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

Overall reactions – no kinetic information Overall reactions – no kinetic information Magnitude and sign of free energy (  G) don’t give specific information about rates Magnitude and sign of free energy (  G) don’t give specific information about rates Only describes tendency to proceed any particular direction Only describes tendency to proceed any particular direction Rates might be determined from distance from equilibrium Rates might be determined from distance from equilibrium

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

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

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

Elementary and Overall Reactions Elementary reactions – describe exact reaction mechanism or pathway Elementary reactions – describe exact reaction mechanism or pathway H + + OH - = H 2 O CO 2 + OH - = HCO 3 - H 4 SiO 4 º = SiO 2(qtz) + 2H 2 O

Overall Reactions – don’t include reaction mechanism or pathway Overall Reactions – don’t include reaction mechanism or pathway Really is sum of multiple reactions Really is sum of multiple reactions CaCO 3(cal) + CO 2 + H 2 O = Ca HCO 3 -

Steps in calcite dissolution Steps in calcite dissolution Detachment of Ca 2+ and CO 3 2- from surface Detachment of Ca 2+ and CO 3 2- from surface Diffusion (or transportation) of Ca 2+ and CO 3 - from surface Diffusion (or transportation) of Ca 2+ and CO 3 - from surface Conversion of CO 3 - to HCO 3 - and H 2 CO 3 to HCO 3 - in solution Conversion of CO 3 - to HCO 3 - and H 2 CO 3 to HCO 3 - in solution Conversion of CO 2(aq) to H 2 CO 3 Conversion of CO 2(aq) to H 2 CO 3 Dissolution of CO 2(g) Dissolution of CO 2(g) Slowest step is “Rate Limiting Step” Slowest step is “Rate Limiting Step”

Order of reaction Expression of dependence of reaction rate on concentrations of species involved Expression of dependence of reaction rate on concentrations of species involved Zeroeth order reactions don’t depend on concentration of any species Zeroeth order reactions don’t depend on concentration of any species It depends only on concentration of A or B, then 1 st order It depends only on concentration of A or B, then 1 st order If depends on m A 2, second order If depends on m A 2, second order A + B = AB

If depends on m A and m B If depends on m A and m B Second order overall Second order overall First order with respect to A and B First order with respect to A and B Reaction order can be higher Reaction order can be higher These are rare These are rare

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

Units of rate constants (k’s): Units of rate constants (k’s): Zeroeth order – mole/cm 3 sec Zeroeth order – mole/cm 3 sec First order – 1/sec First order – 1/sec Second order – cm 3 /mol sec Second order – cm 3 /mol sec

Reaction rates – on board Reaction rates – on board

Zeroeth order Rate is slope of A/t A=A o -kt Rate independent of A AoAo

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

Examples: Examples: Organic C and calcite dissolution Organic C and calcite dissolution