Aquatic Chemical Kinetics Look at 3 levels of chemical change: –Phenomenological or observational...

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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

Transcript of Aquatic Chemical Kinetics Look at 3 levels of chemical change: –Phenomenological or observational...

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

• 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

k

kKeq

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 = 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:

nXkdt

Xd)(

)(

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 Rate Law

Integrated Rate Law Units for k

0 A=A0-kt mol/cm3 s

1 ln A=lnA0-kt s-1

2 cm3/mol s

kAdt

Ad

][

2][kA

dt

Ad

kdt

Ad

][

ktAA

0

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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

Zero 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/T

kdt

Ad

][

First Order

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

kAdt

Ad

][

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

kAdt

Ad

][ )(

0][

][ ktt eA

A ktA

A t 0][

][ln

)log(]log[]log[ 0kt

t eAA 0]log[434.0]log[ AktA t

Pseudo- 1nd Order• For a bimolecular reaction: A+B products

)])([]([]][[ 0022 xBxAkBAkdt

dx

If [B]0 is held constant, the equation above reduces to:

)0])([]([]][[ 0022 BxAkBAkdt

dx

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+ + ¼ O2 + H+ Fe3+ + ½ H2O

2][

][ 22

OPFekdt

Fed

2nd Order• For a bimolecular reaction: A+B products

)])([]([]][[ 0022 xBxAkBAkdt

dx

tkBA

AB

BAxBA

xAB

BA 20

0

0000

00

00 ][][

][][ln

][][

1

)]([][

)]([][ln

][][

1

0

0002 ][

][log)][]([43.0

][

][log

A

BtBAk

B

A

t

t

[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:

02

21 ][1A

kt

If one reactant (B) is kept constant (pseudo-1st order rxns):

02

21 ][2lnA

kt

0

021 ][5.0

][ln12ln

A

A

kkt

3rd order Kinetics

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

)])([])([]([]][][[ 00023 xCxBxAkCBAkdt

dx

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

back-reaction term:

• With reaction progress

• In summary there is a definite role that approach to equilibrium plays on overall forward reaction kinetics!

][][][

PkAkdt

Adrf

)])([]([ 00 xPxAkdt

dxf

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/2.303R

2303.2

log

RT

E

dT

kd A

Activation EnergyReaction ‘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 of those 2 determines the pathway

Consecutive Reactions

A B C

Reaction sequence when k1≈k2:

k1 k2

][][

Akdt

Adi

][][][

BkAkdt

Bdiii

][][

Bkdt

Cdii