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Aquatic Chemical 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

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How can you tell if any system is at equilibrium? Beware of steady state (non-equilibrium) conditions where proportions of reactants are constant, but due to flux in-out and relative rates of reaction!

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Thermodynamic or kinetic descriptions? When a reaction is reversible and the rate is fast compared to residence time thermodynamic description When a reaction is irreversible, OR it’s reaction rate is slower than the residence time kinetic description Partial Equilibrium system where some reactions fast, others are slow – sound familiar?

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Time Scales

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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

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Equilibrium and reversible kinetics For any reaction AT equilibrium, K eq is related to the forward (k+) and reverse (k-) reaction rates Example: Fe 2+ + H + + 0.25 O 2 = Fe 3+ + 0.5 H 2 O Log K=8.48, if k + =100 mol/min, then k - =3x10 -7 mol/min

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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 = 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

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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

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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!

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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

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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

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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

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First Order Rate is dependent on concentration of a reactant or product –Pyrite oxidation, sulfate reduction are examples

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First Order Find rate constant 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

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Pseudo- 1 nd Order For a bimolecular reaction: A+B products If [B] 0 is 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 – USE this in lab to determine order of reactions and rate constants of different reactions

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Second Order Rate is dependent on two reactants or products (bimolecular for elementary rxn): Fe 2+ oxidation is an example: Fe 2+ + ¼ O 2 + H + Fe 3+ + ½ H 2 O

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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 A≠B)

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Half-life Time required for one-half of the initial reactant to react Half-lives tougher to quantify if A≠B for 2 nd order reaction kinetics – but if A=B: If one reactant (B) is kept constant (pseudo-1 st order rxns):

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3 rd order Kinetics Ternary molecular reactions are more rare, but catalytic reactions do need a 3 rd component…

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Reversible Reactions 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 = k f [A] –Rate reverse can be: dB/dt = k r [B] –At equilibrium: Rate forward = Rate reverse k f [A] = k r [B] K eq = [A] / [B] = k f / k r

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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!

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T effect of reaction rates Arrhenius Expression: k=A F exp(-E A /RT) Where rate k is dependent on Temperature, the ‘A’ factor (independent of T) and the Activation Energy, E A differentating: So that a plot of log K vs. 1/T is a straight line whose slope = -E A /2.303R

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Activation Energy Reaction‘typical’ range of E A (kcal/mol) Physical adsorption2 – 6 Aqueous diffusion<5 ‘Biotic’ reactions5 - 20 Mineral dissolution/precipitation8- 36 Dissolution controlled by surface reaction 10 - 20 Isotopic exchange in solution18 - 48 Solid state diffusion in minerals20 - 120

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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

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Consecutive Reactions A B C Reaction sequence when k 1 ≈k 2 : k1k1 k2k2

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