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REACTION KINETICS

REACTION KINETICS. Pierre Glynn, March 2003 (w/ notes from Alex Blum). General Concepts. Transport vs. Reaction Control Elementary vs. Overall Reactions Detailed Balancing Microscopic Reversability Temperature Dependance Transition State Theory Michaelis-Menten Kinetics

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REACTION KINETICS

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  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: Overall 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.

  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 EA required for a molecular reaction. The preexponential factor A may depend on pH, solution chemistry, surface characteristics, and many other factors including temperature.

  9. Activation Energy (EA) • Reaction rates are exponentially dependent on EA • EA depends on the direction of a reaction • Catalysis lowers the EA required for a reaction (note activated complex) Exothermic reaction Endothermic reaction EA from http://www.ucdsb.on.ca/tiss/stretton/chem2/rate03

  10. 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.

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

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

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

  14. Surface speciation kinetic model • Fast reversible adsorption reaction to form a surface species • Irreversible dissolution reaction at that surface species

  15. 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 Log Rate (mol/m2/s) -4.0 Log (DSurface charge) (mol/m2) -6.5

  16. Michaelis-Menten kinetics • Based on enzyme kinetics • 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 • Assumes that the concentration of ES is at steady-state (d(ES)/dt = 0)

  17. Measurements needed are: • the total amount of enzyme, ET = E + ES • the concentration of substrate, S • the measured steady state velocity: V = k2 (ES) • The maximal velocity is measured, Vmax = k2 (ET), using the highest substrate concentration • The Michaelis-Menten constant, KM = (k-1 + k2)/k1, is simply the substrate concentration that gives a reaction velocity half of Vmax. Also, for a slow reaction, k2 << k-1, KM = k-1/k1 = Keq • The Michaelis-Menten equation is:

  18. Surface Area • Critical to rate calculations and predictions • Geometric area estimation (often requires averaging or stochastic theory) • BET measurements, usually w/ N2 (4Å compared to 3Å for H2O) • Surface roughness (BET/Geometric): • SR = 5 - 12 for fresh ground silicate • SR = 300 - 2000 for deeply weathered natural silicates

  19. Feldspar dissolution kinetics and composition

  20. %An

  21. Silicate dissolution kinetics and pH

  22. Albite pH

  23. K-feldspar pH

  24. Silicate weathering reactions

  25. Conclusions: silicate weathering • Natural weathering rates in soils are 102 to 105 slower than exp. rates • Weathering rates in aquifers depend on (water chem)/(res. time)/(extent of react)?? • Accumulation of solutes retards dissolution rates?? • Discrepancies betw. natural and exp. rates are consistent w/ models of solute accumulation in pores

  26. Silicate weathering & the C cycle

  27. Exercise K1 • 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? • (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 KM & Vmax values of 80 and 0.83 mM SO4/day, resp.

  28. Norman landfill

  29. Norman landfill

  30. Exercise K1 (cont) • Enter the Rates keyword in PHREEQC to describe the Michaelis-Menten type rate law for SO4 reduction using the constants determined by Ulrich et al. (2003). Notice that in the screen shot, the KM & Vmax constants have been converted into units of moles SO4 per second. Call the rate law “Sulfate_reduction”. • 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”.

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

  32. Exercise K1 (cont) • Write the reaction for SO4 reduction with CH2O oxidation. How many moles of CH2O are used per ml of SO4 reduced? Use the KINETICS keyword to enter the CH2O formula, it’s stoich. coeff., and the total amount added (hint: use the DOC value). • Specify output steps at 1 second, 0.1, 1, 10, 20, 40, 60, 80 and 100 years. • Graph the decay of SO4, and the increase in S(-2) and C(4) w/ time. • How long does it take to oxidize the dissolved organic carbon? • What are the final concentrations of SO4, S(-2), and TDIC?

  33. Exercise K1 (cont) • 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? • Compare the Michaelis Menten constant with the SO4 concentration obtained after 100 years of reaction. What is the order of the rate law then?

  34. Exercise K1 (part 2) • 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. • Specify output steps at 1 second, 0.1, 1, 10, 20, 40, 60, 80 and 100 years. • Graph the decay of SO4, and the increase in S(-2) and C(4), and Ba w/ time. • How do the values compare with those observed in the leachate-contaminated water?

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