Chapter 2 – kinetics

Corrections to the textCorrections to the text

Table 1.1 MgTable 1.1 Mg2+2+ = 1280 mg/L = 1280 mg/L Table 1.1 electroneutrality is usually Table 1.1 electroneutrality is usually

15%, which indicates analytical 15%, which indicates analytical errors and/or missing solute. The errors and/or missing solute. The Mississippi River sample has an Mississippi River sample has an error of about 50%; those data will error of about 50%; those data will be replaced. be replaced.

Table 1.3a Davies equationTable 1.3a Davies equation The final term has a coefficient of 0.3The final term has a coefficient of 0.3 The example has a coefficient of 0.2The example has a coefficient of 0.2 Davies suggested a value from 0.2 to Davies suggested a value from 0.2 to

0.30.31

Chemical KineticsChemical Kinetics

Material from the handoutMaterial from the handout

Two views of Two views of equilibriumequilibrium

Based on the minimum energyBased on the minimum energy Thermodynamic perspectiveThermodynamic perspective Approach used after tonightApproach used after tonight

Based on kineticsBased on kinetics Forward reaction rateForward reaction rate Reverse reaction rateReverse reaction rate Equilibrium occurs when the net rate Equilibrium occurs when the net rate

= 0= 0

An overviewAn overview

Expressions/analysis of irreversible Expressions/analysis of irreversible reactions reactions 0, 10, 1stst, and 2, and 2ndnd order order

Elementary and non-elementary Elementary and non-elementary reactionsreactions

Series and parallel reactionsSeries and parallel reactions Reversible reactionsReversible reactions Effect of temperature on kineticsEffect of temperature on kinetics

Kinetic expressions Kinetic expressions for…for…

Basic irreversible reactions:Basic irreversible reactions:

Zero order: Zero order: A A P P

11stst order : order : A A P P

22ndnd order: order: A + A A + A P P

22ndnd order : order : A + B A + B P P

An example: Given these An example: Given these batch experimental batch experimental

data, estimate data, estimate the rate constantthe rate constant

Time (d)Time (d) 00 55 1010 1515 2020 2525 3030

C (mg/L)C (mg/L) 2525 1515 99 66 33 22 11

Maybe it’s a 1Maybe it’s a 1stst order order reactionreaction

Integrate…Integrate…

Convenient linear formConvenient linear form

Is a 1Is a 1stst order model order model appropriate?appropriate?

tt (d) (d) 00 55 1010 1515 2020 2525 3030

CC (mg/L) (mg/L) 2525 1515 99 66 33 22 11

ln ln CC 3.223.22 2.712.71 2.202.20 1.791.79 1.101.10 0.690.69 00

Plot ln(Plot ln(CC) = ) = ff((tt) ) Look for straight lineLook for straight line Slope = Slope = kk

ln C = -0.1057 t + 3.26

R2 = 0.9961

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35

Time (d)

Ln C

11stst order assessment: k order assessment: k -0.11 d -0.11 d-1-1

Kinetic expressions for Kinetic expressions for elementary reactionselementary reactions

Kinetic expressions for Kinetic expressions for elementary reactions - elementary reactions -

IIII

Differential rate Differential rate analysisanalysis

Apply differential Apply differential approachapproach

t (min) [A] (mg/L)

0 10

2 5.8

4 3.7

6 2.6

8 1.9

10 1.5

Example

Data manipulationData manipulation

t (min) [A] (mg/L) A]/t [A]avg Ln(-A]/t)

0 10 - -

2 5.8 -2.1 7.97.9 0.740.74

4 3.7 -1.05 4.754.75 0.0490.049

6 2.6 -0.55 3.153.15 -0.598-0.598

8 1.9 -0.35 2.252.25 -1.05-1.05

10 1.5 -0.02 1.71.7 -1.61-1.61

Example

[A]avg = average concentration during the period t.

Integral analysisIntegral analysis

Example

n = 1.51kn = exp(-2.34) = 0.096

y = 1.5102x - 2.3399

R2 = 0.9964

-2

-1.5

-1

-0.5

0

0.5

1

0 0.5 1 1.5 2 2.5

ln(Aavg)

ln(- A

/t)

Example

y = 0.0573x + 0.067

R2 = 0.9861

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10

Time (min)

1/A

y = -0.1884x + 2.1705

R2 = 0.9794

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Time (min)

ln (

A)

What about 1st and 2nd order kinetics?

Which model is correct? Which model is correct?

n = 1.51 provides the best fit; n = 1 or 2 is not too bad

Elementary and Elementary and non-elementary non-elementary

reactionsreactions

Elementary reactionsElementary reactions

An enzyme-catalyzed An enzyme-catalyzed reactionreaction

Pseudo 1Pseudo 1stst order order reactionsreactions

Experimental designExperimental design

Multiple step reactions Multiple step reactions are commonare common

For example, reactions in series:For example, reactions in series:

AA BB CC

Reactions in parallel: Reactions in parallel:

AA BB

AA CC

Reactions in series Reactions in series exampleexample

Reaction Reaction AA BB is a 0 order reaction is a 0 order reaction

kk00 = 10 = 10-5-5 mg.L mg.L-1-1.min.min-1-1

Reaction Reaction BB CC is a 1 is a 1stst order reaction order reaction

kk11 = 0.01 min = 0.01 min-1-1 Assume all concentrations can be Assume all concentrations can be

expressed as mg of carbon per Lexpressed as mg of carbon per L Initial concentrationsInitial concentrations

AA00 = 10 = 10-3-3 mg/L mg/L BB00 = = CC00 = 0 mg/L = 0 mg/L

Determine Determine AA, , BB, and , and CC = = ff((tt) )

Rate expressionsRate expressions

27

Integrate for Integrate for BB

28

Rearrange to solve for Rearrange to solve for BB

29

0.E+00

2.E-04

4.E-04

6.E-04

8.E-04

1.E-03

1.E-03

0 50 100 150 200 250 300

Time (min)

Con

entr

atio

n (m

g C

/ L

)

ABC

Parallel reactions Parallel reactions exampleexample

Quiz 1Quiz 1

Imagine you can follow a molecule of copper from the source to the mouth of the Mississippi River. Assume that the average concentration of dissolved copper remains constant at 5 g/L. The total dissolved solids, however, increases significantly from source to mouth.

Would you expect the activity to increase, decrease, or remain the same? Why?

From the perspective of a fish, what is more important, the activity or the concentration of copper? Briefly explain your answer.

32

Reversible reactions Reversible reactions

Relating Relating AA and and BB

Substitute to simplifySubstitute to simplify

Integrate for Integrate for AA

Rearrange to solve for Rearrange to solve for AA

Some special conditionsSome special conditions

Similar analysis for Similar analysis for BB

Irreversible reactions?Irreversible reactions?

If the reverse reaction is very slow If the reverse reaction is very slow relative to the forward reaction… relative to the forward reaction…

Examples of irreversible reactions: Examples of irreversible reactions: PrecipitationPrecipitation LifeLife

Temperature effects Temperature effects

Assessing experimental Assessing experimental datadata

Plot ln(Plot ln(kk) versus 1/) versus 1/TT

Intercept = ln(Intercept = ln(kkArAr) )

Slope = - Slope = - EEArAr//RR

Example for the Q-10 Example for the Q-10 rule rule

Suppose a biochemical rate Suppose a biochemical rate doubles…doubles…

For a system increase from For a system increase from TT = 10 = 10C C to 20to 20C.C.

Estimate the activation energy for Estimate the activation energy for the reactionthe reaction

Arrhenius equation at Arrhenius equation at any any TT

Solve for Solve for EEArAr

Summary of key pointsSummary of key points

Models for simple kineticsModels for simple kinetics Basic elementary reactions Basic elementary reactions 0, 10, 1stst, or 2, or 2ndnd order models order models Evaluation of experimental dataEvaluation of experimental data

Complex reaction mechanisms are Complex reaction mechanisms are likelylikely Parallel or series combinations Parallel or series combinations

Temperature effects Temperature effects

How does water How does water temperature temperature affect pH? affect pH?

Equilibrium expression:Equilibrium expression:{H{H++} {OH} {OH--} = } = KKww = 10 = 10-14.0-14.0 (T = 25 C) (T = 25 C)

Charge balance in pure water:Charge balance in pure water:[H[H++] = [OH] = [OH--] ]

What is the pH at T = 1 What is the pH at T = 1 C? C?

van’t Hoff equationvan’t Hoff equation

SubstituteSubstitute

49

Neutral pH at Neutral pH at TT = 1 = 1CC