IC-1/38 Lecture Kinetics

IC-2/38 Lecture What is Kinetics ? Analysis of reaction mechanisms on the molecular scale Derivation of rate expressions Design and analysis of experiments to test rate equations and derive kinetic parameters Theoretical prediction of rate constants How can we improve it?

IC-3/38 Lecture Basic surface interactions Reactions take place on the metal surface Desorption Reaction Molecular adsorption Dissociativ adsorption Diffusion CO CO 2 O

IC-4/38 Lecture Reaction Scheme + AdsorptionDesorption CO O2O2 CO 2 catalyst adsorptionreactiondesorption reaction coordinate Energy Reaction

IC-5/38 Lecture Heterogeneous Catalysis Adsorption Reaction Desorption

IC-6/38 Lecture The ‘Mean-Field’Approximation B A A A A B B A A A A B BB B B B B B B randomordered r = N k  A  B r < N k  A  B N=total number of sites N A =Number of sites occuppied by A N B =Number of sites occuppied by B N * =Number of free sites  A =N A /N  B =N B /N  * =(N-N A -N B )/N

IC-7/38 Lecture Monte Carlo Simulations r << N k  A  B

IC-8/38 Lecture Experimental Evidence by STM 8x8 nm a b Scanning Tunneling Microscopy of Oxygen Atoms on Ruthenium Joost WintterlinFHI - Berlin

IC-9/38 Lecture The Heat of Adsorption is Always …… Negative !!!! G = H - T S

IC-10/38 Lecture Reaction Scheme + AdsorptionDesorption CO O2O2 CO 2 catalyst adsorptionreactiondesorption reaction coordinate Energy Reaction

IC-11/38 Lecture Adsorption Associative Adsorption: CO, N 2, Ar, He, etc At equilibrium:

IC-12/38 Lecture Langmuir Isotherm  A = K A p A 1 + K A p A

IC-13/38 Lecture Irving Langmuir ( ) worked at General Electrics oxygen adsorption on tungsten filaments of light bulbs 1932: Nobel Prize in Chemistry Langmuir Adsorption Isotherm:  A = K A p A 1 + K A p A

IC-14/38 Lecture Adsorption Dissociative Adsorption: N 2, O 2, CO, H 2 etc. For equilibrium =0

IC-15/38 Lecture Adsorption Competitive Adsorption:

IC-16/38 Lecture The Fuel Cell

IC-17/38 Lecture H2H2 H 2 /25 ppm CO H 2 /250 ppm CO H.-F. Oetjen et al. (1996) Pt electrode CO severely reduces efficiency

IC-18/38 Lecture Langmuir - Hinshelwood Kinetics Irving Langmuir Nobel Prize Langmuir Isotherm 1927 Kinetics of Catalytic Reactions Cyril Norman Hinshelwood Nobel Prize 1956

IC-19/38 Lecture Eley - Rideal Mechanism direct reaction between gas phase and adsorbed species Unlikely !!

IC-20/38 Lecture The Langmuir-Hinselwood (LH) mechanism Net reaction over catalyst Elementary steps

IC-21/38 Lecture The Complete Solution

IC-22/38 Lecture The Steady State Approximation Interesting solution for many processes, but we lose time dependence Last eq. not independent, i.e. n-1 eq. for n elementary steps

IC-23/38 Lecture The Quasi-equilibrium Approximation Assumes one step is rate limiting while the rest are in Quasi-equilibrium RLS Notice

IC-24/38 Lecture The Quasi-equilibrium Approximation Notice only valid when step 3 is rate limiting!

IC-25/38 Lecture Steps with Similar Rates while step 2 and 4 are in quasi-equilibrium Assume step 1 and 3 are slow i.e. rate limiting steps (rls) Resulting in a reduced problem as comparred to the complete solution rls

IC-26/38 Lecture Simplifications to the Quasi-equilibrium Approximation: Irreversible steps How does this approximation describe the approach towards equilibrium? Irreversible steps: Assume for example that step 4 is irreversible k 4 - =0 K 4 -1 =0    0  r 3 - =0

IC-27/38 Lecture Simplifications to the Quasi-equilibrium Approximation: The MARI Approximation The Most Abundent Reaction Intermediate approximation (MARI) Assume for example that specie A bonds much stronger than B and AB- A will then become MARI What are examples of MARI??

IC-28/38 Lecture Simplifications to the Quasi-equilibrium Approximation: Nearly empty Surface Typical for high temperatures In that case is it simple to find the maximum of the rate as a function of gas-composition:

IC-29/38 Lecture Reaction order What is the reaction order n AB ?

IC-30/38 Lecture Apparent activation energy as function of molefraction

IC-31/38 Lecture Apparent activation energy as function of molefraction Notice that    and  S x both depends on T, but in a more weak manner than exponential. It can give problems in an Arrhenius plot. E app Asumptions: p are assumed independent of T, i.e. we keep the pressure fixed. The rate constant can be written as The equilibrium constants as

IC-32/38 Lecture Coverage and reaction order and apparent activation energy as function of molefraction Notice: n A, n B, and E app varies with pressure for fixed temperature

IC-33/38 Lecture CO Oxidation Reaction Scheme The overall reaction is: The elementary step on a surface are:

IC-34/38 Lecture CO Oxidation the mechanics For the 3 elementary steps in Quasi equilibrium we easily obtain the langmuir equation for adsorption and desorption

IC-35/38 Lecture CO Oxidation- the rate The rate limiting step: From equilibrium we have

IC-36/38 Lecture CO Oxidation- Temperature limits Low Temperature limit: CO will become MARI The CO 2 interacts so weakly that step 4 can be considered irreversible ~ ~ ~ Find reaction orders in this limit. n O2 =0.5, n CO =-1

IC-37/38 Lecture CO Oxidation- Temperature limits The CO 2 interacts so weakly that step 4 can be considered irreversible High Temperature limit: Very low concentration of surface species ~1~1 ~ Find reaction orders in this limit. n O2 =0.5, n CO =1

IC-38/38 Lecture CO Oxidation-Results