Post on 09-May-2018
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 2
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 3
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.
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 4
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 5
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 6
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 7
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
(+)
(-)
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 8
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.
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 9
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)
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 10
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 11
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 12
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.
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 13
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).
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 14
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 15
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 16
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.
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 17
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?
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 18
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?
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 19
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
What the observed rate constant kmeans?
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 20
first-order kinetics
• two possible cases:(1) adsorption equilibrium during the
reaction in Henry fashion (or low-concentration part of Langmuirian fashion) for the equation
r = I nkeh[S]/ kr = I(aC keh/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 = bSC
S: specific surface area
light-intensity dependence
first order
vs.
at higher intensity region
zeroth order
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 21
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
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 22
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.
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 23
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?
2017/06/15—Advanced Course in Environmental Catalytic Chemistry 24
comments on this lecture
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