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Geochemical Kinetics

Geochemical Kinetics. Look at 3 levels of chemical change: Phenomenological or observational Measurement of reaction rates and interpretation of data in terms of rate laws based on mass action Mechanistic

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Geochemical Kinetics

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  1. Geochemical Kinetics • Look at 3 levels of chemical change: • Phenomenological or observational • Measurement of reaction rates and interpretation of data in terms of rate laws based on mass action • Mechanistic • Elucidation of reaction mechanisms = the ‘elementary’ steps describing parts of a reaction sequence (or pathway) • Statistical Mechanical • Concerned with the details of mechanisms  energetics of molecular approach, transition states, and bond breaking/formation

  2. Time Scales

  3. Reactions and Kinetics • Elementary reactions are those that represent the EXACT reaction, there are NO steps between product and reactant in between what is represented • Overall Reactions represent the beginning and final product, but do NOT include one or more steps in between. FeS2 + 7/2 O2 + H2O  Fe2+ + 2 SO42- + 2 H+ 2 NaAlSi3O8 + 9 H2O + 2 H+  Al2Si2O5(OH)4 + 2 Na+ + 4 H4SiO4

  4. Extent of Reaction • In it’s most general representation, we can discuss a reaction rate as a function of the extent of reaction: Rate = dξ/Vdt where ξ (small ‘chi’) is the extent of rxn, V is the volume of the system and t is time Normalized to concentration and stoichiometry: rate = dni/viVdt = d[Ci]/vidt where n is # moles, v is stoichiometric coefficient, and C is molar concentration of species i

  5. Rate Law • For any reaction: X  Y + Z • We can write the general rate law: Rate = change in concentration of X with time, t Order of reaction Rate Constant Concentration of X

  6. Reaction Order • ONLY for elementary reactions is reaction order tied to the reaction • The molecularity of an elementary reaction is determined by the number of reacting species: mostly uni- or bi-molecular rxns • Overall reactions need not have integral reaction orders – fractional components are common, even zero is possible

  7. General Rate Laws

  8. First step in evaluating rate data is to graphically interpret the order of rxn • Zeroth order: rate does not change with lower concentration • First, second orders: Rate changes as a function of concentration

  9. Zero Order • Rate independent of the reactant or product concentrations • Dissolution of quartz is an example: SiO2(qtz) + 2 H2O  H4SiO4(aq) log k- (s-1) = 0.707 – 2598/T

  10. First Order • Rate is dependent on concentration of a reactant or product • Pyrite oxidation, sulfate reduction are examples

  11. First Order Find order from log[A]t vs t plot  Slope=-0.434k k = -(1/0.434)(slope) = -2.3(slope) k is in units of: time-1

  12. 1st-order Half-life • Time required for one-half of the initial reactant to react

  13. Second Order • Rate is dependent on two reactants or products (bimolecular for elementary rxn): • Fe2+ oxidation is an example: Fe2+ + ¼ O2 + H+ Fe3+ + ½ H2O

  14. General Rate Laws

  15. 2nd Order • For a bimolecular reaction: A+B  products [A]0 and [B]0 are constant, so a plot of log [A]/[B] vs t yields a straight line where slope = k2 (when A=B) or = k2([A]0-[B]0)/2.3 (when A≠B)

  16. Pseudo- 1nd Order • For a bimolecular reaction: A+B  products If [A]0 or [B]0 are held constant, the equation above reduces to: SO – as A changes B does not, reducing to a constant in the reaction: plots as a first-order reaction

  17. 2nd order Half-life • Half-lives tougher to quantify if A≠B for 2nd order reaction kinetics – but if A=B: If one reactant (B) is kept constant (pseudo-1st order rxns):

  18. 3rd order Kinetics • Ternary molecular reactions are more rare, but catalytic reactions do need a 3rd component…

  19. Zero order reaction • NOT possible for elementary reactions • Common for overall processes – independent of any quantity measured [A]0-[A]=kt

  20. Pathways • For an overall reaction, one or a few (for more complex overall reactions) elementary reactions can be rate limiting Reaction of A to P  rate determined by slowest reaction in between If more than 1 reaction possible at any intermediate point, the faster of those 2 determines the pathway

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