1Chemical Kinetics

Texts: Atkins, 8th edtn., chaps. 22, 23 & 24Specialist: “Reaction Kinetics” Pilling & Seakins (1995)

Revision Photochemical Kinetics Photolytic activation, flash photolysis Fast reactions Theories of reaction rates

– Simple collision theory– Transition state theory

2Overview of kinetics Qualitative description

– rate, order, rate law, rate constant, molecularity, elementary, complex, temperature dependence, steady-state, ...

Reaction dynamics– H (2S) + ICl (v, J) HI (v´, J´) + Cl (2P1/2)

Modelling of complex reactions C & E News, 6-Nov-89, pp.25-31– stratospheric O3 tropospheric hydrocarbons H3CCO2ONO2

– combustion chemical vapour deposition: SiH4 Si films

3Rate of reaction symbol:R,v,…Stoichiometric equation

m A + n B = p X + q Y

Rate = (1/m) d[A]/dt = (1/n) d[B]/dt = (1/p) d[X]/dt = (1/q) d[Y]/dt– Units: (concentration/time)– in SI mol/m3/s, more practically mol dm–3 s–1

4Rate Law

How does the rate depend upon [ ]s? Find out by experiment

The Rate Law equation R = kn [A] [B] … (for many reactions)

– order, n = + + … (dimensionless)

– rate constant, kn (units depend on n)

– Rate = kn when each [conc] = unity

5Experimental rate laws?CO + Cl2 COCl2

Rate = k [CO][Cl2]1/2

– Order = 1.5 or one-and-a-half order

H2 + I2 2HI

Rate = k [H2][I2]– Order = 2 or second order

H2 + Br2 2HBr

Rate = k [H2][Br2] / (1 + k’ {[HBr]/[Br2]} )– Order = undefined or none

6Determining the Rate Law Integration

– Trial & error approach– Not suitable for multi-reactant systems– Most accurate

Initial rates– Best for multi-reactant reactions– Lower accuracy

Flooding or Isolation– Composite technique– Uses integration or initial rates methods

7Integration of rate laws

Order of reactionFor a reaction aA products

the rate law is:

nA

A

n

n

Akdt

Adr

akkdefining

Aakdt

Ad

Akdt

Ad

ar

][][

][][

][][1

rate of change in theconcentration of A

8First-order reaction

)()][]ln([

][

][

][

][

][][

00

0

][

][

1

0

ttkAA

dtkA

Ad

dtkA

Ad

Akdt

Adr

At

t

A

A

A

A

A

t

9First-order reaction

tkAA

ttkAA

At

At

0

00

]ln[]ln[

)(]ln[]ln[

A plot of ln[A] versus t gives a straightline of slope -kA if r = kA[A]1

10First-order reaction

tkt

tkt

At

At

A

A

eAA

eA

A

tkA

A

ttkAA

0

0

0

00

][][

][

][

][

][ln

)(]ln[]ln[

11A Passume that -(d[A]/dt) = k [A]1

0 5 10 151

2

3

4

5

6

7

8

[H2O

2] / m

ol d

m-3

Time / ms

12Integrated rate equationln [A] = -k t + ln [A]0

0 5 10 15

0.2

0.4

0.6

0.8

1.0

ln [H 2

O2]

/ m

ol d

m-3

Time / ms

13Half life: first-order reaction

2/10

0

0

][

][21

ln

][

][ln

tkA

A

tkA

A

A

At

The time taken for [A] to drop to half its original value is called the reaction’s half-life, t1/2. Setting [A] = ½[A]0

and t = t1/2 in:

14Half life: first-order reaction

2/12/1

2/1

693.0693.0

693.02

1ln

tkor

kt

tk

AA

A

15When is a reaction over? [A] = [A]0 exp{-kt}

Technically [A]=0 only after infinite time

16Second-order reaction

tA

A

t

A

A

A

dtkA

Ad

dtkA

Ad

Akdt

Adr

][

][ 02

2

2

0][

][

][

][

][][

17Second-order reaction

tkAA

ttkAA

At

At

0

00

][

1

][

1

)(][

1

][

1

A plot of 1/[A] versus t gives a straightline of slope kA if r = kA[A]2

18Second order test: A + A P

2 4 6 8 1010

12

14

16

18

20

22

24

(1 / [A]0)

1 / [A

]

Time / ms

19Half-life: second-order reaction

2/10

2/10

2/10

0

][

1

][

1

][

1

][

2

][

1

][

1

tAk

ortkA

tkAA

tkAA

AA

Ao

At

20Rate law for elementary reaction Law of Mass Action applies:

– rate of rxn product of active masses of reactants

– “active mass” molar concentration raised to power of number of species

Examples:– A P + Q rate = k1 [A]1

– A + B C + D rate = k2 [A]1 [B]1

– 2A + B E + F + G rate = k3 [A]2 [B]1

21Molecularity of elementary reactions? Unimolecular (decay) A P

- (d[A]/dt) = k1 [A]

Bimolecular (collision) A + B P

- (d[A]/dt) = k2 [A] [B]

Termolecular (collision) A + B + C P

- (d[A]/dt) = k3 [A] [B] [C]

No other are feasible! Statistically highly unlikely.

22

CO + Cl2 COCl2

Exptal rate law: - (d[CO]/dt) = k [CO] [Cl2]1/2

– Conclusion?: reaction does not proceed as written

– “Elementary” reactions; rxns. that proceed as written at the molecular level.

Cl2 Cl + Cl (1) ● Decay Cl + CO COCl (2) ● Collisional COCl + Cl2 COCl2 + Cl (3) ● Collisional Cl + Cl Cl2 (4) ● Collisional

– Steps 1 thru 4 comprise the “mechanism” of the reaction.

23- (d[CO]/dt) = k2 [Cl] [CO]

If steps 2 & 3 are slow in comparison to 1 & 4

then, Cl2 ⇌2Cl or K = [Cl]2 / [Cl2]

So [Cl] = K × [Cl2]1/2

Hence:

- (d[CO] / dt) = k2 × K × [CO][Cl2]1/2

Predict that: observed k = k2 × K Therefore mechanism confirmed (?)

24H2 + I2 2 HI Predict: + (1/2) (d[HI]/dt) = k [H2] [I2] But if via:

– I22 I– I + I + H2 2 HI rate = k2 [I]2 [H2]– I + II2

Assume, as before, that 1 & 3 are fast cf. to 2Then: I2 ⇌2 I or K = [I]2 / [I2] Rate = k2 [I]2 [H2] = k2 K [I2] [H2] (identical)

Check? I2 + h 2 I (light of 578 nm)

25Problem In the decomposition of azomethane, A, at a pressure of

21.8 kPa & a temperature of 576 K the following concentrations were recorded as a function of time, t:Time, t /mins 0 30 60 90 120[A] / mmol dm3 8.70 6.52 4.89 3.67 2.75

Show that the reaction is 1st order in azomethane & determine the rate constant at this temperature.

26 Recognise that this is a rate law question dealing with the integral method.

- (d[A]/dt) = k [A]? = k [A]1

Re-arrange & integrate (bookwork) Test: ln [A] = - k t + ln [A]0

Complete table:Time, t /mins 0 30 60 90 120ln [A] 2.16 1.88 1.59 1.30 1.01 Plot ln [A] along y-axis; t along x-axis Is it linear? Yes. Conclusion follows.Calc. slope as: -0.00959 so k = + 9.610-3 min-1

27More recent questions …

Write down the rate of rxn for the rxn:C3H8 + 5 O2 = 3 CO2 + 4 H2O

for both products & reactants [8 marks]For a 2nd order rxn the rate law can be written:

- (d[A]/dt) = k [A]2

What are the units of k ? [5 marks] Why is the elementary rxn NO2 + NO2 N2O4 referred to as

a bimolecular rxn? [3 marks]

28Temperature dependence? C2H5Cl C2H4 + HCl

k/s-1 T/K 6.1 10-5 700 30 10-5 727 242 10-5 765

Conclusion: very sensitive to temperature Rule of thumb: rate doubles for a 10 K rise

29Details of T dependenceHood k = A exp{ -B/T }Arrhenius k = A exp{ - E / RT }A A-factor or

pre-exponential factork at T

E activation energy(energy barrier) J mol -1 or kJ mol-1

R gas constant. T e m pe ra ture

R a te o f rxn

30Arrhenius eqn. k=A exp{-E/RT}Useful linear form: ln k = -(E/R)(1/T) + ln A

Plot ln k along Y-axis vs (1/T) along X-axisSlope is negative -(E/R); intercept = ln A Experimental Es range from 0 to +400 kJ mol-1

Examples:– H + HCl H2 + Cl 19 kJ mol-1

– H + HF H2 + F 139 kJ mol-1

– C2H5I C2H4 + HI 209 kJ mol-1

– C2H6 2 CH3 368 kJ mol-1

31Practical Arrhenius plot, origin not included

0.0009 0.0010 0.0011 0.0012 0.0013 0.0014 0.0015-8

-6

-4

-2

0

2

4

6

8

Intercept = 27.602 from which A = 1.1 x 1012 dm3 mol-1 s-1

Slope = -22,550 from which E = 188 kJ/mol

ln k

/(dm

3 mol

-1 s

-1)

K / T

32Rate constant expression

RT

EAk Aexp

212

1

212

1

2

1

2

1

11ln

11exp

)(

)(

exp

TTR

E

k

k

TTR

E

k

k

RT

ERT

E

A

A

k

k

A

A

A

A

1

4

202.51314.8

58.6158

1012526.1314.8

693.0

15.303

1

15.293

1

314.82

1ln

molkJEE

E

E

AA

A

A

33Photochemical activation Initiation of reaction by light absorption; very important

– photosynthesis; reactions in upper atmosphere No. of photons absorbed? Einstein-Stark law: 1 photon

responsible for primary photochemical act (untrue)S0 + h S1* Jablonski diagram

S* S0 + h fluorescence, phosphorescence

S* + M S0 + M collisional deactivation (quenching)

S* P + Q photochemical reaction

34Example & Jablonski diagram A ruby laser with frequency

doubling to 347.2 nm has an output of 100J with pulse widths of 20 ns.

If all the light is absorbed in 10 cm3 of a 0.10 mol dm-

3 solution of perylene, what fraction of the perylene molecules are activated?

S 3

S 2

S 1

S 0

T 1

IN TE R N A L C O N V E R SIO N

1 0 4 - 1 0 1 2 s -1

IN TE R SY STE M C R O SSIN G

1 0 4 - 1 0 1 2 s -1

F L U O R E S C E N C E

1 0 6 - 1 0 9 s -1P H O S P H O R E S C E N C E

1 0 -2 - 1 0 4 s -1

35

# of photons = total energy / energy of 1 photon Energy of photon?

# of photons = 100 / 5.725 10−19 = 1.7467 1020 # of molecules: 0.1 mol in 1000 cm3, => 1 10−3 mol in 10 cm3

=> 6.022 1020 moleculesfraction activated: 1.7467 1020 / 6.022 1020 = 0.29

J

m

msJshc

19

9

1834

10725.5

102.347

)103()10626.6(

36Key parameter: quantum yield, = (no. of molecules reacted)/(no. of photons absorbed)

Example: 40% of 490 nm radiation from 100 W source transmitted thru a sample for 45 minutes; 344 mmol of absorbing compound decomposed. Find .

Energy of photon? = hc / (6.62610−34 J s)(3.00108 m s−1)/(49010−9 m) = 4.060−19

JPower: 100 Watts = 100 J s-1

Total energy into sample = (100 J s−1)(4560 s)(0.60)= 162 kJ Photons absorbed = (162,000)/(4.060−19) = 4.01023

Molecules reacted? (6.0231023) = 2.07 1023

= 2.07 1023 /4.01023 = 0.52

37Quantum yield

Significance? = 2.0 for 2HI H2 + I2 reactionHI + h H• + I• (i) primary = 1H• + HI H2 + I• (p)I• + I• I2 (t) For H2 + Cl2 2HCl > 106

Is constant? No, depends on , T, solvent, time. / nm >430 405 400 <370 0 0.36 0.50 1.0

for NO2NO+O

38

Absolute measurement of FA, etc.? No; use relative method. Ferrioxalate actinometer:

C2O42 + 2 Fe3+ 2 Fe2+ + 2 CO2

= 1.25 at 334 nm but fairly constant from 254 to 579 nm For a reaction in an organic solvent the photo-reduction of

anthraquinone in ethanol has a unit quantum yield in the UV.

D E T E C T O R

39Rates of photochemical reactions

Br2 + h Br + Br

Definition of rate: where nJ is stoichiometric

coefficient (+ve for products)Units: mol s-1

So FA is moles of photons absorbed per second

Finally, the reaction rate per unit volume in mol s-1 m-3

or mol m-3 s-1

Rate

1

2

2 2

2

J

J

A A

A

dn

dt

dn Br

dtF I

n Br V Br

d Br

dt

F

V

( )

40Stern-Volmer Apply SS approx. to M*:d[M*]/dt = (FA/V) - kF[M*] - kQ[M*][Q] Also (FF / V)= kF[M*]

So: (FA / FF ) = 1 + (kQ /kF) [Q]

And hence:Plot reciprocal of fluorescent intensity versus [Q]

Intercept is (1/FA) and slope is = (kQ / kF) (1/FA) Measure kF in a separate experiment; e.g. measure the half-

life of the fluorescence with short light pulse & [Q]=0 since d[M*]/dt = - kF[M*] then [M*]=[M*]0 exp(-t/)

M + hM* FA / V M* M + h FF / V M* + QM + Q

41Problem 23.8 (Atkins)Benzophenone phosphorescence with triethylamine asquencher in methanol solution. Data is:

[Q] / mol dm-31.0E-3 5.0E-3 10.0E-3

FF /(arbitrary) 0.41 0.25 0.16

Half-life of benzophenone triplet is 29 s. Calculate kQ.

42

0.000 0.002 0.004 0.006 0.008 0.0102.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

Y = A + B * X

Parameter Value Error------------------------------------------------------------A 1.96549 0.10995B 424.53279 16.96558

1/F

F

[Q] / mol dm-3

43Flash photolysis [RK, Pilling & Seakins, p39 on] Fast burst of laser

light– 10 ns, 1 ps down to

femtosecond High concentrations

of reactive species instantaneously

Study their fate Transition state

spectroscopy J. Phys. Chem. a 4-6-98

X eA R CL A M P

A rFE X C IM E RL A S E R

S S H E A T A B L ER E A C T IO NV E S S E L

44Flash photolysis Adiabatic

– Light absorbed => heat => T rise– Low heat capacity of gas => 2,000 K– Pyrolytic not photolytic– Study RH + O2 spectra of OH•, C2, CH, etc

Isothermal– Reactant ca. 100 Pa, inert gas 100 kPa– T rise ca. 10 K; quantitative study possible– precursor + h CH subsequent CH + O2

45Example [RK, Pilling & Seakins, p48]

CH + O2 products

Excess O2 present

[O2]0 = 8.81014 molecules cm-3

1st order kinetics

Follow [CH] by LIFt / s 20 30 40 60

IF 0.230 0.144 0.088 0.033

Calculate k1 and k2

20 30 40 50 60 70 80-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

ln (I

F)

Time / s

46Problem In a flash-photolysis experiment a radical, R, was produced

during a 2 s flash of light and its subsequent decay followed by kinetic spectrophotometry: R + R R2

The path-length was 50 cm, the molar absorptivity, , 1.1104 dm3/mol/cm.

Calculate the rate constant for recombination.– t / s 0 10 15 25 40 50– Absorbance 0.75 0.58 0.51 0.41 0.32 0.28

How would you determine ?

47Photodissociation [RK, p. 288]

Same laser dissociates ICN at 306 nm & is used to measure [CN] by LIF at 388.5 nm

Aim: measure time delay between photolysis pulse and appearance of CN by changing the timing of the two pulses.

Experimentally: 205 fs; separation 600 pm [C & E News 7-Nov-88]

F S L A S E R IC NS A M P L E

M O V A B L E M IR R O R 3 0 m = 1 0 0 fs

F R E Q U E N C YS U B T R A C T O R

P R O B E P U L S E

P H O T O P U L S E

Beam Splitter

48TS spectroscopy; Atkins p. 834

Changing the wavelength of the probing pulse can allow not just the final product, free CN, to be determined but the intermediates along the reaction path including the transition state.

For NaI one can see the activated complex vibrate at (27 cm-1) 1.25 ps intervals surviving for 10 oscillations– see fig. 24.75 Atkins 8th ed.

49Fast flow tubes; 1 m3/s, inert coating, t=d/v In a RF discharge: O2 O + Oorpass H2 over heated

tungsten filament or O3 over 1000oC quartz, etc.

Use non-invasive methods for analysis e.g. absorption, emissionGas titration: add stable NO2 (measurable flow rate) Fast O+NO2 NO+O2 then O+NO NO2

NO2h

End-point? Lights out when flow(NO2) = flow(O)

N O 2

O 2

50ClO + NO3 J. Phys. Chem. 95:7747 (1991) 1.5 m long, 4 cm od, Pyrex tube with sliding injector to vary

reaction time F + HNO3 NO3 + HF [NO3] monitor at 662 nm F + HCl Cl + HF followed by Cl + O3 ClO + O2

M S

He

F 2 / He

HC l

He

HNO 3 / HeF 2 / He

SLIDING INJE CTOR

RF

51Problem [RK, Pilling & Seakins, p36]

HO2 + C2H4 C2H5

+ O2 C2H5O2

MS determines LH channel 11%, RH channel 89%

C2H5 signal 6.14 3.95 2.53 1.25 0.70 0.40

Injector d / cm 3 5 7 10 12 15

Linear flow velocity was 1,080 cm s-1 at 295 K & 263 Pa.Calculate 1st order rate constant; NB [O2]0>>[C2H5

]0

52Flow tubes; pros & cons Mixing time restricts timescale to millisecond range Difficult to work at pressures > (atm/100) Wall reactions can complicate kinetics

– coat with Teflon or halocarbon wax; or vary tube diameter Cheap to build & operate, sensitive detection available

– Resonance fluorescence– Laser induced fluorescence– Mass spectrometry– Laser magnetic resonance

53Resonance fluorescence Atomic species (H, N, O, Br, Cl, F) mainly not molecular Atomic lines are very narrow; chance of absorption by

another species is highly unlikely Resonance lamp: microwave discharge dissociates H2

H atoms formed in electronically excited state; fluoresce, emitting photon which H-atoms in reaction vessel absorb & re-emit them where they can be detected by PMT

Lamp: H2 H H* H + h

Rxn cell: H + h H* H + h

54LIF; detection of OH Excitation pulse at 282 nm to

upper state of OH with lifetime of ns; fluorescence to ground state at 308 nm

IF n relative concentrations not

absolute (drawback). Right angle geometry Good candidates:

– CN, CH, CH3O, NH, H, SO

v '= 2

v '= 1

v '= 0

v ''= 2

v ''= 1

v ''= 0

2 8 2 n m 3 0 8 n m

55Reactions in shock waves

Wide range of T’s & P’s accessible; 2,000 K, 50 bar routine Thermodynamics of high-T species eg Ar up to 5,000 K Study birth of compounds: C6H5CHO CO* + C6H6

Energy transfer rxns.: CO2 + M CO2* + M Relative rates, use standard rxn as “clock”

Diaphragm

Driver TubeDriven Tube

TestRegion

He

ToVacuumSystem

TestMixture

Diaphragm

Driver TubeDriven Tube

TestRegion

He

ToVacuumSystem

TestMixture

56

CH* Chemiluminescence (431 nm) Detected at Endwall and Sidewall

Experiments: Ignition Delay Time

PMT Detector

Lens

Filter (310 nm)

Slit

Endwall

Shock Tube

SidewallO

H*

Time

Ignition

OH

*

Time

Ignition

• Use endwall for ignition

• Use sidewall for profiles

57Mode of action of shock tube Fast bunsen-burner (ns)

Shock wave acts as a piston compressing & heating the gas ahead of it

Study rxns behind incident shock wave or reflected shock wave (ms-s times)

Non-invasive techniques T & p by computation from

measured shock velocity

P

D IS T A N C E

T 1

T 2

T 3

T

58Shock Tube Simulation

59Problem A single-pulse shock tube used to study 1st order reaction

C2H5I C2H4 + HI; to avoid errors in T measurement a comparative study was carried out with C3H7I C3H6 +

HI for which kB=9.11012 exp(-21,900/T) s-1. For a rxn time of 220 s 5% decomp. of C3H7I occurred. What was the temp. of the shock wave? [900 K]

For C2H5I 0.90% decomp. occurred; evaluate kA. If at 800 K (kA/kB) = 0.102 compute the Arrhenius

equation for kA. [5.81013 exp(-25,260/T) s-1]