Transcript Document 7256091

Acid Lake Remediation
pH Probe
“Acid Rain”
Peristaltic
Pump
“Lake”
Lake Effluent
pH Meter
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!

Where is the acid coming from?






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
HNO3  H   NO3
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 when the hydrogen ion
concentration changes? ________________
reactions
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
 carbonate,
 organic
 acetic
bicarbonate, carbonic acid
acids
acid (pK = 4.7)
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
 ANC has units of _______________
moles of protons/L or eq/L
 Possible reactants
HCO

3
2
3
CO

3
2
3
OH

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


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
Suppose we add 3 ANC = éëHCO3- ùû+ 2 éëCO3- 2 ùû+ éëOH - ùû- éëH + ùû
mM Ca(OH)2 to
-3
é
ù
ANC
=
OH
=
6x10
distilled water.
ë
û
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
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
ANC  CT (1  2 2 ) +
Kw
[H  ]
- [H + ]
[H + ] = é
HCO
3ù
ë
û
 Which
species dominate when ANC < 0?
[H + ]
More Complications:
Open to the Atmosphere
 Natural
waters exchange
carbon dioxide with the
atmosphere
é
ëCO2( aq ) ù
û = PCO2 K H
 0CT  PCO K H
2
The total concentration of carbonate
species is affected by this exchange
CT 
ANC 
PCO K H
2
0
(1  2 2 ) 
Kw
H 

 H  
PCO K H
2
0
ANC example (continued)
 Suppose
we aerate the Ca(OH)2 solution.
What happens to the pH?
ANC 
PCO K H
2
(a1  2a2 ) +
a0
 All
Kw
[H  ]
- [H + ]
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) Beware of precision!
 graphical
methods (CEE 653)
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
_____
CMFR equation
Completely Mixed Flow Reactor
 e  C e
C  Cin 1 
 Equation
t
t


0
applies to any conservative
species.
 C0
= time zero concentration in reactor
 Cin = influent concentration
 C = concentration in the reactor as a function
of time
Three equations for ANC!
 CMFR
for conservative species. (True
whether volatile or nonvolatile!)
 e  ANC e
ANC  ANCin  1  If
-t/θ
-t/θ
0
Nonvolatile...
ANC  CT a  a  
 What
is CT?
CT  CT e
Kw
 H  
H 

-t/θ
0
 If
Volatile...
ANC 
PCO K H
2
a
 a  a  
Kw
 H  
H 

Spreadsheet Hints
 Use
names to make your equations easier to
understand
 Use Visual Basic for complex equations
 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?
2
Conservative ANC
Non-volatile
Volatile
ANC measured
ANC (meq/L)
1.5
1
0.5
0
-0.5
0
400
800
time (s)
1200
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...
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
Ve =
- VS ANCS
ANCS =
T = titrant
S = sample
- Ve ANC T
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
ANC conservation
ANCS =
- Ve ANC T
VS
 VT  Ve N T  VS  VT ANC T  S
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  H  
For pH << pK1
When is this true? ____________
 VT  Ve NT  VS  VT H  

H V


Ve  VT
S
 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.
VS  VT  
H
VS
 Define


NTVT
VS
F1 as:

NTVe
VS
VS  VT 
F1 
[H ]
VS
Gran Plot
Vt 
N tVe
V0
First Gran Function
F1 
Nt
V0
y  mx  by
m 
Nt
by  
V0
V0
bx 
 by
m
N tVe

N tVeV0
V0 N t
 Ve
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
0
0
1
2
3
4
5
Volume of Titrant (mL)
Ve
6
Gran Plot using Compumet
slope =
Nt
Vo
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.
V ·N
ANC 
 The
e
t
V0
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
ANC  HCO 3   2CO 3 2   OH    H  
Titration Technique
 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
Fossil Fuels to Acid Lakes
Source of acid rain
 Fate of strong acids in the environment
 Carbonate species and reactions
 Definition of acid neutralizing capacity
 Equilibrium with atmospheric carbon dioxide
 Lake susceptibility to acidification
 Lake remediation
 ANC measurements

Acid Rain Precursor Sources
SO2
NOx
Utilities
Transport
Ind/Mfg Process
Ind. Combustion
Other
Combustion
Utilities
Other
Transport
NAPAP Emissions Inventory, Nov. 1989.
Utilities
Acid Rain Precursor Control
 Emission
controls
 neutralize
 Taller
acid at source (scrubbers)
stacks
 combustion
products can travel 1000+ km
 down wind regions suffer pollutant damage
 sends pollutants further away, but does not
mitigate problem
 Allowances
What Are Allowances?
An allowance authorizes a unit within a utility or
industrial source to emit one ton of SO2 during a
given year or any year thereafter.
 Allowances are fully marketable commodities.
Once allocated, allowances may be bought, sold,
traded, or banked for use in future years.
Allowances may not be used for compliance prior
to the calendar year for which they are allocated.
 8.95 million tons of SO2 annually (250 Gmole of
H+/year)

Acid Rain Experiment
pH Probe
“Acid Rain”
Peristaltic
Pump
“Lake”
Soil Column
Lake Effluent
pH Meter
Acid Precipitation and
Remediation of Acid Lakes
Sources of ANC

Carbonates obtained from dissolution of minerals
such as
CaCO3 (calcite or aragonite)
 MgCO3 (magnesite)
 CaMgCO3 (dolomite)
 ...


Minerals that are insoluble or of very limited
solubility don’t contribute much to ANC
granite (very insoluble silicates)
 quartz (very insoluble silicon dioxide)

What determines lake
susceptibility to acidification?
Acidification = f(acid inputs, ANC)
 Acid inputs = f(power plants, wind currents...)
 Acid Neutralizing Capacity = f(?)


Suppose only water input into lake is precipitation



only source of ANC is minerals on lake bottom
lake will soon have pH of acid rain
Suppose only water input is through groundwater


soluble minerals will neutralize acid
minerals in watershed
ANC=f(_______________________)
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
 ________________