Page 323 - Water and wastewater engineering

7-40 WATER AND WASTEWATER ENGINEERING

17. Show, by writing the chemical reactions, how caustic soda may be used instead of lime
in softening.
18. Design an upflow solids contact basin from a manufacturer’s data given the design
flow rate.
19. Design a recarbonation system for lime/soda softening given the flow rate and treated
water composition.

7-10 PROBLEMS
7-1. Using Equations 6-3, 7-31 , 7-32 , and the equilibrium constant expression for the ion-
ization of water, derive two equations that allow calculation of the bicarbonate and
carbonate alkalinities in mg/L as CaCO 3 from measurements of the total alkalinity
( A ) and the pH.
Answers (in mg/L as CaCO 3 ):

⎧ A K ⎫
⎪
⎪

50 000 a b [ H ] a W b⎬
⎨
,

,
⎭ ⎭

HCO ⎩ ⎪ 50 000 [ H ] ⎪
3
2K
1 a 2 b
[H ]
2 = 2K 2
CO 3 a b (HCO 3 )
[H ]

where A total alkalinity, mg/L as CaCO 3
K 2 second dissociation constant of carbonic acid
11
4.68 10 at 25 C
K W ionization constant of water
14
1 10 at 25 C

HCO bicarbonate alkalinity in mg/L as CaCO 3
3
2
CO carbonate alkalinity in mg/L as CaCO 3
3
7-2. If a water has a carbonate alkalinity of 120.00 mg/L as the ion and a pH of 10.30,
what is the bicarbonate alkalinity in mg/L as the ion?
7-3. Calculate the bicarbonate and carbonate alkalinities, in mg/L as CaCO 3 , of a water
having a total alkalinity of 233.0 mg/L as CaCO 3 and a pH of 10.47.
7-4. What is the pH of a water that contains 120 mg/L of bicarbonate ion and 15mg/L of
carbonate ion?
7-5. Calculate the bicarbonate and carbonate alkalinities, in mg/L as CaCO 3 , of the
water described in the following mineral analysis for a water sample taken from
Well No. 1 at the Eastwood Manor Subdivision near McHenry, Illinois (Woller and
Sanderson, 1976a).