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 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 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 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 Equilibrium and reversible kinetics For any reaction AT equilibrium Keq is related to the forward k and reverse k reaction rates k K eq k Example Fe2 H 0 25 O2 Fe3 0 5 H2O Log K 8 48 if k 100 mol min then k 3x10 7 mol min Extent of Reaction In it s 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 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 d X n k X dt 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 General Rate Laws Reaction order 0 1 2 Rate Law d A k dt Integrated Rate Law Units for k A A0 kt mol cm3 s ln A lnA0 kt s 1 d A kA dt 3 cm mol s 1 1 d A kt kA2 A A0 dt 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 d A k dt 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 d A kA dt Rate is dependent on concentration of a reactant or product Pyrite oxidation sulfate reduction are examples First Order d A kA dt A t e kt A 0 log A t log A 0 log e kt ln A t kt A 0 log A t 0 434kt log A 0 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 Pseudo 1nd Order For a bimolecular reaction A B products dx k 2 A B k 2 A 0 x B 0 x dt If B 0 is held constant the equation above reduces to dx k 2 A B k 2 A 0 x B 0 0 dt 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 Second Order Rate is dependent on two reactants or products bimolecular for elementary rxn Fe2 oxidation is an example Fe2 O2 H Fe3 H2O 2 d Fe 2 k Fe PO2 dt 2nd Order For a bimolecular reaction A B products dx k 2 A B k 2 A 0 x B 0 x dt B 0 A 0 x B 0 A 1 1 ln ln k 2t A 0 B 0 A 0 B 0 x A 0 B 0 A 0 B A t B 0 log 0 43k 2 A 0 B 0 t log B t A 0 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 Half life Time required for one half of the initial reactant to react A ln 2 1 t1 2 0 ln k k 0 5 A 0 Half lives tougher to quantify if A B for 2nd order reaction kinetics but if A B t1 2 1 A 0 k2 If one reactant B is kept constant pseudo 1st order rxns t1 2 ln 2 A 0 k2 3 order Kinetics rd Ternary molecular reactions are more rare but catalytic reactions do need a 3 rd component dx k3 A B C k 2 A 0 x B 0 x C 0 x dt 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 kf A Rate reverse can be dB dt kr B At equilibrium Rate forward Rate reverse kf A kr B Keq A B kf kr Reversible Kinetics Kinetics of reversible reactions requires a backreaction term d A k f A k r P dt With reaction progress dx k f A 0 x P 0 x dt In summary there is a definite role that approach to equilibrium plays on overall forward reaction kinetics T effect of reaction rates Arrhenius Expression k AFexp EA RT Where rate k is dependent on Temperature the A factor independent of T and the Activation Energy EA differentating d log k EA 2 dT 2 303RT So that a plot of log K vs 1 T is a straight line whose slope EA 2 303R Activation Energy Reaction typical range of EA kcal mol Physical adsorption 2 6 Aqueous diffusion 5 Biotic reactions 5 20 Mineral dissolution precipitation 8 36 Dissolution controlled by surface reaction 10 20 Isotopic exchange in solution 18 48 Solid state diffusion in minerals 20 120 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 …