9
.
223 10 6
.

and the pH log [H ] 5.65.
e. The acid dose must be sufficient to convert the bicarbonate to carbonic acid at a pH of
5.65. Using the equilibrium expression for the first dissociation of carbonic acid and
finding p K a 1 6.35 from Appendix A,

[H ][HCO 3 ]
K
a1
[HCO ]
2 3
7
where K a 1 10 6.35 4.47 10 .
Assuming the starting concentration of H 2 CO 3 is negligible (that is, zero in the equation
below) and with the recognition that each mole of carbonic acid formed reduces the bi-
carbonate by one mole, this expression becomes

[H ][HCO 3 X]
K
a1
[ 0 X]

where X [H ] required to react with [HCO ].
3

3
The bicarbonate alkalinity (HCO ) was calculated in step (a) as 6.2 10 moles/L.
3
6

.
.
447 10 7 [ 223 10 ][ 6 20 10 3 moles/L ]X
.
0
[0 X]
[ 223 . 10 6 ][ 6 20 . 10 3 moles/L X]
X

.
447 10 7
2
.
X 3 09 10 4 99X.
3 09 10 2 3
.

.
X 5 16 10 moles/L
.
5 99
3

f. Therefore, the sulfuric acid must supply 5.16 10 moles/L of H . Because each mole

of sulfuric acid dissociates to produce 2 moles of H , the dose of sulfuric acid is
5 16 10 3 moles/L 3
.
2 58 10 moles/L
.
2