Monroe L. Weber-Shirk S chool of Civil and Environmental
Engineering Acid Rain Lake pH Probe Peristaltic Pump Acid Lake
Remediation
Slide 2
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!
Slide 3
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.
Fate of Strong Acids in the Environment Strong acids completely
dissociate in water 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 to the
hydrogen ions if it isnt pure water? ________________ 1 reactions
0.1 M pK=-1 pK 1 = -3, pK 2 =1.9
Slide 7
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,
bicarbonate, carbonic acid organic acids (A - ) acetic acid (pK =
4.7) When K A = [H + ] then [A - ] = [HA]
Slide 8
Carbonate System species definition 6.3 10.3 Dissociation
Constant
Slide 9
Acid Neutralizing Capacity (ANC) The ability to neutralize
(react with) acid ANC has units of _______________ or eq/L Possible
reactants moles of protons/L 2
Slide 10
Alpha Notation All species concentrations are related to the
hydrogen ion concentration Total carbonate species 1
Slide 11
Hydrogen Ion Concentration: The Master Variable (pH, pK 1, pK
2, C T )
Slide 12
pH Diagram Add acid to a carbonate solution at pH 9. What
happens?
Slide 13
ANC 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? 2.22 p(OH)= 14 - 2.22 = 11.78 pH= no carbonates
[H + ] is small
Slide 14
negative ANC: + or -! 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?
Slide 15
ANC Relationships At what pH is ANC=0? Which species dominate
when ANC = 0? Which species dominate when ANC < 0?
Slide 16
Where does ANC =0?
Slide 17
More Complications: Open to the Atmosphere Natural waters
exchange carbon dioxide with the atmosphere The total concentration
of carbonate species is affected by this exchange Henrys constant
Is ANC affected? _____ NO!
Slide 18
ANC Example (continued) Suppose we aerate the 3 mM 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, C
T =0.0057M)spreadsheets Solve for pH rather than for [H+] to make
it possible for goal seek to find a solution! graphical methods
(CEE 653) Beware of precision!
Slide 19
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 Completely Mixed Flow Reactor equation for our well mixed
lake ANC CTCT
Slide 20
Completely Mixed Flow Reactor Q, C in Q, __ C Mass in Mass out
= Increase of Mass in reactor V, C Hydraulic Residence Time Mass
balance
Slide 21
Completely Mixed Flow Reactor Equation applies to any
conservative species. C 0 = time zero concentration in reactor C in
= influent concentration C = concentration in the reactor as a
function of time Set up integration and effluent! What is C when t
is large? _______ C in
Slide 22
Three Equations for C T ! CMFR for conservative species. (True
if nonvolatile!) If in equilibrium with atmospheric CO 2... Can we
measure C T ? Assuming no carbonates in influent
Slide 23
What is the measured concentration of carbonates? Measured C T
? What is ANC?
Slide 24
Spreadsheet Hints Use names to make your equations easier to
understand Use Visual Basic for complex equations (see course
website) 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 required!
Slide 25
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 10 -1.5 mol/(L atm) Visual Basic Functions
for ANC ANC for a closed system ANC for an open system 10 -3.5
atm
Slide 26
Results? If your results dont jive where do you look? Units of
ANC? Units of C T ? How is t defined? ??
Slide 27
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
Slide 28
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
Slide 29
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 NaHCO 3 into a lake? Used CaCO
3 instead of NaHCO 3 ?
Slide 30
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 CaCO
3 (calcite or aragonite) MgCO 3 (magnesite) CaMgCO 3 (dolomite)
...
Slide 31
Lake and/or Watershed Remediation Add a soluble mineral such as
lime (CaO) or sodium bicarbonate (NaHCO 3 ) Application options
________________ meter into stream apply directly to lake spread on
watershed
Slide 32
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... Why not titrate to
target pH? f(C t )
Slide 33
Conservation of ANC V e = ___________ volume = volume of
titrant added so that ANC = 0 Need to find ANC T and V e T =
titrant S = sample equivalent
Slide 34
ANC of Titrant Why? ___________ N T = [H + ] 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. Could solve for Ve, but what is ANC?
Slide 35
ANC of Titrated Sample When is this true? ____________ For
pH
Gran Plot 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007
0.0008 0.0009 0123456 Volume of Titrant (mL) First Gran Function
VeVe Algorithm for choosing points to include? Minimum value of F 1
before it is worth attempting analysis? 3 points with F 1
>0.0001pH