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1、,Metastability and stability,Why do metastable phases form?,Ostwalds 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 Ferri
2、hydrite instead of hematite,Classical Nucleation Theory,The nucleus increases in Gibbs 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 8 with ca. 90 H2
3、O molecules,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 = 4r2 Where is the interfacial energy or interfacial surfac
4、e 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.,Geochemical Kinetics,Look at 3 levels of chemical change: Phenomenological or observational Measurement of reaction rate
5、s 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, transit
6、ion states, and bond breaking/formation,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 syntheti
7、c 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+ C) fluid interacting with basalts,What else affects disequilibrium?,Physical forces gas rising, con
8、vection 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 r
9、epresent 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
10、 + 2 Na+ + 4 H4SiO4,Extent of Reaction,In its most general representation, we can discuss a reaction rate as a function of the extent of reaction: Rate = d/Vdt where (small chi) is the extent of rxn, V is the volume of the system and t is time Normalized to concentration and stoichiometry: rate = dn
11、i/viVdt = dCi/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:,Rate = change in concentration of X with time, t,Order of reaction,Rate Constant,Concentration of X,Reaction Order,O
12、NLY 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 pos
13、sible,General Rate Laws,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
14、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 logAt vs t plot Slope=-0.434k k = -(1/0.434)(slope) = -2.
15、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+ + O2 + H+ Fe3+ + H2O,General Rate Laws,2nd Order,For a bi
16、molecular reaction: A+B products,A0 and B0 are constant, so a plot of log A/B vs t yields a straight line where slope = k2 (when A=B) or = k2(A0-B0)/2.3 (when AB),Pseudo- 1nd Order,For a bimolecular reaction: A+B products,If A0 or B0 are held constant, the equation above reduces to:,SO as A changes
17、B does not, reducing to a constant in the reaction: plots as a first-order reaction,2nd order Half-life,Half-lives tougher to quantify if AB for 2nd order reaction kinetics but if A=B:,If one reactant (B) is kept constant (pseudo-1st order rxns):,3rd order Kinetics,Ternary molecular reactions are mo
18、re 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 A0-A=kt,Reversible Reactions,Preceeding only really accurate if equilibrium is far off i.e, there is little reaction in
19、 the opposite direction For A = B Rate forward can be: dA/dt = kfA Rate reverse can be: dB/dt = krB At equilibrium: Rate forward = Rate reverse kfA = krB Keq = A / B = kf / kr,Reversible Kinetics,Kinetics of reversible reactions requires a back-reaction term: With reaction progress In summary there
20、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,Reaction of A to P rate determined by slowest reaction in between If more than 1 r
21、eaction possible at any intermediate point, the faster of those 2 determines the pathway,Consecutive Reactions,A B C Reaction sequence when k1k2:,k1,k2,Consecutive Reactions,A B C Reaction sequence when k1k2:,k1,k2,Secular Equilibrium*,Secular equilibrium is a kinetic steady-state NOT thermodynamic equilibrium! For our consecuative reaction: ABC, if kiiki, then at some time t, A / B ratio remains constant,