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

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: Rate = change in concentration of X with time, t Order of reaction Rate Constant Concentration of X

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 Reaction order Rate Law Integrated Rate Law Units for k A=A0-kt mol/cm3 s 1 ln A=lnA0-kt s-1 2 cm3/mol s

Zeroth order: rate does not change with lower concentration 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 Graphs of different rates of reaction copy the chapter from Langmuir for them!

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 Reaction order Rate Law Integrated Rate Law Units for k A=A0-kt mol/cm3 s 1 ln A=lnA0-kt s-1 2 cm3/mol s

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)

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

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):

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

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