Metastability and stability Why do metastable phases form?



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Metastability and stability



Why do metastable phases form?



Classical Nucleation Theory



Classical Nucleation theory and the Ostwald Step Rule





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


Nonequilibrium

  • Equilibrium = DEATH for all organisms

  • Why? available metabolic energy:

  • GR=G0 + 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



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



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



Time Scales



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



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



Rate Law

  • For any reaction: X  Y + Z

  • We can write the general rate law:



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



General Rate Laws



First step in evaluating rate data is to graphically interpret the order of rxn

  • 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



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



First Order

  • Rate is dependent on concentration of a reactant or product

    • Pyrite oxidation, sulfate reduction are examples


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



1st-order Half-life

  • Time required for one-half of the initial reactant to react



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



General Rate Laws



2nd Order

  • For a bimolecular reaction: A+B  products



Pseudo- 1nd Order

  • For a bimolecular reaction: A+B  products



2nd order Half-life

  • Half-lives tougher to quantify if A≠B for 2nd order reaction kinetics – but if A=B:



3rd order Kinetics

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



Zero order reaction

  • NOT possible for elementary reactions

  • Common for overall processes – independent of any quantity measured

  • [A]0-[A]=kt



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


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!



Pathways

  • For an overall reaction, one or a few (for more complex overall reactions) elementary reactions can be rate limiting



Consecutive Reactions

  • A  B  C

  • Reaction sequence when k1≈k2:



Consecutive Reactions

  • A  B  C

  • Reaction sequence when k1≈k2:



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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