Geochemical Kinetics Look at 3 levels of chemical change: –Phenomenological or observational...

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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 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 Slide 2 Time Scales Slide 3 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. FeS 2 + 7/2 O 2 + H 2 O Fe 2+ + 2 SO 4 2 + 2 H + 2 NaAlSi 3 O 8 + 9 H 2 O + 2 H + Al 2 Si 2 O 5 (OH) 4 + 2 Na + + 4 H 4 SiO 4 Slide 4 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 i /v i Vdt = d[C i ]/v i dt where n is # moles, v is stoichiometric coefficient, and C is molar concentration of species i Slide 5 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 Slide 6 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 bimolecular rxns Overall reactions need not have integral reaction orders fractional components are common, even zero is possible Slide 7 General Rate Laws Reaction orderRate Law Integrated Rate LawUnits for k 0A=A 0 ktmol/cm 3 s 1ln A=lnA 0 kts 1 2cm 3 /mol s Slide 8 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 Slide 9 Zero Order Rate independent of the reactant or product concentrations Dissolution of quartz is an example: SiO 2(qtz) + 2 H 2 O H 4 SiO 4(aq) log k  (s 1 ) = 0.707 2598/T Slide 10 First Order Rate is dependent on concentration of a reactant or product Pyrite oxidation, sulfate reduction are examples Slide 11 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 Slide 12 1 st order Halflife Time required for onehalf of the initial reactant to react Slide 13 Second Order Rate is dependent on two reactants or products (bimolecular for elementary rxn): Fe 2+ oxidation is an example: Fe 2+ + O 2 + H + Fe 3+ + H 2 O Slide 14 General Rate Laws Reaction orderRate Law Integrated Rate LawUnits for k 0A=A 0 ktmol/cm 3 s 1ln A=lnA 0 kts 1 2cm 3 /mol s Slide 15 2 nd 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 = k 2 (when A=B) or = k 2 ([A] 0 [B] 0 )/2.3 (when AB) Slide 16 Pseudo 1 nd 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 firstorder reaction Slide 17 2 nd order Halflife Halflives tougher to quantify if AB for 2 nd order reaction kinetics but if A=B: If one reactant (B) is kept constant (pseudo1 st order rxns): Slide 18 3 rd order Kinetics Ternary molecular reactions are more rare, but catalytic reactions do need a 3 rd component Slide 19 Zero order reaction NOT possible for elementary reactions Common for overall processes independent of any quantity measured [A] 0 [A]=kt Slide 20 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 Slide 21 Initial Rate, first order rxn example For the example below, lets determine the order of reaction A + B C Next, lets solve the appropriate rate law for k Run #Initial [A] ([A] 0 )Initial [B] ([B] 0 )Initial Rate (v 0 ) 11.00 M 1.25 x 10 2 M/s 21.00 M2.00 M2.5 x 10 2 M/s 32.00 M 2.5 x 10 2 M/s Slide 22 Rate Limiting Reactions For 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 pathway Slide 23 Activation Energy, E A Energy required for two atoms or molecules to react Slide 24 Transition State Theory The activation energy corresponds to the energy of a complex intermediate between product and reactant, an activated complex A + B C AB It can be derived that E A = RT + H C Slide 25 Collision Theory collision 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. Slide 26 T dependence on k Svante Arrhenius, in 1889, defined the relationship between the rate constant, k, the activation energy, E A, and temperature in Kelvins: or: Where A is a constant called the frequency factor, and e EA/RT is the Boltzmann factor, fraction of atoms that aquire the energy to clear the activation energy Slide 27 Arrhenius Equation y = mx + b Plot values of k at different temperatures: log k vs 1/T slope is E A /2.303R to get activation energy, E A Slide 28 Activation Energy E A can be used as a general indicator of a reaction mechanism or process (ratelimiting) Reaction / ProcessE A range Ion exchange>20 Biochemical reactions520 Mineral dissolution / precipitation836 Mineral dissolution via surface rxn1020 Physical adsorption26 Aqueous diffusion