Acid Lake Remediation
pH Probe
“Acid Rain”
Peristaltic
Pump
“Lake”
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Where Are We Going?
 Source of Acid Rain
 Fate of strong acids in the environment
 Reactions
 Carbonate System
 Dissociation constants
 p notation
 Alpha notation
 Acid Neutralizing Capacity
 Defined
 Measured – Gran Plot
 A conservative property!
What is the Acid Source?
 Coal fired electric plants (and other fossil fuels)
 Gaseous emissions of sulfur oxides and nitrogen oxides +
water + sunlight form sulfuric acid and nitric acid
 Tall stacks send pollutants into the troposphere
 Prevailing winds carry pollutants from Midwestern
industrialized areas into New England and Canada.
 About half of the acidity in the atmosphere falls back to
earth through dry deposition as gases and dry particles.
 The combination of acid rain plus dry deposited acid is
called acid deposition.
Acid Rain Formation
Combustion product precursors to acid rain
NO
SO2
Reactions
SO2  OH   HOSO2 
HO2  NO  NO2  OH 
HOSO2   SO3  HO2 
SO3  H 2O  H 2 SO4
OH   NO2  HNO3
Strong acids
H 2 SO4
Sulfuric acid
HNO3
Nitric acid
Where is Acid Rain Falling?
Fate of Strong Acids in the
Environment
Strong acids completely dissociate in water
pK=-1
HNO3  H   NO3
pK1= -3, pK2=1.9
H 2 SO4  2 H   SO4 2
If 0.1 M of nitric acid is added to 1 liter of pure
water, what is the concentration of H+? _________
0.1 M
1
 What is the pH? [px = -log(x)] ________


What else can happen to the hydrogen ions if it
reactions
isn’t pure water? ________________
Fate of Strong Acids: Reactions
Weak acids/bases can react with the added
H+ and reduce the final concentration of H+
Examples of weak acids and bases in the
environment:
carbonates
HCO3
H 2CO3
CO3 2

carbonate, bicarbonate, carbonic acid
+
HA
®
H
+
A
organic acids (A )
acetic acid (pK = 4.7)
When KA = [H+] then [A-] = [HA]
+
é
ùé
ù
H
A
ë
ûë
û
KA =
HA
Carbonate System
species
definition
H
CO2( aq )
K1
pK1  6.3
HCO3  H   CO3 2
K2
K 2  1010.3
HCO3
CO3 2
*
é
H
CO
ë 2 3ù
û= é
ëH 2CO3 ù
û
ëCO2( aq ) ù
û+ é
H 2CO3*  H   HCO3
K1  10 6.3
H 2CO3
pK 2  10.3
+
é
ùé
H
HCO
3 ù
ë ûë
û = K Dissociation
1
*
Constant
é
ù
H
CO
2
3
ë
û
+
-2
é
ùé
H
CO
ë ûë 3 ù
û= K
2
é
ù
HCO
3 û
ë
Acid Neutralizing Capacity
(ANC)
The ability to neutralize (react with) acid
moles of protons/L or
ANC has units of _______________
eq/L
Possible reactants
HCO 3
CO32

3
OH
2
3

ANC  [HCO ]+ 22[CO ]+[OH ]-[H ]
-
+
Alpha Notation
 All species concentrations are related to the
hydrogen ion concentration
*
-2
ù
é
ù
é
CT = é
H
CO
+
HCO
+
CO
3 û ë
3 ù
ë 2 3û ë
û
*
é
H
CO
ë 2 3 ù=
û a 0CT
é
HCO
3 ù=
ë
û a 1CT
CT  CT ( 0  1   2 )
CT  Total carbonate species
-2
é
CO
ë 3 ù=
û a 2CT
 0  1   2  1
Kw
+
é
ù
ANC = CT (a 1 + 2a 2 ) +
H
ë
û
+
é
ù
H
ë û
Hydrogen Ion Concentration:
The Master Variable
0 
1
1
1
K1

K1 K 2
[ H  ] [ H  ]2


1
*
-2
é
ëH 2CO3 ù
û+ é
ëHCO3 ù
û+ é
ëCO3 ù
û
*
*
*
é
ëH 2CO3 ù
û é
ëH 2CO3 ù
û é
ëH 2CO3 ù
û
é
HCO ù
K1
ë
û
=
+
*
é
ù
é
H
H
CO
ë û ë 2 3ù
û
3

  
=

+
é
ùé
H
HCO
3 ù
ë ûë
û= K
1
*
é
ù
H
CO
ë 2 3û
-2
é
CO
K2
3 ù
ë
û
=
+
é
ù
é
H
HCO
3 ù
ë û ë
û
  

 2   
    


    
ANC  CT (1  2 2 ) 
Kw
H 

ANC  f (pH, pK1, pK2, CT)
 H  
pH Diagram
4
5
6
7
8
9
10 11 12 13 14
1
alpha0
alpha1
alpha2
 0.1
0.01
pK1
pH
pK 2
*
é
H
CO
ë 2 3 ù=
û a 0CT
é
HCO
3 ù=
ë
û a 1CT
-2
é
CO
ë 3 ù=
û a 2CT
Add acid to a
carbonate
solution at pH 9.
What happens?
ANC Example
no carbonates
 Suppose we add 3 ANC = éëHCO3- ùû+ 2 éëCO3- 2 ùû+ éëOH - ùû- éëH + ùû
mM Ca(OH)2 to
+] is small
-3
[H
é
ù
ANC
=
OH
=
6x10
ë
û
distilled water.
What is the ANC?
p(OH)= 2.22
 What is the
14
K
10
resulting pH if the
w

H  

 1.67x10 12
system is closed
OH   6x10 3
to the
atmosphere?
pH= 14 - 2.22 = 11.78
ANC: + or -!
 ANC = capacity to react with H+
HCO 3  H   H 2 CO *3
minus the concentration of H+

*
CO 2

2H

H
CO
3
2
3
 ANC can be positive or __________
negative
OH   H   H 2 O
 ANC is conservative
 Example: 10 liters of a solution with an ANC of
0.1 meq/L is mixed with 5 liters of a solution with
an ANC of -1 meq/L. What is the final ANC?
0.1 meq I
-1 meq I
F
F
a10 LfH L Ka5 LfH L K 4 meq
meq
=
0.267

10 L + 5 L
15 L
L
ANC Relationships
At what pH is ANC=0?
Which species dominate when ANC = 0?
-2
+
ù
é
ù
é
ù
é
ANC = é
HCO
+
2
CO
+
OH
H
3û
ë
ë 3 û ë
û ë ù
û
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
[H  ]
[H + ] = é
HCO
3ù
ë
û
+
- [H ]
concentration (moles/L)
ANC  CT (1  2 2 ) +
Kw
1
H2CO3
HCO3
CO3
H+
OH-
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
pH
Which species dominate when ANC < 0?
[H + ]
Where does ANC =0?
-2
+
ù
é
ù
é
ù
é
ANC = é
HCO
+
2
CO
+
OH
H
3û
ë
ë 3 û ë
û ë ù
û
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
concentration (moles/L)
1
H2CO3
HCO3
CO3
H+
OH-
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
pH
More Complications:
Open to the Atmosphere
Henry’s constant
Natural waters exchange
carbon dioxide with the
atmosphere
é
ëCO2( aq ) ù
û = PCO2 K H
é
ëCO2( aq ) ù
û = a 0CT
The total concentration of carbonate
species is affected by this exchange
a 0CT = PCO2 K H
Is ANC affected? _____
NO!
ANC 
PCO K H
2
0
(1  2 2 ) 
CT 
Kw
H 

 H  
PCO K H
2
0
ANC Example (continued)
 Suppose we aerate the 3 mM Ca(OH)2 solution.
What happens to the pH?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1
2
(a1  2a2 ) +
a0
Kw

+
- [H ]
[H ]
concentration (moles/L)
ANC 
PCO K H
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
 All the alphas are functions of pH and it is not
possible to solve explicitly for [H+].
 Solution techniques
 numerical methods - spreadsheets - goal seeking
(pH=9, CT=0.0057M)
 Solve for pH rather than for [H+] to make it possible for goal
seek to find a solution! Beware of precision!
 graphical methods (CEE 653)
H2CO3
HCO3
CO3
H+
OH-
0.1
pH
Open vs. Closed to the
Atmosphere
What is conserved in an open (volatile)
ANC
system? _____________
What is conserved in a closed (nonvolatile)
CT
system? _____________
ANC
For conservative species we can use the
Completely Mixed Flow Reactor equation
for our well mixed lake
Completely Mixed Flow Reactor
C
Q, __
Q, Cin
V, C
Mass in – Mass out = Increase of Mass in reactor
dC
QCin - QC = V
dt
V
dC
dt =
Q (Cin - C )
Mass balance
V
=q
Q
Hydraulic
=Residence
Time
Completely Mixed Flow Reactor
t
C
dC
dt = q ò
ò
C - C)
0
C0 ( in
(
C = Cin 1 -
e
-t
q
Set up integration
)+C e
-t
q
0
Cin
What is C when t is large? _______
 Equation applies to any conservative species.
 C0 = time zero concentration in reactor
 Cin = influent concentration and effluent!
 C = concentration in the reactor as a function of time
Three Equations for CT!
CMFR for conservative species. (True if
nonvolatile!)
CT  CT e
-t/θ
0
Assuming no carbonates in influent
If in equilibrium with atmospheric CO2...
CT 
PCO2 K H
a
Can we measure CT?
What is the measured concentration
of carbonates?
Measured CT?
ANC  CT a  a  
CT 
Kw
 H  
H 

Kw



ANC 

H


 H 
 a  a 
What is ANC?
 e  ANC e
ANC  ANCin  1 -
-t/θ
-t/θ
0
Spreadsheet Hints
required!
Use names to make your equations easier to
understand
Use Visual Basic for complex equations
(see course website)
Completely Mixed Flow Reactor (CMFR)
Function CMFR(Influent, t, theta, initial)
CMFR = Influent * (1 - Exp(-t / theta)) + initial * (Exp(-t / theta))
End Function
alphas
Function alpha0CO2(pH)
alpha0CO2 = 1 / (1 + 10 ^ (-6.3) / invp(pH) + 10 ^ (-6.3) * 10 ^ (-10.3) / invp(pH) ^ 2)
End Function
Function invp(x)
invp = 10 ^ (-x)
End Function
Visual Basic Functions for ANC
ANC for a closed
system
Kw
ANC  C T (1  2 2 ) +  - [H + ]
[H ]
Function ANCclosed(pH, Ct)
ANCclosed = Ct * (alpha1CO2(pH) + 2 * alpha2CO2(pH)) + 10 ^ (-14) / invp(pH) - invp(pH)
End Function
ANC for an open
system
10-3.5 atm
Function ANCopen(pH)
ANCopen = ANCclosed(pH, invp(5) / alpha0CO2(pH))
End Function
CT 
10-1.5 mol/(L atm)
PCO K H
2
0
Results?
ANC  CT a  a  
Total carbonates (mmol/L)
 If your results don’t
jive where do you
look?
 Units of ANC?
 Units of CT?
 How is t defined?
q?
2
Kw
Ct conservative
1.5
Ct equilibrium
1
0.5
0
0
0.5
1
time (t/q)
 H  
H 

Ct measured
1.5
Acid Rain Lab Report
 Checklist at website
 Spreadsheet report (will write a full combined
report after measuring ANC next week)
 Strong recommendation: finish the lab by Monday
night
 Use your time efficiently!
 What is the ANC of the acid rain?
 Assume pH = 3.0, but there is some uncertainty
 Note any differences between lab manual
guidelines and what happened in the lab
Acid Rain Lab Report
 Make sure you understand which assumptions might be
incorrect
 Mass conservation
 No exchange with the atmosphere
 Equilibrium with the atmosphere
 High expectations for
 Well designed spreadsheets
 Thoughtful analysis
 Work done with pride
 Alternate analysis: solve for pH as f(t) based on both
models and compare with measured pH
Reflections
Our lake was idealized and missing many of
the interesting (and confounding) factors of
real lakes
What would happen if I
Dumped 1000 lb scoops of NaHCO3 into a
lake?
Used CaCO3 instead of NaHCO3?
What Determines Lake
Susceptibility to Acidification?
Acidification = f(acid inputs, ANC)
Acid inputs = f(power plants, cars, wind
currents, mine tailings)
Acid Neutralizing Capacity = f(?)
Carbonates obtained from dissolution of
minerals such as
CaCO3 (calcite or aragonite)
MgCO3 (magnesite)
CaMgCO3 (dolomite)
...
Lake and/or Watershed
Remediation
Add a soluble mineral such as lime (CaO)
or sodium bicarbonate (NaHCO3)
Application options
spread on watershed
________________
meter into stream
________________
apply directly to lake
________________
Measuring ANC: Gran Titration
The sample is titrated with a strong acid to
"cancel" the sample ANC
At the equivalence point the sample ANC is
zero
Further titration will result in an increase in
the number of moles of H+ equal to the
number of moles of H+ added.
Use the fact that ANC is conservative...
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
concentration (moles/L)
Why not titrate to target pH? f(Ct)
1
H2CO3
HCO3
CO3
H+
OH-
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
pH
Conservation of ANC
VT ANC T  VSANCS  VS  VT ANC T S
Ve  VT such that ANC T S  0
equivalent volume
Ve= ___________
= volume of titrant
added so that ANC = 0
Ve ANC T  VSANCS  0
-V ANCS
Ve = S
ANCT
ANCS =
T = titrant
S = sample
- Ve ANC T
Need to find ANCT and Ve
VS
ANC of Titrant
ANC T   N T
+]
N
=
[H
T
Why? ___________
VT ANC T  VSANCS  VS  VT ANC T  S
- VT N T  Ve N T  VS  VT ANC T  S
 VT  Ve N T  VS  VT ANC T  S
ANC conservation
ANCS =
- Ve ANC T
VS
Could solve for Ve,
but what is ANC?
This equation is always true, but when do we know what
ANC is? When
_______________________________________
pH is so low that no reactions are occurring.
ANC of Titrated Sample
 VT  Ve NT  VS  VT  ANCT  S
+
ANCT +S @- é
H
ë ù
û
For pH << pK1
When is this true? ____________
+
- (VT - Ve ) NT = - (VS + VT ) é
H
ë ù
û
+
é
ù
H
(VS + VT )
ë
û
Ve = VT NT
Finally! An equation for equivalent volume!
Gran Function
A better measure of the equivalent volume
can be obtained by rearranging the equation
so that linear regression on multiple titrant
volume - pH data pairs can be used.
+
é
H
VS  VT   NTVT NTVe
ë ù
û(VS + VT )
Ve = VT -
NT
Define F1 as:
H  
VS
VS  VT 
F1 
[H ]
VS

VS
VS
Nt
NtVe
F1 = Vt Vs
Vs
y  mx  by
Nt
m=
Vs
NtVe
by = Vs
First Gran Function
Gran Plot
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
0
0
1
- by
N tVeVs
bx =
=
= Ve
m
Vs N t
2
3
4
5
6
Volume of Titrant (mL)
Ve
Minimum value of F1 before it is worth attempting analysis?
pH<4.3
3 points with F1>0.0001
Algorithm for choosing points to include?
Gran Plot using pH
slope =
Nt
Vs
abscissa intercept of Ve
F1 plotted as a function of Vt. The abscissa has units of mL
of titrant and the ordinate is a Gran function with units of
[H+].
Calculating ANC
The ANC is obtained from the equivalent
volume.
ANC =
Ve ·Nt
Vs
The ANC of the acid rain can be estimated
from its pH. At low pH (< pK1) most of the
carbonates will be carbonic acid and thus
for pH below about 4.3 the ANC equation
simplifies to
-2
+
ù
é
ù
é
ù
é
ANC = é
HCO
+
2
CO
+
OH
H
3û
ë
ë 3 û ë
û ë ù
û
Titration Technique
Accuracy is important
Titrate with digital pipette ________________
Measure pH before first addition of titrant
Measure pH after each addition of titrant
After ANC is consumed Gran function will be
linear
What should the incremental titrant volume
be?
Techniques to speed up titration
Titrant Incremental Volume
None except your patience
Minimum? _______________________
Maximum?
Constraints?
Number of data points _____________
3 or more
Before reaching pH___
3
How do we determine titrant volume?
H+ is conservative!
Pre Lab Question
 Compare the ability of Cayuga lake and Wolf pond (an
Adirondack lake) to withstand an acid rain runoff event
(from snow melt) that results in 20% of the original lake
water being replaced by acid rain. The acid rain has a pH
of 3.5 and is in equilibrium with the atmosphere. The ANC
of Cayuga lake is 1.6 meq/L and the ANC of Wolf Pond is
70 µeq/L. Assume that carbonate species are the primary
component of ANC in both lakes, and that they are in
equilibrium with the atmosphere. What is the pH of both
bodies of water after the acid rain input? Remember that
ANC is the conservative parameter (not pH!).
What went wrong?
Absorbance v. Concentration of Methylene Blue
1.2
y = 0.2056x + 0.0327
R2 = 0.9994
Absorbance
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
Concentration (mg/L)
Create hypotheses and test them!
5
Improve this graph?
extinction coefficient v. wavelength
0.3
E (L/mgcm)
0.25
mg/L 1
0.2
mg/L 2
mg/L 3
0.15
mg/L 4
mg/L 5
0.1
0.05
0
190
290
390
490
590
wavelength (nm)
690
790
Better, what is missing?
Epsilon v. Wavelength
0.25
0.2
epsilon
1 mg/L
0.15
2 mg/L
3 mg/L
4 mg/L
0.1
5 mg/L
0.05
0
250
350
450
550
650
750
wavelength (nm)
Figure 2: Calculated epsilon values at different wavelengths for varied concentrations of methylene blue solution.
Fundamentals lab
Graphs with lots of data (done)
Standard deviation has units!
Dependency