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REACTION KINETICS Pierre Glynn, March 2003 (w/ notes from Alex Blum)

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Presentation on theme: "REACTION KINETICS Pierre Glynn, March 2003 (w/ notes from Alex Blum)"— Presentation transcript:

1 REACTION KINETICS Pierre Glynn, March 2003 (w/ notes from Alex Blum)

2 General Concepts  Transport vs. Reaction Control  Elementary vs. Overall Reactions Detailed Balancing Microscopic Reversability  Temperature Dependance  Transition State Theory  Michaelis-Menten Kinetics  Surface Area  Silicate mineral dissolution kinetics & weathering

3 Transport vs. Reaction Control a) Transport control b) Surface reaction control c) Mixed Transport and surface-reaction control

4 Transport limitations: diffusion in solution solid-state diffusion Reaction limitations: surface reaction control surface characteristics crystal defects impurities crystal morphology

5 Elementary vs. overall reactions Reactions are the result of molecular collisions; & almost invariably depend on the collision of no more than 2 molecular species at a time. Overall reactions, such as: do not reveal the sequential, and possibly parallel, sets of molecular interactions, i.e. elementary reactions, that are actually involved.

6 Example of fast reactions (only 1 elementary step): Example of a two step reaction: Determining a rate law requires knowledge of the rate-limiting elementary reaction (usually only one). Allows accounting for the stoichiometry and the reaction order. If this is not possible (eg. for an overall reaction), rate laws are determined experimentally. Overall reaction:

7 Principle of Detailed Balancing: The net rate of a reaction is the difference between the forward and the backward microscopic rates (eg. microscopic dissolution vs. precipitation). Principle of Microscopic Reversability: The forward and the backward reactions have the same molecular mechanism.

8 Activation Energies and Temperature Dependence Reaction rates are often exponentially dependent on temperature, and are also highly depend on the activation energy E A required for a molecular reaction. The preexponential factor A may depend on pH, solution chemistry, surface characteristics, and many other factors including temperature.

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10 from Exothermic reaction Endothermic reaction EAEA Activation Energy (E A ) 1) Reaction rates are exponentially dependent on E A 2) E A depends on the direction of a reaction 3) Catalysis lowers the E A required for a reaction (note activated complex)

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12 Transition State Theory Applies statistical mechanics to individual elementary reactions. Meaningless for overall reactions. Focuses on the activated complex, the molecular configuration present at the top of the energy barrier (actually a saddle point) between reactants and products in an elementary reaction. Assumes this complex is a true chemical species and assumes that the initial reactants are always at equilibrium with the complex.

13 Transition State Theory Predicts that the rate is proportional to the number of activated complexes and to their rate of decomposition. Applies near equilibrium.

14 TST is somewhat similar to the idea that the rate is proportional to the deviation from equilibrium (or the degree of supersaturation or undersaturation).

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16 (From Burch et al., 1993)  G = -8 kcal/mol => log Q/K = -3.7 => Sat = 0.02%

17 1)Fast reversible adsorption reaction to form a surface species 2)Irreversible dissolution reaction at that surface species Surface speciation kinetic model

18 Log (  Surface charge) (mol/m 2 ) Log Rate (mol/m 2 /s) Surface complexation theory allows guessing the form of the “activated complex”. In this case (dissolution of Amelia albite; Blum, 1994, GCA), the dissolution rate is proportional to the degree of protonation, or deprotonation of the surface

19 Michaelis-Menten kinetics 1) Based on enzyme kinetics 2)Similar to TST theory; based on the idea of an “activated complex”, or an “enzyme-substrate” (ES) compound, whose concentration controls the rate of reaction 3)Assumes that the concentration of ES is at steady-state (d(ES)/dt = 0)

20 1) Measurements needed are: the total amount of enzyme, E T = E + ES the concentration of substrate, S the measured steady state velocity: V = k 2 (ES) 2)The maximal velocity is measured, V max = k 2 (E T ), using the highest substrate concentration 3)The Michaelis-Menten constant, K M = (k -1 + k 2 )/k 1, is simply the substrate concentration that gives a reaction velocity half of V max. Also, for a slow reaction, k 2 << k -1, K M = k -1 /k 1 = K eq 4)The Michaelis-Menten equation is:

21 Surface Area Critical to rate calculations and predictions Geometric area estimation (often requires averaging or stochastic theory) BET measurements, usually w/ N 2 (4Å compared to 3Å for H 2 O) Surface roughness (BET/Geometric): – SR = for fresh ground silicate – SR = for deeply weathered natural silicates

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23 Feldspar dissolution kinetics and composition

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25 %An

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27 Silicate dissolution kinetics and pH

28 pH Albite

29 pH K-feldspar

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34 Silicate weathering reactions

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40 Conclusions: silicate weathering 1)Natural weathering rates in soils are 10 2 to 10 5 slower than exp. rates 2)Weathering rates in aquifers depend on (water chem)/(res. time)/(extent of react)?? 3)Accumulation of solutes retards dissolution rates?? 4)Discrepancies betw. natural and exp. rates are consistent w/ models of solute accumulation in pores

41 Silicate weathering & the C cycle

42 1)Enter the 2 waters from the Norman, OK, landfill into a PHREEQC input file. Assume a temperature of 16.6 C for both. Units are mg/L. Do not enter DOC. Which water is contaminated? How did you specify redox conditions? Exercise K1 2)(Ulrich et al., 2003) used field and lab techniques to identify the biogeochemical factors affecting the rate of sulfate reduction in the leachate contaminated water. They obtained a Michaelis-Menten type relationship with K M & V max values of 80 and 0.83  M SO4/day, resp.

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44 Norman landfill

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46 3)Enter the Rates keyword in PHREEQC to describe the Michaelis-Menten type rate law for SO 4 reduction using the constants determined by Ulrich et al. (2003). Notice that in the screen shot, the K M & V max constants have been converted into units of moles SO 4 per second. Call the rate law “Sulfate_reduction”. Exercise K1 (cont) 4)Use the SELECTED_OUTPUT keyword to have PHREEQC output total concentrations on S(6), S(-2), C(4), and info on the kinetics of “Sulfate_reduction”.

47 Michaelis-Menten kinetics for sulfate reduction (constants from Ulrich et al., ES&T, 2003)

48 Exercise K1 (cont) 5)Write the reaction for SO 4 reduction with CH 2 O oxidation. How many moles of CH 2 O are used per ml of SO 4 reduced? Use the KINETICS keyword to enter the CH 2 O formula, it’s stoich. coeff., and the total amount added (hint: use the DOC value). 6)Specify output steps at 1 second, 0.1, 1, 10, 20, 40, 60, 80 and 100 years. 7)Graph the decay of SO4, and the increase in S(-2) and C(4) w/ time. 8)How long does it take to oxidize the dissolved organic carbon? 9)What are the final concentrations of SO 4, S(-2), and TDIC?

49 Exercise K1 (cont) 10) Examine the SO4 concentration in the initial water and compare it to the Michaelis-Menten constant. Which one is significantly smaller? What does that say about the order of the rate law applicable at the beginning of the SO4 reduction process? 11) Compare the Michaelis Menten constant with the SO4 concentration obtained after 100 years of reaction. What is the order of the rate law then?

50 Exercise K1 (part 2) 10) Ulrich et al. claim that barite dissolution provides the source of most of the S(6) in the Norman waters. In a new simulation, use the background water from near the Norman landfill. Maintain equilibrium with barite. Use the rate law and the kinetics keywords previously defined in part 1, but provide a input of organic carbon up to 10x greater. 11)Specify output steps at 1 second, 0.1, 1, 10, 20, 40, 60, 80 and 100 years. 12)Graph the decay of SO4, and the increase in S(-2) and C(4), and Ba w/ time. 13)How do the values compare with those observed in the leachate-contaminated water?

51 1)Enter the 2 Sierra Spring waters from Garrels & Christ into a PHREEQC input file. Assume a temperature of 25 C for both. Units are mmol/L. Exercise K2 2)Using the most dilute water, add the RATE laws and suggested KINETICS blocks that are present in the phreeqc.dat file, to simulate the kinetic reaction of the water with albite and K-spar. 3)Ignoring other possible reactions, how long would it take to obtain a water with Si, Na and K concentrations similar to those in the “Perennial Spring”?

52 Exercise K2 (part 2) 4) Examine the rate and kinetic blocks for K-spar and albite dissolution. Write out, and explain the rate laws and equations used.

53 Exercise K3 1)Examine the rate and kinetic blocks for Pyrite dissolution present in the phreeqc.dat file. Write out, and explain the rate laws and equations used. 2)Simulate the reaction of pyrite (as stipulated in the phreeqc.dat example) with a O2-equilibrated recharge water such as the OK recharge water (used in sorption exercise S3). How long does it take to react away the oxygen dissolved in one unit volume of water? Given the initial concentration of pyrite specified, how many volumes of recharge water would it take to consume all the pyrite?

54 Exercise K4 1)Examine the rate and kinetic blocks for Organic carbon reaction, using Monod kinetics, present in the phreeqc.dat file. Write out, and explain the rate laws and equations used. 2)Simulate the kinetic reaction specified using a water equilibrated with atmospheric O2 and and a log pCO2 of –1.5. What is the initial organic carbon concentration specified? How long does it take for the reactants to disappear? 3)Repeat the problem using the background water from the Norman landfill 4)Repeat the problem using the contaminated water from the Norman landfill


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