|
Metastability and stability Why do metastable phases form?
|
tarix | 31.07.2018 | ölçüsü | 6,7 Mb. | | #59691 |
|
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
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
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
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: ABC, if kii>ki, then at some time t, [A] / [B] ratio remains constant
Dostları ilə paylaş: |
|
|