Aquatic Chemical Kinetics

1. Aquatic Chemical 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. How can you tell if any system is at equilibrium? • Beware of steady state (non-equilibrium) conditions where proportions of reactants are constant, but due to flux in-out and relative rates of reaction!

3. Thermodynamic or kinetic descriptions? • When a reaction is reversible and the rate is fast compared to residence time  thermodynamic description • When a reaction is irreversible, OR it’s reaction rate is slower than the residence time  kinetic description • Partial Equilibrium  system where some reactions fast, others are slow – sound familiar?

4. Time Scales

5. 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

6. Equilibrium and reversible kinetics • For any reaction AT equilibrium, Keq is related to the forward (k+) and reverse (k-) reaction rates • Example: Fe2+ + H+ + 0.25 O2 = Fe3+ + 0.5 H2O Log K=8.48, if k+=100 mol/min, then k-=3x10-7 mol/min

7. 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

8. 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

9. 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!

10. General Rate Laws

11. 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

12. 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

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

14. First Order Find rate constant 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

15. Pseudo- 1nd Order • For a bimolecular reaction: A+B  products If [B]0 is 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 – USE this in lab to determine order of reactions and rate constants of different reactions

16. 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

17. 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)

18. Half-life • Time required for one-half of the initial reactant to react • 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):

19. 3rd order Kinetics • Ternary molecular reactions are more rare, but catalytic reactions do need a 3rd component…

20. Reversible Reactions • Preceeding only really accurate if equilibrium is far off i.e, there is little reaction in the opposite direction • For A = B • Rate forward can be: dA/dt = kf[A] • Rate reverse can be: dB/dt = kr[B] • At equilibrium: Rate forward = Rate reverse kf[A] = kr[B] Keq = [A] / [B] = kf / kr

21. Reversible Kinetics • Kinetics of reversible reactions requires a back-reaction term: • With reaction progress • In summary there is a definite role that approach to equilibrium plays on overall forward reaction kinetics!

22. T effect of reaction rates • Arrhenius Expression: k=AFexp(-EA/RT) Where rate k is dependent on Temperature, the ‘A’ factor (independent of T) and the Activation Energy, EA differentating: So that a plot of log K vs. 1/T is a straight line whose slope = -EA/2.303R

23. Activation Energy

24. 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

25. Consecutive Reactions A  B  C Reaction sequence when k1≈k2: k1 k2