EEA Grants
Norway Grants
Introduction to
kinetics and catalysis
Ing. Marcela Králová Ph.D., CEITEC
20.4.2015
Content
• Kinetics
• Reaction lows
• Reactions orders and its determination
• Theory of chemical reactions
• Homogeneous catalysis
• Heterogeneous catalysis
• Photocatalysis
Kinetics
•
Deal with the rates of chemical processes
•
Chemical processes – sequence of one or more single
step
•
Elementary process – transition between two
atomic/molecular state separated by a potential barrier
• Activation energy
• Low barrier = fast reaction
• High barrier = slow reaction
•
Elementary reactions
• Single reactive collision (bimolecular step)
• Dissociations/isomerisation (unimol.step)
• Termolecular step
•
Goals of the study:
• Reaction mechanisms
• Absolute reaction rate
Measuring the reaction rate
•
Gas syringe method:
•
For gas reaction
•
Gas is collected in the syringe
•
Push out against the plunger
•
The volume can be read on the syringe
•
Volume can be converted to a change in concentration
Measuring the reaction rate
•
Changes in mass:
•
For gas reaction
•
Calculation of mass loss
•
Gas escapes from the reaction flask
•
•
Mass of precipitation:
For reaction where the precipitation is formed
•
Using stopwatch
Reaction rate
•
Reaction rate:
• Rate at which reactants are used up
• Products are formed
• Units: concentration per time (mol.dm-3.s-1)
N2 + 3H2  2NH3
v
d N 2 
x
dt
v
v
d H 2 
 3x
dt
d N 2 
1 d H 2  1 d NH 3 


x
dt
3 dt
2 dt
v
d NH 3 
 2x
dt
Rate laws
•
•
Differential rate low:
•
Changes of reaction rate with the concentration
•
Reaction rate is proportional to the rate of conc.
changes
•
Rate is proportional to derivative of concentration
Integrated rate low:
•
Relates the concentration to time
Rate laws
•
Differential rate law (Guldberg-Waag low):
v = k[A]a[B]b[C]c
k …………………… rate constant
powers………….. partial order of the reaction with
respect to the reactant
overall order….. sum of the powers
N2 + 3H2  2NH3
𝑣 = 𝑘[N2][H2]3
Zero-order reactions
•
Rate is independent on the concentration of the reactant
•
Examples:
• some photochemical
• enzymatic catalyzed reactions
• reverse Haber process:
2NH3(g)  3H2(g) + N2(g)
Zero-order reactions
v
AP
dc A
 k  c 0A  k
dt
[k] = moldm-3s-1

dc A
k
dt
cA
t
c A0
0
  dc A   kdt
c A  c A0  kt
Zero-order reactions
•
Half-life 1/2:
• Required time for half of the reactants to be
depleted
c A  c A0  kt
c A0
 c A0  k 1 / 2
2
1/ 2 
c A0
2k
First order reactions
• Rate is dependent on the concentration of one
reactant
• Other reactant can be present, but each will be
zero-order
• Examples:
• AP
• A+B  P; where one component is in excess
First order reactions
A→P
[k] = s-1
dc
v   A  k  c 1A  k  c A
dt

dcA
 k  cA
dt
cA
dc A t
 
  kdt
c A0 c A
0
c A  c A0  e kt
ln
c A0
 kt
cA
First order reactions
• Whenever the concentration of a reactant falls
off exponentially, the kinetics follow the first
order
First order reactions
•
Half-life 1/2:
ln
c A0
 kt
cA
ln
c A0
 k  1 / 2
c A0
2
1/ 2  lnk2
First order reactions
• A+B→P
• Excess of one reactant
• Concentration of the other reactants can be include
in rate constant
v  k  c A  cB
v  k´  cA
Second order reactions
• Rate is dependent on the concentration of
• one second-order reactant (2A  P)
• two first order reactants (A+B  P)
Second order reactions
2A → P
[k] = dm3mol-1s-1
dc
v   A  k  c 2A
dt

dcA
 k  c 2A
dt
1
1

 k t
c A c A0
cA
dc A t
  2   kdt
c A0 c A
0
c
1 A
 k t
c 
 A  c A0
Second order reactions
• Whenever the reciprocal of the concentration
versus time is linear, the kinetics follow the
second order
Second order reactions
•
Half-life 1/2:
1
1

 k 1 / 2
c A0 c A0
2
1
 k  1 / 2
c A0
 1/ 2  kc1
A0
Second order reactions
A+B→P
[k] = dm3mol-1s-1
dc
v   A  k  c A  cB
dt

dcA
 k  c A  cB
dt
x  c A0  c A  cB0  cB
k t 
c (c  x )
1
 ln B 0 A0
c A0  cB 0
c A0 (cB 0  x )
Summary
Reaction
order
Differntial
rate law
d  A

k
dt
Zero
First
Second


d  A
 k  A
dt
Integrated
rate low
Charact
kinetic
plot
Scope of
kinetic
plot
Units of
rate
constant
A  A0   kt
[A] vs t
-k
moldm-3
s-1
ln[A] vs t
-k
s-1
k
dm3mol-1
s-1
 A   A0  e
kt
d  A
1
1
 k  A2

 kt
dt
 A  A0 
1/[A] vs t
Determination of rate low
from experimental data
•
Overall reaction order:
•
not deduced from chemical equation
•
determined experimentally
•
concentration measurement of one or more
reactants
Determination of rate low
from experimental data
•
Integral method:
•
Concentration as a function of time
•
Comparison the time dependence
LINEAR
c A  f (t )...N  0
ln c A  f (t )...N  1
1
 f (t )...N  3
2
cA
1
 f (t )...N  2
cA
Determination of rate low
from experimental data
•
Half lives:
•
Only for reaction where is dependence:
• 1/2 = k/cA0(N-1)
• two experiments with different cA0
• receive two half time
ln( 1 / 2 )1  ln(k )  ( N  1)  ln c A0(1)
ln( 1 / 2 )2  ln(k )  ( N  1)  ln c A0( 2)
subtracted
ln
N  1
 1 / 2(1)
 1 / 2( 2)
ln
c A0 ( 2 )
c A0(1)
Determination of rate low
from experimental data
•
Differential method:
•
Initial concentration same for all reactants
• cA0 = cB0 = cC0 = c0
• v0 = kc0N
v0(1)  k  c0N(1)
divide
v0( 2 )  k  c0N( 2 )
ln
N
ln
v0(1)
v0 ( 2 )
c0(1)
c0( 2 )
Determination of rate low
from experimental data
•
Isolation method:
• Determination of partial reaction order
• Different initial concentration of same reactant
• cA0(1) = 2cA0(2)
• v0 = kc0N
v0(1)  k  cA0(1)  cB 0(1)  cC 0(1)



v0( 2 )  k  ( 2c A0( 2 ) )  cB 0( 2 )  cC 0( 2 )
divide
v0(1)
v0 ( 2 )
1
 
2
Collision theory
• Explain:
• How chemical reaction occur
• Why reaction rate is different for different
reaction
• Criteria:
• Sufficient kinetic energy (activation energy)
• Proper orientation
• Sufficient collision
Collision theory
A + B → C • A and B are gasses
• Frequency of collision is proportional to the
concentration of A and B
• Doubling of cA, the frequency of A-B collision double
• The rate at witch molecules collide affect the
overall reaction rate
Collision theory
Activation energy
• A and B are gasses
• Reactant sufficient kinetic energy to
break the chemical bonds
• Reactants bonds are broken
• Products bonds are formed
• Reactants must be moving enough
• The minimum energy with which
molecules must be moving is
called activation energy
• Rate increases with the temperature
Collision theory
Molecular orientation
and
Effective collision
• Sufficient activation energy not
garantee succesfull collision
• Necessity of right orientation
• Molecules in liquid or gas –
constant, random motion –
probability of collision
• Effective collision - one in
which molecules collide with
sufficient energy and proper
orientation, so that a reaction
occur
Theory of transition state
• Postulate the existence of hypothetical transition
state
• It occurs between reactants and products state
• Formed species is called activated complex
• Based upon collision theory
Theory of transition state
• Activated complex:
• Reactant-product hybrid
• Exist at the peak of the reaction coordinate
• Transition state
Theory of transition state
• Factors determines if the reaction occur or
not:
• Concentration of the activated complex
• The rate at which the activated complex breaks
apart
• The mechanism by which the activated complex
breaks apart
• Back to reactants
• Towards products
Collision theory versus
Theory of transition state
• Collision theory:
• Successful collision
• Enough energy
• Proper orientation
• Theory of transition state:
• Successful collision
• Enough energy
• Proper orientation
PRODUCTS
ACTIVATED
COMPLEX
Catalysis
• Catalysts:
•
•
•
•
•
Reduced activation energy
Increase the reaction rate
Do not change during the reaction
Affect the kinetics
Do not affect the equilibrium state
• Homogeneous catalysis:
•
Same phase as a reactants (g; l)
• Heterogeneous catalysis:
•
Catalysts (s) and reactants (g; l)
Homogeneous catalysis
• Examples:
•
•
•
Acid catalysis
Organometallic catalysis
Enzymatic catalysis
• Advantage:
•
•
Mix into the reaction mixture
High degree of interaction: catalyst-reactant
• Disadvantage:
•
Irrecoverable after the reaction
Heterogeneous catalysis
• Mechanisms:
•
•
•
•
•
•
Diffusion of reactants to surface of catalyst
Adsorption of reactants onto the surface at active
sites
Interaction between the reactant and catalysts
surface
Chemical reaction
Desorption of products
Diffusion of products
Heterogeneous catalysis
• Advantage:
•
Separation form the reaction mixture
• Disadvantage:
•
Saturation of catalyst surface
Photocatalysis
•
Absorption of UV light
•
Creation of e- and h+
REDUCTION:͘
e- + O2 → ●O2●O - + ●OOR
2
→ unstable products → CO2 + H2O
OXIDATION:͘
H2O + h+ → ●OH + H+
●OH
+ org. molecule + O2 → ●OOR → → → → → CO2 + H2O
Photocatalysis
• TiO2:
•
•
High activity; chemical biological inertness
Photostable; nontoxicity
•
High recombination; absorption only in UV
• Application:
•
•
•
Self-cleaning
Depollution
De-odorizing
Thank you for your attention
• This project is funded by the Norwegian Financial Mechanism. Registration
number: NF-CZ07-ICP-1-040-2014. Name of the project: „Formation of
research surrounding for young researchers in the field of advanced
materials for catalysis and bioapplications“