“Acid Rain” “Lake” Lake Effluent pH Probe Peristaltic Pump pH Meter Acid Lake Remediation

“Acid Rain”

“Lake”

Lake Effluent

pH Probe

Peristaltic Pump

pH Meter

Acid Lake RemediationAcid Lake Remediation

Where Are We Going?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!

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?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.

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 FormationAcid Rain Formation

22 HOSOOHSO 22 HOSOOHSO

232 HOSOHOSO 232 HOSOHOSO

4223 SOHOHSO 4223 SOHOHSO

OHNONOHO 22 OHNONOHO 22

32 HNONOOH 32 HNONOOH

2SO2SO NONO

Combustion product precursors to acid rainCombustion product precursors to acid rain

ReactionsReactions

Strong acidsStrong acids

42SOH 42SOH Sulfuric acidSulfuric acid 3HNO3HNO Nitric acidNitric acid

Where is Acid Rain Falling?Where is Acid Rain Falling?

Fate of strong acids in the environment

Fate of strong acids in the environment

Strong acids completely dissociate in water Strong acids completely dissociate in water2

442 2 SOHSOH 2442 2 SOHSOH 33 NOHHNO 33 NOHHNO

If 0.1 M of nitric acid is added to 1 liter of pure water, what is the concentration of H+? _________

What is the pH? [px = -log(x)] ________

What else can happen when the hydrogen ion concentration changes? ________________

If 0.1 M of nitric acid is added to 1 liter of pure water, what is the concentration of H+? _________

What is the pH? [px = -log(x)] ________

What else can happen when the hydrogen ion concentration changes? ________________

11

reactionsreactions

0.1 M0.1 M

Fate of Strong Acids: ReactionsFate 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, bicarbonate, carbonic acid

organic acids acetic acid (pK = 4.7)

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, bicarbonate, carbonic acid

organic acids acetic acid (pK = 4.7)

Carbonate SystemCarbonate System

H H 23CO 23CO

3HCO3HCO)(2 aqCO )(2 aqCO

32COH 32COH

*2 3 2( ) 2 3aqH CO CO H COé ùé ù é ù= +ë û ë ûë û

*2 3 2( ) 2 3aqH CO CO H COé ùé ù é ù= +ë û ë ûë û

23

23

H COK

HCO

+ -

-

é ùé ùë ûë û=é ùë û

23

23

H COK

HCO

+ -

-

é ùé ùë ûë û=é ùë û

31*

2 3

H HCOK

H CO

+ -é ùé ùë ûë û=é ùë û

31*

2 3

H HCOK

H CO


3*32

1 HCOHCOH K 3*32

1 HCOHCOH K

233

2 COHHCO K 233

2 COHHCO K

3.102 10K 3.102 10K

3.61 10K 3.61 10K

2pK 2pK

1pK 1pK

speciesspecies

definitiondefinition

6.3

10.3

DissociationConstant

Acid Neutralizing Capacity (ANC)

Acid Neutralizing Capacity (ANC)

The ability to neutralize (react with) acid ANC has units of _______________ or eq/L Possible reactants

The ability to neutralize (react with) acid ANC has units of _______________ or eq/L Possible reactants

OH OH

CO3 2

CO3 2

HCO3

HCO3

moles of protons/Lmoles of protons/L

ANC [HCO3 ]+ 2[CO3

2 ]+[OH- ] - [H+ ]ANC [HCO3 ]+ 2[CO3

2 ]+[OH- ] - [H+ ]22

Alpha NotationAlpha Notation

All species concentrations are related to the hydrogen ion concentration

All species concentrations are related to the hydrogen ion concentration

* 22 3 3 3TC H CO HCO CO- -é ù é ù é ù= + +ë û ë û ë û

* 22 3 3 3TC H CO HCO CO- -é ù é ù é ù= + +ë û ë û ë û Total carbonate speciesTotal carbonate speciesTC TC

11 210 210

*2 3 0 TH CO Caé ù=ë û

*2 3 0 TH CO Caé ù=ë û 3 1 THCO Ca-é ù=ë û3 1 THCO Ca-é ù=ë û

23 2 TCO Ca-é ù=ë û


)( 210 TT CC )( 210 TT CC

1 2( 2 ) wT

KANC C H

Ha a +

+é ù= + + - ë ûé ùë û

1 2( 2 ) wT

KANC C H

Ha a +

+é ù= + + - ë ûé ùë û

Hydrogen Ion Concentration:The Master Variable

Hydrogen Ion Concentration:The Master Variable

][][1

1

2

2110

H

KK

H

K

][][1

1

2

2110

H

KK

H

K

1

1

2

2

H

H

KCANC w

T )2( 21

H

H

KCANC w

T )2( 21

fANC fANC (pH, pK1, pK2, CT)(pH, pK1, pK2, CT)

31*

2 3

H HCOK

H CO


31*

2 3

H HCOK

H CO


31*

2 3

HCOK

H H CO

-

+

é ùë û=é ù é ùë û ë û

31*

2 3

HCOK

H H CO

-

+


232

3

COK

H HCO

-

+ -


232

3

COK

H HCO

-

+ -


pH DiagrampH Diagram

0.01

0.1

1

4 5 6 7 8 9 10 11 12 13 14

pH

alpha0

alpha1

alpha2



3 1 THCO Ca-é ù=ë û3 1 THCO Ca-é ù=ë û2

3 2 TCO Ca-é ù=ë û2


2pK2pK1pK1pK

Add acid to a carbonate solution at pH 9. What happens?

ANC ExampleANC Example

Suppose we add 3 mM Ca(OH)2 to distilled water. What is the ANC?

What is the resulting pH if the system is closed to the atmosphere?

Suppose we add 3 mM Ca(OH)2 to distilled water. What is the ANC?

What is the resulting pH if the system is closed to the atmosphere?

12

3

14w 1.67x10

6x10

10

OH

KH

12

3

14w 1.67x10

6x10

10

OH

KH

23 3ANC HCO 2 CO OH H- - - +é ù é ù é ù é ù= + + -ë û ë û ë û ë û


3ANC OH 6x10- -é ù= =ë û3ANC OH 6x10- -é ù= =ë û

2.222.22p(OH)=p(OH)=

14 - 2.22 = 11.7814 - 2.22 = 11.78pH=pH=

negative

ANC

ANC = capacity to react with H+ minus the concentration of H+

ANC can be positive or __________ 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?

HCO3 H H2CO3

*

CO3 2 2H H2CO3

*

OH H H2O

10 L0.1 meq

L5 L

-1 meqL

10 L +5 L

a f a fFH IK FH IK

4 meq15 L

meq0.267

L=-

ANC relationshipsANC relationships

At what pH is ANC=0? Which species dominate when ANC = 0?

Which species dominate when ANC < 0?

At what pH is ANC=0? Which species dominate when ANC = 0?

Which species dominate when ANC < 0?

][H-][H

K+)2(CANC +w

21T

][H-][H

K+)2(CANC +w

21T

+3[H ] HCO-é ù=ë û

+3[H ] HCO-é ù=ë û

+[H ]+[H ]



More Complications: Open to the AtmosphereMore Complications:

Open to the Atmosphere

Natural waters exchange carbon dioxide with the atmosphere

Natural waters exchange carbon dioxide with the atmosphere

22( )aq CO HCO P Ké ù=ë û 22( )aq CO HCO P Ké ù=ë û

HCOT KPC20 HCOT KPC20

0

2

HCO

T

KPC

0

2

HCO

T

KPC

H

H

KKPANC wHCO )2( 21

0

2

H

H

KKPANC wHCO )2( 21

0

2

The total concentration of carbonate species is affected by this exchangeThe total concentration of carbonate species is affected by this exchange

ANC example (continued)ANC example (continued)

Suppose we aerate the Ca(OH)2 solution. What happens to the pH?

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)

graphical methods (CEE 653)

Suppose we aerate the Ca(OH)2 solution. What happens to the pH?

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)

graphical methods (CEE 653)

][-][

+)2( +21

0

2 HH

Kaa

a

KPANC wHCO

][-

][+)2( +

21

0

2 HH

Kaa

a

KPANC wHCO

Beware of precision!Beware of precision!

Open vs. Closed to the Atmosphere

What is conserved in an open (volatile) system? _____________

What is conserved in a closed (nonvolatile) system? _____________

For conservative species we can use the _____ equation

ANCANC

ANCANC CTCT

CMFRCMFR

Completely Mixed Flow Reactor

Equation applies to any conservative species. C0 = time zero concentration in reactor

Cin = influent concentration

C = concentration in the reactor as a function of time

eett

0in C1CC

Three equations for ANC!Three equations for ANC!

CMFR for conservative species. (True whether volatile or nonvolatile!)

If Nonvolatile...

What is CT?

If Volatile...

CMFR for conservative species. (True whether volatile or nonvolatile!)

If Nonvolatile...

What is CT?

If Volatile...

H

H w

T

KaaCANC

H

H w

T

KaaCANC

HH

2 wHCO Kaa

a

KPANC

HH

2 wHCO Kaa

a

KPANC

ee-t/θ-t/θ

in ANC - ANCANC 01 ee-t/θ-t/θ

in ANC - ANCANC 01

e-t/θ

TT C C 0 e

-t/θ

TT C C 0

Spreadsheet Hints

Use names to make your equations easier to understand

Use Visual Basic for complex equations Completely Mixed Flow Reactor (CMFR)

alphas

Function CMFR(Influent, t, theta, initial)CMFR = Influent * (1 - Exp(-t / theta)) + initial * (Exp(-t / theta))End Function

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

Function ANCopen(pH)ANCopen = ANCclosed(pH, invp(5) / alpha0CO2(pH))End Function

Function ANCclosed(pH, Ct)ANCclosed = Ct * (alpha1CO2(pH) + 2 * alpha2CO2(pH)) + 10 ^ (-14) / invp(pH) - invp(pH)End Function

CT

PCO2KH

0

ANC CT(1 22)+

Kw

[H ]- [H+]

10-1.5 mol/(L atm)10-1.5 mol/(L atm)

Visual Basic Functions for ANCVisual Basic Functions for ANC

ANC for a closed system

ANC for an open system

ANC for a closed system

ANC for an open system

10-3.5 atm10-3.5 atm

Results?Results?

-0.5

0

0.5

1

1.5

2

0 400 800 1200

time (s)

AN

C (

meq

/L)

Conservative ANCNon-volatileVolatileANC measured

Measuring ANC: Gran TitrationMeasuring 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...

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 ANCConservation of ANC

STTSSSTT ANCVVANCVANCV STTSSSTT ANCVVANCVANCV

0ANCsuch that VV STTe 0ANCsuch that VV STTe

0ANCVANCV SSTe 0ANCVANCV SSTe

T

SSe

ANC

ANCV-=V

T

SSe

ANC

ANCV-=V

S

TeS

V

ANCV-=ANC

S

TeS

V

ANCV-=ANC

Ve= ___________ volume = volume of titrant added so that ANC = 0

Ve= ___________ volume = volume of titrant added so that ANC = 0

Need to find ANCT and VeNeed to find ANCT and Ve

T = titrantS = sampleT = titrantS = sample

equivalentequivalent

ANC of TitrantANC of Titrant

TT NANC TT NANC

STTSTeTT ANCVVNVNV- STTSTeTT ANCVVNVNV-

STTSTeT ANCVVNVV STTSTeT ANCVVNVV

Why? ___________Why? ___________

STTSSSTT ANCVVANCVANCV STTSSSTT ANCVVANCVANCV

NT = [H+]NT = [H+]

S

TeS

V

ANCV-=ANC

S

TeS

V

ANCV-=ANC

ANC conservation

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 SampleANC of Titrated Sample

HVVNVV TSTeT HVVNVV TSTeT

When is this true? ____________When is this true? ____________ HANC ST HANC ST

STTSTeT ANCVVNVV STTSTeT ANCVVNVV

T

TSTe

N

VVHVV

T

TSTe

N

VVHVV

For pH << pK1For pH << pK1

Finally! An equation for equivalent volume!

Gran FunctionGran 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.

Define F1 as:

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.

Define F1 as:

S

eT

S

TT

S

TS

V

VN

V

VNH

V

VV S

eT

S

TT

S

TS

V

VN

V

VNH

V

VV

][H1

S

TS

VVV

F ][H1

S

TS

VVV

F

Gran Plot

ybmxy

0V

Nm t

00

1

V

VNV

V

NF et

tt

e

t

etyx V

NV

VVN

m

bb

0

0

00.00010.00020.00030.00040.00050.00060.00070.00080.0009

0 1 2 3 4 5 6

Volume of Titrant (mL)

Fir

st G

ran

Fu

nct

ion

0V

VNb et

y

Ve

Gran Plot using CompumetGran Plot using Compumet

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+].

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+].

abscissa intercept of Veabscissa intercept of Ve

slope = slope = o

t

V

N

o

t

V

N

Calculating ANCCalculating ANC

The ANC is obtained from the equivalent volume.

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

The ANC is obtained from the equivalent volume.

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

0

· ANC

V

NV te

HOHCO2HCOANC 233 HOHCO2HCOANC 233

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 LakesFossil 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

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 SourcesAcid Rain Precursor Sources

NAPAP Emissions Inventory, Nov. 1989.

Utilities

Transport

Ind/Mfg Process

Ind. Combustion

OtherCombustion

Other

SO2

Utilities

NOxUtilities

Transport

Acid Rain Precursor ControlAcid Rain Precursor Control

Emission controls neutralize acid at source (scrubbers)

Taller stacks combustion products can travel 1000+ km down wind regions suffer pollutant damage sends pollutants further away, but does not

mitigate problem Allowances

Emission controls neutralize acid at source (scrubbers)

Taller 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?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)

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”

“Lake”

Lake Effluent

pH Probe

Peristaltic Pump

pH MeterSoil Column

Acid Rain ExperimentAcid Rain Experiment

Acid Precipitation and Remediation of Acid Lakes

Acid Precipitation and Remediation of Acid Lakes

Sources of ANCSources 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)

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?

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 ANC=f(_______________________)

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 ANC=f(_______________________)minerals in watershedminerals in watershed

Lake and/or Watershed Remediation

Add a soluble mineral such as lime (CaO) or sodium bicarbonate (NaHCO3)

Application options ________________ ________________ ________________

meter into streammeter into stream

apply directly to lakeapply directly to lake

spread on watershedspread on watershed

“Acid Rain” “Lake” Lake Effluent pH Probe Peristaltic Pump pH Meter Acid Lake Remediation

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