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Chemical Kinetics

- Texts Atkins, 8th edtn., chaps. 22, 23 24
- Specialist Reaction Kinetics Pilling Seakins

(1995) - Revision
- Photochemical Kinetics
- Photolytic activation, flash photolysis
- Fast reactions
- Theories of reaction rates
- Simple collision theory
- Transition state theory

Overview 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

Rate of reaction symbolR,v,

- Stoichiometric equation
- m A n B p X q Y
- Rate - (1/m) dA/dt
- - (1/n) dB/dt
- (1/p) dX/dt
- (1/q) dY/dt
- Units (concentration/time)
- in SI mol/m3/s, more practically mol dm3 s1

Rate Law

- How does the rate depend upon s?
- Find out by experiment
- The Rate Law equation
- R kn Aa Bb (for many reactions)
- order, n a b (dimensionless)
- rate constant, kn (units depend on n)
- Rate kn when each conc unity

Experimental rate laws?

- CO Cl2 COCl2
- Rate k COCl21/2
- Order 1.5 or one-and-a-half order
- H2 I2 2HI
- Rate k H2I2
- Order 2 or second order
- H2 Br2 2HBr
- Rate k H2Br2 / (1 k HBr/Br2 )
- Order undefined or none

Determining 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

Integration of rate laws

- Order of reaction
- For a reaction aA products
- the rate law is

rate of change in the concentration of A

First-order reaction

First-order reaction

A plot of lnA versus t gives a straight line of

slope -kA if r kAA1

First-order reaction

A P assume that -(dA/dt) k A1

Integrated rate equationln A -k t ln A0

Half life first-order reaction

- The time taken for A to drop to half its

original value is called the reactions

half-life, t1/2. Setting A ½A0 and t t1/2

in

Half life first-order reaction

When is a reaction over?

- A A0 exp-kt
- Technically A0 only after infinite time

Second-order reaction

Second-order reaction

A plot of 1/A versus t gives a straight line of

slope kA if r kAA2

Second order test A A P

Half-life second-order reaction

Rate law for elementary reaction

- Law of Mass Action applies
- rate of rxn µ product of active masses of

reactants - active mass molar concentration raised to power

of number of species - Examples
- A P Q rate k1 A1
- A B C D rate k2 A1 B1
- 2A B E F G rate k3 A2 B1

Molecularity of elementary reactions?

- Unimolecular (decay) A P
- - (dA/dt) k1 A
- Bimolecular (collision) A B P
- - (dA/dt) k2 A B
- Termolecular (collision) A B C P
- - (dA/dt) k3 A B C
- No other are feasible! Statistically highly

unlikely.

CO Cl2 COCl2

- Exptal rate law - (dCO/dt) k CO

Cl21/2 - 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.

- (dCO/dt) k2 Cl CO

- If steps 2 3 are slow in comparison to 1 4
- then, Cl2 ? 2Cl or K Cl2 / Cl2
- So Cl ÖK Cl21/2
- Hence
- - (dCO / dt) k2 ÖK COCl21/2
- Predict that observed k k2 ÖK
- Therefore mechanism confirmed (?)

H2 I2 2 HI

- Predict (1/2) (dHI/dt) k H2 I2
- But if via
- I2 2 I
- I I H2 2 HI rate k2 I2 H2
- I I I2
- Assume, as before, that 1 3 are fast cf. to 2
- Then I2 ? 2 I or K I2 / I2
- Rate k2 I2 H2 k2 K I2 H2

(identical) - Check? I2 hn 2 I (light of 578 nm)

Problem

- 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 dm-3 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.

- Recognise that this is a rate law question

dealing with the integral method. - - (dA/dt) k A? k A1
- Re-arrange integrate (bookwork)
- Test ln A - k t ln A0
- Complete table
- Time, t /mins 0 30 60 90 120
- ln 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

More 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
- - (dA/dt) k A2
- What are the units of k ? 5 marks
- Why is the elementary rxn NO2 NO2 ? N2O4

referred to as a bimolecular rxn? 3 marks

Temperature 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

Details of T dependence

- Hood
- k A exp -B/T
- Arrhenius
- k A exp - E / RT
- A A-factor or
- pre-exponential factor
- º k at T
- E activation energy
- (energy barrier) J mol -1 or kJ mol-1
- R gas constant.

Arrhenius eqn. kA 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-axis
- Slope 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

Practical Arrhenius plot, origin not included

Rate constant expression

Photochemical 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 hn S1 Jablonski diagram
- S S0 hn fluorescence,

phosphorescence - S M S0 M collisional deactivation

(quenching) - S P Q photochemical reaction

Example 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?

- 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, gt 1 ? 10-3

mol in 10 cm3 - gt 6.022 ? 1020 molecules
- fraction activated 1.7467 ? 1020 / 6.022 ? 1020

0.29

Key parameter quantum yield, F

- F (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

F. - Energy of photon? e hc / l
- Þ (6.62610-34 J s)(3.00108 m s-1)/(49010-9 m)

4.0610-19 J - Power 100 Watts 100 J s-1
- Total energy into sample (100 J s-1)(4560

s)(0.60) 162 kJ - Photons absorbed (162,000)/(4.0610-19)

4.01023 - Molecules reacted? (6.0231023) (0.344) 2.07

1023 - Þ F 2.07 1023 / 4.01023 0.52

Quantum yield

- Significance? F 2.0 for 2HI H2 I2 reaction
- HI hn H I (i) primary f 1
- H HI H2 I (p)
- I I I2 (t)
- For H2 Cl2 2HCl F gt 106
- Is F constant? No, depends on l, T, solvent,

time. - l / nm gt430 405 400 lt370
- F 0 0.36 0.50 1.0
- for NO2NOO

F?

- Absolute measurement of FA, etc.? No use

relative method. - Ferrioxalate actinometer
- C2O42- 2 Fe3 2 Fe2 2 CO2
- F 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.

Rates of photochemical reactions

- Br2 hn 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

Stern-Volmer

- M hn M FA / V
- M M hn FF / V
- M Q M Q

- Apply SS approx. to M
- dM/dt (FA/V) - kFM - kQMQ
- Also (FF / V) kFM
- 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 Q0 since dM/dt - kFM

then MM0 exp(-t/t)

Problem 23.8 (Atkins)

- Benzophenone phosphorescence with triethylamine

as - quencher in methanol solution.
- Data is
- Q / mol dm-3 1.0E-3 5.0E-3 10.0E-3
- FF /(arbitrary) 0.41 0.25 0.16
- Half-life of benzophenone triplet is 29 ms.
- Calculate kQ.

(No Transcript)

Flash 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

Flash photolysis

- Adiabatic
- Light absorbed gt heat gt T rise
- Low heat capacity of gas gt 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 hn CH subsequent CH O2

Example RK, Pilling Seakins, p48

- CH O2 products
- Excess O2 present
- O20 8.81014 molecules cm-3
- 1st order kinetics
- Follow CH by LIF
- t / ms 20 30 40 60
- IF 0.230 0.144 0.088 0.033
- Calculate k1 and k2

Problem

- In a flash-photolysis experiment a radical, R,

was produced during a 2 ms flash of light and its

subsequent decay followed by kinetic

spectrophotometry R R R2 - The path-length was 50 cm, the molar

absorptivity, e, 1.1104 dm3/mol/cm. - Calculate the rate constant for recombination.
- t / ms 0 10 15 25 40 50
- Absorbance 0.75 0.58 0.51 0.41 0.32 0.28
- How would you determine e?

Photodissociation RK, p. 288

Beam Splitter

- 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 t 20530 fs separation 600

pm C E News 7-Nov-88

TS 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.

Fast flow tubes 1 m3/s, inert coating, td/v

- In a RF discharge O2 O O or pass H2 over

heated tungsten filament or O3 over 1000oC

quartz, etc. - Use non-invasive methods for analysis e.g.

absorption, emission - Gas titration add stable NO2 (measurable flow

rate) - Fast ONO2 NOO2 then ONO NO2 NO2 hn
- End-point? Lights out when flow(NO2) flow(O)

ClO NO3 J. Phys. Chem. 957747 (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

Problem 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

O20gtgtC2H50

Flow tubes pros cons

- Mixing time restricts timescale to millisecond

range - Difficult to work at pressures gt (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

Resonance 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 hn
- Rxn cell H hn H H hn

LIF 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 µ n²
- relative concentrations not absolute (drawback).
- Right angle geometry
- Good candidates
- CN, CH, CH3O, NH, H, SO

Reactions in shock waves

- Wide range of Ts Ps 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

Experiments Ignition Delay Time

CH Chemiluminescence (431 nm) Detected at

Endwall and Sidewall

Shock Tube

Endwall

Ignition

Slit

Lens

Filter (310 nm)

- Use endwall for ignition
- Use sidewall for profiles

PMT Detector

Sidewall

Ignition

Mode 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-ms times) - Non-invasive techniques
- T p by computation from measured shock velocity

Shock Tube Simulation

Problem

- 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 kB9.11012

exp(-21,900/T) s-1. For a rxn time of 220 ms 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

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