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Acid Lake Remediation pH Probe Peristaltic Pump “Acid Rain” “Lake”
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 Reactions Strong acids Sulfuric acid Nitric acid
Fate of Strong Acids in the Environment • Strong acids completely dissociate in water pK1= -3, pK2=1.9 pK=-1 • 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 isn’t pure water? ________________ 0.1 M 1 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, bicarbonate, carbonic acid • organic acids (A-) • acetic acid (pK = 4.7) When KA = [H+] then [A-] = [HA]
Carbonate System species definition Dissociation Constant 6.3 10.3
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
Alpha Notation • All species concentrations are related to the hydrogen ion concentration Total carbonate species 1
Hydrogen Ion Concentration:The Master Variable (pH, pK1, pK2, CT)
pH Diagram Add acid to a carbonate solution at pH 9. What happens?
p(OH)= pH= ANC Example no carbonates • 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? [H+] is small 2.22 14 - 2.22 = 11.78
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? negative
ANC Relationships • At what pH is ANC=0? • Which species dominate when ANC = 0? • Which species dominate when ANC < 0?
More Complications: Open to the Atmosphere Henry’s constant • Natural waters exchange carbon dioxide with the atmosphere The total concentration of carbonate species is affected by this exchange Is ANC affected? _____ NO!
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, CT=0.0057M) • 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!
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 CT ANC
Completely Mixed Flow Reactor C Q, __ Q, Cin V, C Mass in – Mass out = Increase of Mass in reactor Mass balance Hydraulic Residence Time
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 Set up integration Cin What is C when t is large? _______ and effluent!
Three Equations for CT! • CMFR for conservative species. (True if nonvolatile!) • If in equilibrium with atmospheric CO2... • Can we measure CT? Assuming no carbonates in influent
What is the measured concentration of carbonates? • Measured CT? • What is ANC?
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) • alphas Function CMFR(Influent, t, theta, initial) CMFR = Influent * (1 - Exp(-t / theta)) + initial * (Exp(-t / theta)) End Function Function invp(x) invp = 10 ^ (-x) End Function Function alpha0CO2(pH) alpha0CO2 = 1 / (1 + 10 ^ (-6.3) / invp(pH) + 10 ^ (-6.3) * 10 ^ (-10.3) / invp(pH) ^ 2) End Function
Visual Basic Functions for ANC • ANC for a closed system • ANC for an open system Function ANCclosed(pH, Ct) ANCclosed = Ct * (alpha1CO2(pH) + 2 * alpha2CO2(pH)) + 10 ^ (-14) / invp(pH) - invp(pH) End Function 10-3.5 atm 10-1.5 mol/(L atm) Function ANCopen(pH) ANCopen = ANCclosed(pH, invp(5) / alpha0CO2(pH)) End Function
Results? • If your results don’t jive where do you look? • Units of ANC? • Units of CT? • How is t defined? q?
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... f(Ct) Why not titrate to target pH?
Conservation of ANC T = titrant S = sample equivalent Ve= ___________ volume = volume of titrant added so that ANC = 0 Need to find ANCT and Ve
ANC of Titrant NT = [H+] Why? ___________ ANC conservation 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 For pH << pK1 When is this true? ____________ 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. • Define F1 as:
Gran Plot 0.0009 0.0008 0.0007 0.0006 0.0005 First Gran Function 0.0004 0.0003 0.0002 0.0001 0 0 1 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 = 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. • 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
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 • Minimum? _______________________ • Maximum? • Constraints? • Number of data points _____________ • Before reaching pH___ • How do we determine titrant volume? • H+ is conservative! None except your patience 3 or more 3
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? Create hypotheses and test them!
Better, what is missing? 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