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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 - PowerPoint PPT Presentation

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Aquatic Chemical Kinetics

Geochemical KineticsLook at 3 levels of chemical change:Phenomenological or observationalMeasurement of reaction rates and interpretation of data in terms of rate laws based on mass actionMechanisticElucidation of reaction mechanisms = the elementary steps describing parts of a reaction sequence (or pathway)Statistical MechanicalConcerned with the details of mechanisms energetics of molecular approach, transition states, and bond breaking/formation1Time Scales

2Reactions and KineticsElementary reactions are those that represent the EXACT reaction, there are NO steps between product and reactant in between what is representedOverall 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 H4SiO43Extent of ReactionIn its most general representation, we can discuss a reaction rate as a function of the extent of reaction:Rate = d/Vdtwhere (small chi) is the extent of rxn, V is the volume of the system and t is timeNormalized to concentration and stoichiometry:rate = dni/viVdt = d[Ci]/vidtwhere n is # moles, v is stoichiometric coefficient, and C is molar concentration of species i4Rate LawFor any reaction: X Y + ZWe can write the general rate law:

Rate = change in concentration of X with time, tOrder of reactionRate ConstantConcentration of X5Reaction OrderONLY for elementary reactions is reaction order tied to the reactionThe 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

6General Rate LawsReaction orderRate LawIntegrated Rate LawUnits for k0A=A0-ktmol/cm3 s1ln A=lnA0-kts-12cm3/mol s

7

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

Zeroth order: rate does not change with lower concentrationFirst, second orders:Rate changes as a function of concentration8Graphs of different rates of reaction copy the chapter from Langmuir for them!

Zero OrderRate independent of the reactant or product concentrationsDissolution of quartz is an example:SiO2(qtz) + 2 H2O H4SiO4(aq)

log k- (s-1) = 0.707 2598/T

9First OrderRate is dependent on concentration of a reactant or productPyrite oxidation, sulfate reduction are examples

10First OrderFind 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

111st-order Half-lifeTime required for one-half of the initial reactant to react

12Second OrderRate is dependent on two reactants or products (bimolecular for elementary rxn):Fe2+ oxidation is an example:Fe2+ + O2 + H+ Fe3+ + H2O

13General Rate LawsReaction orderRate LawIntegrated Rate LawUnits for k0A=A0-ktmol/cm3 s1ln A=lnA0-kts-12cm3/mol s

142nd OrderFor 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 AB)15Pseudo- 1nd OrderFor 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 reaction162nd order Half-lifeHalf-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):

173rd order KineticsTernary molecular reactions are more rare, but catalytic reactions do need a 3rd component

18Zero order reactionNOT possible for elementary reactionsCommon for overall processes independent of any quantity measured

[A]0-[A]=kt

19PathwaysFor 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 pathway20Initial Rate, first order rxn exampleFor the example below, lets determine the order of reaction A + B C

Next, lets solve the appropriate rate law for kRun #Initial [A] ([A]0) Initial [B] ([B]0)Initial Rate (v0)11.00 M1.00 M1.25 x 10-2 M/s21.00 M2.00 M2.5 x 10-2 M/s32.00 M2.00 M2.5 x 10-2 M/sRate Limiting ReactionsFor an overall reaction, one or a few (for more complex overall reactions) elementary reactions will 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 pathwayActivation Energy, EAEnergy required for two atoms or molecules to react

Transition State TheoryThe activation energy corresponds to the energy of a complex intermediate between product and reactant, an activated complexA + B C AB

It can be derived that EA = RT + DHC Collision Theorycollision theory is based on kinetic theory and supposes that particles must collide with both the correct orientation and with sufficient kinetic energy if the reactants are to be converted into products. The minimum kinetic energy required in a collision by reactant molecules to form product is called the activation energy, Ea. The proportion of reactant molecules that collide with a kinetic energy that is at least equal to the activation energy increases rapidly as the temperature increases.T dependence on kSvante Arrhenius, in 1889, defined the relationship between the rate constant, k, the activation energy, EA, and temperature in Kelvins:

or:

Where A is a constant called the frequency factor, and eEA/RT is the Boltzmann factor, fraction of atoms that aquire the energy to clear the activation energy

Arrhenius Equationy = mx + b

Plot values of k at different temperatures: log k vs 1/T slope is EA/2.303R to get activation energy, EA

Activation EnergyEA can be used as a general indicator of a reaction mechanism or process (rate-limiting)Reaction / ProcessEA rangeIon exchange>20Biochemical reactions5-20Mineral dissolution / precipitation8-36Mineral dissolution via surface rxn10-20Physical adsorption2-6Aqueous diffusion

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