Aquatic Chemical KineticsHow can you tell if any system is at equilibrium?Thermodynamic or kinetic descriptions?Time ScalesReactions and KineticsEquilibrium and reversible kineticsExtent of ReactionRate LawReaction OrderGeneral Rate LawsSlide 11Zero OrderFirst OrderSlide 14Pseudo- 1nd OrderSecond Order2nd OrderHalf-life3rd order KineticsReversible ReactionsReversible KineticsT effect of reaction ratesActivation EnergyPathwaysConsecutive ReactionsAquatic 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/formationHow 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 ScalesReactions 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 H4SiO4Equilibrium and reversible kinetics•For any reaction AT equilibrium, Keq is related to the forward (k+) and reverse (k-) reaction rates•Example:Fe2+ + H+ + 0.25 O2 = Fe3+ + 0.5 H2OLog K=8.48, if k+=100 mol/min, then k-=3x10-7 mol/minkkKeqExtent of Reaction•In it’s most general representation, we can discuss a reaction rate as a function of the extent of reaction:Rate = dξ/Vdtwhere ξ (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 iRate Law•For any reaction: X  Y + Z•We can write the general rate law:nXkdtXd)()(Rate = change in concentration of X with time, tOrder of reactionRate ConstantConcentration of XReaction 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 LawsReaction order Rate LawIntegrated Rate Law Units for k0 A=A0-kt mol/cm3 s1 ln A=lnA0-kt s-12 cm3/mol skAdtAd][2][kAdtAdkdtAd][ktAA011•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 concentrationZero 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/TkdtAd][First Order•Rate is dependent on concentration of a reactant or product–Pyrite oxidation, sulfate reduction are exampleskAdtAd][First OrderFind 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-1kAdtAd][)(0][][ktteAAktAAt0][][ln)log(]log[]log[0ktteAA0]log[434.0]log[ AktAtPseudo- 1nd Order•For a bimolecular reaction: A+B  products)])([]([]][[0022xBxAkBAkdtdxIf [B]0 is held constant, the equation above reduces to:)0])([]([]][[0022 BxAkBAkdtdxSO – 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 reactionsSecond Order•Rate is dependent on two reactants or products (bimolecular for elementary rxn):•Fe2+ oxidation is an example:Fe2+ + ¼ O2 + H+  Fe3+ + ½ H2O2][][22OPFekdtFed2nd Order•For a bimolecular reaction: A+B  products)])([]([]][[0022xBxAkBAkdtdxtkBAABBAxBAxABBA20000000000][][][][ln][][1)]([][)]([][ln][][100002][][log)][]([43.0][][logABtBAkBAtt[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•Half-lives tougher to quantify if A≠B for 2nd order reaction kinetics – but if A=B:0221][1Akt If one reactant (B) is kept constant (pseudo-1st order rxns):0221][2lnAkt 0021][5.0][ln12l nAAkkt 3rd order Kinetics•Ternary molecular reactions are more rare, but catalytic reactions do need a 3rd component…)])( [])([]([]][][[00023xCxBxAkCBAkdtdx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 reversekf[A] = kr[B] Keq = [A] / [B] = kf / krReversible 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!][][][PkAkdtAdrf)])([]([00xPxAkdtdxf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:So that a plot of log K vs. 1/T is a straight line whose slope = -EA/2.303R2303.2logRTEdTkdAActivation EnergyReaction ‘typical’ range of EA (kcal/mol)Physical adsorption 2 – 6Aqueous diffusion <5‘Biotic’ reactions 5 - 20Mineral dissolution/precipitation 8- 36Dissolution controlled by