reaction engineering pt 1

general steps in catalytic reaction mechanisms

adsorption

surface reaction

desorption

difficulties of finding rate of catalytic reactions

rarely follow power rate law

need to develop mechanism and derrive rate law for steps

active site

a point on the surface that can form strong chemical bonds with an adsorbed atom or molecule

where do catalystic reactions happen

at active sites where there are unsaturated atoms

Heterogeneous Catalytic Reaction steps

Mass transfer of A to surface

Diffusion of A from pore mouth to internal catalytic surface

Adsorption of A onto catalytic surface

Reaction on surface

Desorption of product B from surface

Diffusion of B from pellet interior to pore mouth

Diffusion of B from external surface to the bulk fluid (external diffusion)

adsorption mechanisms

dissociation of molecules

Langmuir

molecular adsorption

surface reaction mechanisms

single site

dual site

Eley-Rideal

Eley-Rideal

1 reactant adsorbst to active site and the other stays in the gas phase

dual site

some reactants or products are larger and need 2 sites or need a vacant site adjacent to react.

some catalysts can have different types of sites with preferences for different molecules

Ct

Total number of active sites per unit mass of catalyst divided by Avogadro’s constant

Ct = Cv + Cas

how are adsorpion and desorpion rates related?

rd = - rad

Kd = 1/Kc for he desorption of C

Pseudo steady sate hypothesis

•rate of adsorption =  rate of surface reaction = rate of desorption) 

•No accumulation of species on the surface

•Each species adsorbed on the surface is a reactive intermediate

Net rate of formation of species i adsorbed on the surface is 0, r_i·S=0

why is external diffusion important?

the overall rate of reaction is often limited by the rate of mass transfer of reactants between the bulk fluid and the catalytic surface.

How can mass ransfer limiaion be avoided in the lab

using high velocities or small particles

Biot (Bi) number

determine external diffusion vs reaction rate limitations

k_s:  reaction rate coefficient / k_g:  mass transfer coefficient

Diffusion

spontaneous intermingling or mixing of atoms or molecules by random thermal motion

External diffusion

diffusion of the reactants or products between bulk fluid and external surface of the catalyst

Molar flux (W)

moles pass ing through a specific surface area per unit time

bulk motion (B) + molecular diffusion (J)

Hydrodynamics boundary layer thickness

distance from a solid object to where the fluid velocity is 99% of the bulk velocity U₀

Mass transfer layer thickness

distance d from a solid object to where the concentration of the diffusing species is 99% of the bulk concentration

types of boundary conditions

concentration at boundary known

flux at boundary known - Was = 0, Was = -ra/area, Wab = k(Cab - Cas)

concentration profile is symmetric about a plane

Types of molar flux

equimolar counter diffusion (Wa = -Wb)

dilute Ca (ya = 0)

diffusion of A through stagnant B (Ub = 0)

forced convection (Ja « Ba)

Internal diffusion

diffusion of the reactants or products from the external pellet surface (pore mouth) to the interior of the pellet.

What does effective diffusivity (De) account for?

Tortuosity of paths

Void spaces

Pores having varying cross-sectional areas

Tortuosity

distance molecule travels between 2 pts/actual distance between those 2 pts

Thiele modulus

dimensionless number that compares how fast a reaction happens to how fast reactants can diffuse through a porous catalyst.
It tells you whether reaction kinetics or diffusion limitations dominate

What does large Thiele modulus mean?

internal diffusion is rate limiting

surface rxn is rapid, reactant is consumed very closed to the external surface of pellet (A waste of precious metal inside of pellet)

Internal effectiveness factor

observed rate of rxn / rate if entire interior surface exposed

effect of paricle dimater on internal diffusion

bigger particle = bigger Thiele modulus, more internal diffusion