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Metastability and stability

Metastability and stability. Why do metastable phases form?. Ostwald’s Step Rule: The first solid phase to precipitate is most soluble phase (i.e. the least stable, or metastable, phase). Wilhelm Ostwald (1853 –1932). Aragonite instead of calcite SiO 2 . x(H 2 O) instead of quartz

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Metastability and stability

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  1. Metastability and stability

  2. Why do metastable phases form? Ostwald’s Step Rule: The first solid phase to precipitate is most soluble phase (i.e. the least stable, or metastable, phase) Wilhelm Ostwald (1853 –1932) • Aragonite instead of calcite • SiO2. x(H2O) instead of quartz • FeS instead of pyrite • Ferrihydrite instead of hematite

  3. Classical Nucleation Theory The nucleus increases in Gibb’s free energy as it accretes The size reaches a critical value The free energy decreases with size until a negative value is reached (i.e. a more stable phase) e.g. water at 0oC , critical radius is 8Å with ca. 90 H2O molecules

  4. Classical Nucleation theory and the Ostwald Step Rule • G = Gbulk + Gsurface • The free energy required to make a nucleus is the sum of the free energy gained in making bonds plus the free energy required to make a surface. • Gsurface = 4r2 • Where  is the interfacial energy or interfacial surface tension. • The interfacial free energy increases with decreasing solubility • Therefore the more soluble, least stable phase forms first because it has the lower interfacial energy.

  5. 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

  6. Nonequilibrium • Equilibrium = DEATH for all organisms • Why? available metabolic energy: DGR=DG0 + RTlnQ Biogenic, atmospheric elements (C, N, P, S, O) are in nonequilibrium in natural waters There are thousands of natural organic molecules and even more synthetic ones that are not thermodynamically stable in the presence of O2

  7. Black Smokers • Life thrives here on the H2S and Fe2+ coming out of the vents • H2S and Fe2+ is derived from interaction of hot (350-400+ ºC) fluid interacting with basalts

  8. What else affects disequilibrium? • Physical forces – gas rising, convection cells, particle settling, transport • Biological activity segregates redox species • Mineral reactions affect other reactions, perturbing redox equilibria • How long it lasts, the forces that maintain it  described by kinetics

  9. Time Scales

  10. 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

  11. 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

  12. 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

  13. 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

  14. General Rate Laws

  15. 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

  16. 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

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

  18. 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

  19. 1st-order Half-life • Time required for one-half of the initial reactant to react

  20. 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

  21. General Rate Laws

  22. 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)

  23. 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

  24. 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):

  25. 3rd order Kinetics • Ternary molecular reactions are more rare, but catalytic reactions do need a 3rd component…

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

  27. 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

  28. 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!

  29. 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

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

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

  32. Secular Equilibrium* • Secular equilibrium is a kinetic steady-state  NOT thermodynamic equilibrium! • For our consecuative reaction: ABC, if kii>ki, then at some time t, [A] / [B] ratio remains constant

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