20170615 bo sapporo - 北海道大学触媒科学研究所・...

2017/06/15—Advanced Course in Environmental Catalytic Chemistry 1

June 15, 2017


kinetics

rate (r) of reaction for

A Bis expressed using k (rate constant) and concentrations of A ([A]), as

r = k [A]

[A]: actual concentration for reaction in solution: actual concentration [A] enzymatic (E) reaction: [E-A] surface reaction: [A]ads


Langmuirian-adsorption mechanism in catalyses

0 2 4 6 8 100

5x106

1x107

1.5x107

2x107

1/r

1/C

kSCkKSr1111

0 0.2 0.4 0.6 0.8 10

2x106

4x106

6x106

8x106

C/r

C

kKSC

kSrC 11

r = kSKC/ (1 + KC)1/r = (1/kKS)(1/C) + 1/kS

• Plots (left and right) may give K and kS, but not k or S.


Langmuir-Hinshelwood mechanism

• bimolecular reaction: reaction of two substrates, A and B adsorbed on surface with a reaction rate constant k.

• Common surface cites adsorb substrates A and B with equilibrium constants, KA and KB, respectively.

• Both A and B are adsorbed on the surface in Langmuirian fashion, with a total (saturated) concentration of the surface sites, S.

• Assuming the bulk concentration of A and B, CA and CB, respectively, rate r is proportional to surface concentrations of A and B, and then:

2BBAA

BBAA2

1 CKCKCKCKkSr


Eley-Rideal mechanism

• bimolecular reaction: reaction of two substrates, A and B, adsorbed on surface and coming from the bulk, respectively, with a reaction rate constant k.

• Surface cites adsorb substrates A with equilibrium constants, KA.• A is adsorbed on the surface in Langmuirian fashion, with a total

(saturated) concentration of the surface sites, S.• Assuming the bulk concentration of A and B, CA and CB, respectively,

rate r is proportional to surface concentration of A and B in the bulk, and then:

AA

BAA

1 CKCCkSKr


photocatalytic reaction

Photocatalytic reaction is a kind of photoreaction and therefore cannot be a series reaction: a parallel reaction initiated by photoabsorption with short-live species, e.g., photoexcited electrons and positive holes

electron-holepair

recombi-nation

photo-absorption

redox(chemical)reaction

1

2

3


steady-state approximation

• rate and concentration of INTERMEDIATE species

• automatically approaching the constant rate and concentration

(1) accumulation only = almost linear C increase

(2) Consumption (decrease) retards the linear increment to be upward concave.

(3) Overall rate (r) and C reach constants

0

conc

entra

tion

(C)

0

rate

(r) =

=

rate of increase

rate of decrease

overall rate

(+)

(-)


steady-state approximation for photocatalysis

• the simplest mechanism1) photoabsorption to yield photogenerated electron-positive hole pair (e-h):

I I: photon flux in mol s-1 and : photoabsorption efficiency 2) reaction of e-h with a substrate to give product(s): keh[e-h][S]3) recombination of e-h: kr[e-h]

• approximationlife time of an intermediate, e-h, is small and its concentration is constant

during the reaction

d[e-h]/dt = 0 =[e-h] = r =

I - keh[e-h][S] - kr[e-h]I / (keh[S] + kr)

keh[e-h][S] = I keh[S] / (keh[S] + kr)Derive an equation showing the rate r,

applying steady-state approximation to electron-positive hole pairs.


steady-state approximation for photocatalysis

• the simplest mechanism1) photoabsorption to yield photogenerated electron-positive hole pair (e-h):

I I: photon flux in mol s-1 and : photoabsorption efficiency 2) reaction of e-h with a substrate to give product(s): keh[e-h][S]3) recombination of e-h: kr[e-h]

• approximationlife time of an intermediate, e-h, is small and its concentration is constant

during the reaction

d[e-h]/dt = 0 =[e-h] = r =

I - keh[e-h][S] - kr[e-h]I / (keh[S] + kr)

keh[e-h][S] = I keh[S] / (keh[S] + kr)


kinetics of photoinduced reaction

There are two limits: linear part and saturated part.

concentration of subsrate(s)

rate

of r

eact

ion

proportional to concentration

approaching to the limit, I

keh[S] + krr =

I keh[S]

I


quantum efficiency (yield)

• the first principle of photochemistry: only molecules absorbing a photon can react• number ratio of reacted molecules to absorbed photons, assuming single photon

process:

n(reacted molecules) / n(absorbed photons)

• Processes of heterogeneous photocatalysis may contain reactions with multiple electrons or holes, e.g., water photolysis to give oxygen.

• quantum efficiency for heterogeneous photocatalysis:

n(electrons or holes used in reaction) / n(absorbed photons)

r (electrons or holes used in reaction) / r (absorbed photons)

• apparent quantum efficiency

r (electrons or holes used in reaction) / r(incident photons)

where r(incident photons) is a light flux (I).

I

I


number of electrons or holes for reaction

example 1: acetic acid decomposition

CH3COOH + 2O2 2CO2 + 2H2OAssuming the reduction of 1 mol of oxygen (O2) into 2 mol of water requires 4 positive holes, 8 mol of electron-hole pairs are used in this stoichiometry. Therefore, 1 mol of carbon dioxide production corresponds to 4 mol of photons, at minimum.

example 2: acetaldehyde decomposition

CH3CHO + 5/2 O2 2CO2 + 2H2OAssuming the reduction of 1 mol of oxygen (O2) into 2 mol of water requires 4 positive holes, 10 mol of electron-hole pairs are used in this stoichiometry. Therefore, 1 mol of carbon dioxide production corresponds to 5 mol of photons, at minimum.

example 3: water splitting

2H2O O2 + 2H2Assuming the production of 1 mol of oxygen (O2) from water requires 4 positive holes, 4 mol of electron-hole pairs are used in this stoichiometry. Therefore, 1 mol or 2 mol of oxygen or hydrogen production corresponds to 4 mol of photons, at minimum.


quantum efficiency

• quantum efficiency for heterogeneous photocatalysis:

r (electrons or holes used in reaction) / r (absorbed photons)

= n{I keh[S] / (keh[S] + kr)} / Inkeh[S] / (keh[S] + kr)

• apparent quantum efficiency

r (electrons or holes used in reaction) / r (incident photons)

= {nI keh[S] / (keh[S] + kr)} / In keh[S] / (keh[S] + kr)

where r(incident photons) is a light flux (I).


concentration of substrate

• overall rate of photocatalytic reaction based on steady-state approximation for electron-hole pairs

r = I nkeh[S] / (keh[S] + kr) or

r = I nkeh[S] / kr (when keh[S] << kr)

• meaning of keh[S]: rate of SURFACE REACTION with electron-hole pairs with surface-adsorbed substrate

• two possible cases:(1) adsorption equilibrium during the reaction(2) non-equilibrium due to faster consumption of substrate on the surface

= diffusion-limited process


adsorption and photocatalytic activity

• the larger the adsorbed substrate(s), the higher the activity

• the larger the surface area, the larger the adsorbed amount

an examplelinear relation between the rate and adsorbed silver ion (J. Phys. Chem., 87 (1997) 3550.

Sr

eh kkIr


kinetic analysis

(1) first-order kinetics for a substrate: a linear relation between logarithm of product yield (substrate consumption) and time– adsorption equilibrium during the reaction in Henry fashion (or low-

concentration part of Langmuirian fashion) for the equation– non-equilibrium due to faster consumption of substrate on the surface

= diffusion-limited processrate constant: Ikeh/kr and a (diffusion constant)Checking light intensity dependence, these may be discriminated: first order =

Henry-type adsorption and zeroth order at the higher intensity = diffusion-limited process

(2) reciprocal relation with concentration of substrate: a linear relation between rate and concentration of a substrate– adsorption equilibrium constant K can be estimated and compared with that

obtained in the dark adsorption equilibrium measurement– kS (= Ikeh/kr) can be estimated.


first-order kinetics in photocatalysis

Q What kind of reaction kinetics can interpret the experimental results, if a first-order kinetics, like plots below, is observed?


first-order kinetics

• two possible cases:(1) adsorption equilibrium during the

reaction in Henry fashion (or low-concentration part of Langmuirianfashion) for the equation

r = I nkeh[S]/ kr = aI kehC/ kr

(2) non-equilibrium due to faster consumption of substrate on the surface= diffusion-limited process: The reaction rate is determined by the rate of diffusion with a constant a.

[S] ~ 0r = aC How are these discriminated?




reaction in Henry fashion (or low-concentration part of Langmuirianfashion) for the equation

r = I nkeh[S]/ kr = aI kehC/ kr


[S] ~ 0r = aC

What the observed rate constant kmeans?




reaction in Henry fashion (or low-concentration part of Langmuirian fashion) for the equation

r = I nkeh[S]/ kr = I(aC keh/kr)


[S] ~ 0r = aC = bSC

S: specific surface area

light-intensity dependence

first order

vs.

at higher intensity region

zeroth order


Fick's law of diffusion

• rate (flux; J) of diffusion

• diffusion constant D include area of "hypothetical wall".

• J = DC if surface concentration is zero.

• for particles,

hypothetical wall = thin diffusion layer surrounding the surface

hypotheticalwall

x axis

xCDJ

lowconcentration

side

hypothetical wall high concentration

side


kinetic analysis

(1) first-order kinetics for a substrate: a linear relation between logarithm of product yield (substrate consumption) and time– adsorption equilibrium during the reaction in Henry fashion (or low-

concentration part of Langmuirian fashion) for the equation– non-equilibrium due to faster consumption of substrate on the surface

= diffusion-limited processrate constant: Ikeh/kr and a (diffusion constant)Checking light intensity dependence, these may be discriminated: first order =

Henry-type adsorption and zeroth order at the higher intensity = diffusion-limited process

(2) reciprocal relation with concentration of substrate: a linear relation between rate and concentration of a substrate– adsorption equilibrium constant K can be estimated and compared with that

obtained in the dark adsorption equilibrium measurement– kS (= Ikeh/kr) can be estimated.


meaning of constants

0 2 4 6 8 100

5x106

1x107

1.5x107

2x107

1/r

1/C

bC

ar

11

0 0.2 0.4 0.6 0.8 10

2x106

4x106

6x106

8x106

C/r

C

'' bCarC

Q What do two parameters, a (a') and b (b'), obtained from the slope and intercept of a linear plot, mean?


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