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Kinetics

Kinetics. State of reactions can be described a couple of ways: Equilibrium – overall reactions (our study so far) Kinetics – specific reaction pathways, times for those reactions, and equilibrium along the way. Overall reactions – no kinetic information

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Kinetics

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  1. Kinetics • State of reactions can be described a couple of ways: • Equilibrium – overall reactions (our study so far) • Kinetics – specific reaction pathways, times for those reactions, and equilibrium along the way

  2. Overall reactions – no kinetic information • Magnitude and sign of free energy (DG) don’t give specific kinetic information • Specifically indicates tendency to proceed any particular direction

  3. Is a reaction Kinetic of equilibrium controlled? • Is reaction fast and reversible? – then can be considered equilibrium controlled • Is reaction homogeneous or heterogeneous? • Homogeneous – only one phase (gas, liquid or solid) - more often equilibrium controlled • Heterogeneous – multiple phase. Often slow and kinetic control • Are there sufficient reactants for equilibrium be obtained?

  4. Slow reversible, heterogeneous, and irreversible reactions typically kinetically controlled • Kinetics difficult to apply in natural systems • Biologically mediated (catalyzed) • Often faster than estimated lab rates

  5. Heterogeneous reactions sensitive to surface control • faster than laboratory estimates • Depend on type and density of crystal defects, impurities

  6. Reactions usually multiple steps • Calcite dissolution • Detachment of Ca2+ and CO3- • Diffusion of Ca2+ and CO3- from surface • Conversion of CO3- to HCO3- and H2CO3 to HCO3- • Conversion of CO2(aq) to H2CO3 • Dissolution of CO2(g) • Slowest step is “Rate Limiting Step”

  7. Elementary and Overall Reactions • Elementary reactions – describes exact reaction mechanism or pathway H+ + OH- = H2O CO2 + OH- = HCO3- H4SiO4º = SiO2(qtz) + 2H2O

  8. Overall Reactions – doesn’t include reaction mechanism or pathway • Really is sum of 4 reactions CaCO3(cal) + CO2 + H2O = Ca2+ + 2HCO3-

  9. Order of reaction • Expression of dependence of reaction rate on concentrations of species involved • Zeroeth order reactions don’t depend on concentration of any species • If depends only on concentration of A or B, then 1st order • If depends on mA2, second order A + B = AB

  10. If depends on mA and mB • Second order overall • First order with respect to A and B • Reaction order can be higher • These are rare

  11. Rate of reaction: • Can be written: • k+ represents the reaction rate coefficient • Order • First with respect to A, • Second with respect to B • Third overall – very rare A + 2B = C

  12. A = B • Consider elementary first order reaction • Rates of reaction can be split into forward and reverse rates • Forward rate = k+mA • Reverse rate = k-mB • Here k’s are forward and reverse reaction rate constants

  13. Some approximate half lives and reaction rates Residence time of raindrop shorter than some solute-water reactions - Equilibrium controlled Non- equilibrium Equilibrium

  14. Units of rate constants (k’s): • Zeroeth order – mole/cm3 sec • First order – 1/sec • Second order – cm3/mol sec

  15. Links between equilibrium and kinetics • Overall rate, R is • Forward rate – reverse rate • At equilibrium: k+mA = k-mB

  16. So that • That is the equilibrium constant is equal to the ratio of the forward and reverse reaction rates • Also DGr = 0

  17. Zeroeth order reactions • Dissolution of quartz and other silicates • Independent of concentration • Consider:

  18. Rate law for reactants is: • Rate law for products is: Units: Concentration/time Mol/cm3– sec Negative sign because concentration decreasing

  19. Really want to have an algebraic expression • Need to solve differential equation • Separate variables • Integrate:

  20. Initial conditions are • So

  21. Solution is

  22. Half life • When ½ of A is gone • A = 1/2Ao • t = t1/2, where t1/2 is the time to “half life”

  23. Zeroeth order Rate is slope of A/t Ao Rate independent of A A=Ao-kt

  24. First Order Reactions • Examples • Radioactive decay • Oxidation of organic matter • Sulfate reduction • Gypsum dissolution • Oxidation of pyrite and marcasite

  25. Reaction now • Differential form: • Units of k now t-1 First order

  26. Separate variable and integrate:

  27. Initial conditions: • Implies that C = lnAo A=Ao when t=0

  28. Substituting for C:

  29. At half life, t = t1/2 and A = 1/2Ao • So that Note – here half life does not depend on initial concentration

  30. Temperature dependence • Most rates relate to Arrhenius equation • Where: • R = gas constant • T = temperature • A = coefficient (usually empirical) • DE = activation energy Rate = Ae-DE/RT

  31. Examples: • Organic C and calcite dissolution

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