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CEE 680 |
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14 November 2006 |
SECOND EXAM
Closed book, two pages of notes allowed.
Answer all questions. Please state any additional assumptions you made, and show all work.
1. Carbonate System.
(40% for both parts) You’re treating a drinking water that contains 25 mg/L of alkalinity. The initial pH is 6.2, and you wish to raise this to 8.5 for purposes of corrosion control.
A. (20%) How much of a caustic soda (NaOH) dose do you need to add to accomplish this if the water goes right into the water main?
B. (20%) Answer the above question, but this time assume you have a large finished water reservoir after caustic addition that allows the water to reach equilibrium with the atmosphere before entering the distribution system.
Solution to #1
A. Recognize that alkalinity is conservative, and in a closed system, so is the total carbonates. Calculate total carbonates (CT) for the original water, using the equation for alkalinity. This first requires that you calculate the alpha values for the initial pH.
Next, determine the new alkalinity using this same equation, but inserting the new desired pH, and recalculating the alphas
Original
Water
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Input Data |
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pK1 = |
6.3 |
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pKw = |
14 |
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K1 = |
5.01187E-07 |
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pK2 = |
10.3 |
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5.01187E-11 |
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pK3 = |
50 |
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K3 = |
1E-50 |
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Alk = |
25 |
mg/L = |
0.0005 |
equ/L |
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1 = |
1 |
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pH = |
6.2 |
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Flow = |
60 |
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pH |
H+ |
alpha-0 |
alpha-1 |
alpha-2 |
alpha-3 |
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CT |
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6.2 |
6.31E-07 |
0.557292 |
0.442673 |
3.52E-05 |
5.57E-49 |
1.58E-08 |
0.001131 |
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Treated
(adjusted) Water, closed system:
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New Target
pH = |
8.5 |
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pH |
H+ |
alpha-0 |
alpha-1 |
alpha-2 |
alpha-3 |
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CT |
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8.5 |
3.16E-09 |
0.006173 |
0.978322 |
0.015505 |
4.9E-44 |
3.16E-06 |
0.001131 |
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Required
total Alkalinity = |
0.001144 |
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Alkalinity
to be added = |
0.000644 |
equ/L = |
32.2 |
mg/L as
CaCO3 |
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25.8 |
mg/L as
NaOH |
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B. Here we use the open system term for CT in place of the constant. In other words, CT is no longer a conservative parameter
Treated
(adjusted) Water, open system:
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pKH= |
1.5 |
KH= |
0.031623 |
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ppCO2 = |
3.5 |
pCO2 = |
0.000316 |
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New
Target pH = |
8.5 |
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pH |
H+ |
alpha-0 |
alpha-1 |
alpha-2 |
alpha-3 |
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8.5 |
3.16E-09 |
0.006173 |
0.978322 |
0.015505 |
4.9E-44 |
3.16E-06 |
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Required
total Alkalinity = |
0.001638 |
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Alkalinity
to be added = |
0.001138 |
equ/L = |
56.9 |
mg/L as
CaCO3 |
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45.5 |
mg/L as
NaOH |
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2. Complexation
(40%
for both parts) Aqueous cyanide
forms strong complexes with many metals.
The following two part problem concerns complexes with cadmium and zinc.
A. (20%) On the attached blank graph
template, sketch out a set of alpha curves (vs log[ CN- ]) for the Cadmium-cyanide
system. Point out they key graphical
features that you used to make this sketch (e.g. intersection points). Assume that the pH is high enough so that
there is no significant formation of HCN.
Use the following stability constants from Benjamin’s text. Note that these are all overall formation
constants.
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CdL |
Log b1 = 5.32 |
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CdL2 |
Log b2 = 10.37 |
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CdL3 |
Log b3 = 14.83 |
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CdL4 |
Log b4 = 18.29 |
B. (20%) Attached is an accurate graph of alpha
values (vs log[ CN- ]) for the Zinc-cyanide system. Using this graph determine the
species composition when the total zinc concentration is 0.1 mM and the total
cyanide concentration is 0.5 mM. Assume once again that the pH is high enough
so that there is no significant formation of HCN.
Solution to #2a
First calculate the k values from the
difference of the various betas:
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log value |
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log value |
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k1 = |
5.32 |
B1 = |
5.32 |
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k2 = |
5.05 |
B2 = |
10.37 |
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k3 = |
4.46 |
B3 = |
14.83 |
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k4 = |
3.46 |
B4 = |
18.29 |
Now plot these recognizing that the
intersection points occur where the free ligand concentration is equal to the k
value.
Solution to #2b
To clarify, alpha graph was made based on
the following constants:
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Constants |
Log(Step-wise "K") |
Log(Overall "Beta") |
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1st |
5.7 |
5.7 |
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2nd |
5.4 |
11.1 |
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3rd |
5.0 |
16.1 |
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4th |
3.5 |
19.6 |
Next we applied the complexation
equations that are based on the beta's and the free ligand concentration.
and
Now to solve this, we recognize that the
equilibrium based n-bar is:
And the mass balance based n-bar is:
where "M" is Zinc (Zn), and
"L" is cyanide (CN-).
Below are the “exact” values. What you read from the graph will be close,
but with only single to double digit precision.
3. Multiple Choice.
(20%) Answer all 10 of the following questions. Indicate which of the options is the best choice.
1. The sum of total acidity and total alkalinity on any given sample is equal to
a. the UV absorbance
b. twice the total carbonate
c. the value one
d. half of the hardness
e. zero
2. When a solution spontaneously absorbs CO2 from the atmosphere it:
a. resuts in higher total carbonate
b. drops in pH
c. approaches equilibrium
d. all of the above
e. none of the above
3. Phenolphthalein
a. is a hexadentate ligand
b. is rarely used because noone can spell it
c. complexes calcium forming an insoluble salt
d. is the drug of choice for malaria
e. changes from colorless to red as pH increases
4. H2CO3*:
a. is composed mostly
of aqueous CO2
b. is conservative in closed systems
c. is am ampholyte
d. all of the above
e. none of the above
5. Ion pairs:
a. are always charged
b. are larger than
c. are almost impossible to separate
d.
are outer-sphere complexes
6. The coordination number:
a. is usually 6 or less
b. is related to the charge on the central atom
c. is a function of the size of the ligand
d. all of the above
e. none fo the obove
7. The buffer intensity of the open carbonate system:
a. is independent of the alkalinity
b. is
c. is always higher than the pCO2
d. is at a minimum where the pH = pK1
e. is at a minimum where the pH = pK2
8. Detergent “builders” are used to:
a. help solubilize grease
b. complex trace metals
c. take hardness
cations from the surfactants
d. elevate the acidity
e. reduce the caloric content
9. EDTA
a. stands for ethylene dinitro tetraacetic acid
b. is most commonly used as a pH buffer
c. is a higly potent carcinogen
d. all of the above
e. none of the above
10. The
a. is a means of estimating alkalinity
b. describes the inverse proportionality of acidity to alkalinity
c. includes a number of books, such as The Chapman Report, and The Prize
d. provides a comprehensive description of ligand structure
e. follows the
increase in ligand affinity from Mn(II) to Cu(II)
Selected Acidity Constants (Aqueous Solution, 25°C, I = 0)
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NAME |
FORMULA |
pKa |
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Perchloric acid |
HClO4 = H+ + ClO4- |
-7 STRONG |
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Hydrochloric acid |
HCl = H+ + Cl- |
-3 |
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Sulfuric acid |
H2SO4= H+ + HSO4- |
-3 (&2) ACIDS |
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Nitric acid |
HNO3 = H+ + NO3- |
-0 |
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Hydronium ion |
H3O+ = H+ + H2O |
0 |
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Trichloroacetic acid |
CCl3COOH = H+ + CCl3COO- |
0.70 |
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Iodic acid |
HIO3 = H+ + IO3- |
0.8 |
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Bisulfate ion |
HSO4- = H+ +
SO4-2 |
2 |
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Phosphoric acid |
H3PO4 = H+ + H2PO4- |
2.15 (&7.2,12.3) |
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Citric acid |
C3H5O(COOH)3=
H+ + C3H5O(COOH)2COO- |
3.14 (&4.77,6.4) |
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Hydrofluoric acid |
HF = H+
+ F- |
3.2 |
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m-Hydroxybenzoic acid |
C6H4(OH)COOH = H+ + C6H4(OH)COO- |
4.06 (&9.92) |
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p-Hydroxybenzoic acid |
C6H4(OH)COOH = H+ + C6H4(OH)COO- |
4.48 (&9.32) |
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Nitrous acid |
HNO2 = H+ + NO2- |
4.5 |
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Acetic acid |
CH3COOH = H+ + CH3COO- |
4.75 |
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Propionic acid |
C2H5COOH = H+ + C2H5COO- |
4.87 |
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Carbonic acid |
H2CO3 = H+ + HCO3- |
6.35 (&10.33) |
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Hydrogen sulfide |
H2S = H+ + HS- |
7.02 (&13.9) |
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Dihydrogen phosphate |
H2PO4- = H+ + HPO4-2 |
7.2 |
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Hypochlorous acid |
HOCl = H+
+ OCl- |
7.5 |
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Boric acid |
B(OH)3 + H2O = H+ + B(OH)4- |
9.2 (&12.7,13.8) |
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Ammonium ion |
NH4+ = H+ + NH3 |
9.24 |
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Hydrocyanic acid |
HCN = H+
+ CN- |
9.3 |
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p-Hydroxybenzoic acid |
C6H4(OH)COO- = H+ + C6H4(O)COO-2 |
9.32 |
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Phenol |
C6H5OH = H+ + C6H5O- |
9.9 |
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m-Hydroxybenzoic acid |
C6H4(OH)COO- = H+ + C6H4(O)COO-2 |
9.92 |
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Bicarbonate ion |
HCO3- = H+ + CO3-2 |
10.33 |
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Monohydrogen phosphate |
HPO4-2 = H+ + PO4-3 |
12.3 |
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Bisulfide ion |
HS- = H+ + S-2 |
13.9 |
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Water |
H2O = H+ + |
14.00 |
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Methane |
CH4 = H+ + CH3- |
34 |
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