Kinetics of Surface Reactions

1
Kinetics of Surface Reactions Many reactions
occur on or are catalyzed by surfaces that can
dramatically affect the kinetics of the
reaction Consider the decomposition of phosphine
on glass Trans. Faraday Soc., 17621
(1922) glass surface PH3 (g)
----------------gt 1/4 P4 (g) 3/2 H2 (g) The
surface catalyzed reaction can be described by a
mechanism in which phosphine first reversibly
chemically adsorbs (chemadsorbs) or covalently
bonds to the glass surface
The chemadsorbed species is then converted to
products while bound to the surface and then the
products desorb (this is usually viewed as
occurring as a single step in the mechanism)
regenerating the catalyst surface
Is this an example of homogeneous or
heterogeneous catalysis? The rate limiting step
in surface catalysis is usually the 2nd reaction
desorption step and so we can initially write the
rate law as - d PPH3 / dt k2 q where q is
the fraction of surface sites to which PH3 is
chemadsorbed.
2
An adsorption isotherm describes how the partial
pressure of an adsorbing species varies
isothermally with the fraction of surface
covered. In the Langmuir adsorption isotherm
? Only mononlayer coverage is allowed on
the surface (it is the Brunauer, Emmett, and
Teller or BET isotherm that allows for
multi-layer adsorption). ? All surface sites
are equivalent, i.e., the surface is perfectly
smooth on a microscopic level. In actuality even
well prepared surfaces have quite a bit of
structure
? the ability of a molecule to adsorb or desorb
is independent of the whether molecules are
adsorbed on neighboring sites (the Freundlich
isotherm accounts for nearest neighbor effects).
3
This scanning tunneling microscope (STM) 35 nm x
35 nm image is of single substitutional Cr
impurities (small bumps) on the Fe (001) surface.

This image was orginally published in
Atomic-scale Observations of Alloying at the
Cr-Fe(001) Interface, A. Davies, J.A. Stroscio,
D.T. Pierce, and R.J. Celotta, Phys. Rev. Lett.,
76 4175 (1996). Electron Physics Group and is
taken from the http//physics.nist.gov/GenInt/STM/
stm.html WEB page.
4
In developing the isotherm we assume that an
equilibrium exists between the adsorbed reactants
and these same reactants in the gas phase

• where the rate of adorption is equal to the rate
  of desorption
• rate of adsorption rate of desorption
• yielding an expression
• k1 PPH3 (1 - q) k-1 q
• Can you justify this expression?
• which can be solved for the fraction of surface
  covered by the adsorbed species giving the
  Langmuir adsorption isotherm
• q k1 PPH3 / (k-1 k1 PPH3) K1 PPH3 / (1
  K1 PPH3)
• What is K1?
• Substituting this expression for the fraction of
  surface covered into the rate equation gives
• d PPH3 / dt k2 K1 PPH3 / (1 K1 PPH3)
• Could you solve this differential equation? If
  you could solve it, could you plot some function
  of PPH3 versus time that would allow you to
  determine k2 and K1?

5
A plot of the rate of the surface catalyzed
reaction versus the partial pressure of the
reactant
shows two regions where ? at low partial
pressures the rate has a 1st order dependence
on the partial pressure of the reactant in the
gas phase - d PPH3 / dt k2 K1 PPH3
? at high partial pressures the rate has a 0th
order dependence on the partial pressure of the
reactant in the gas phase - d PPH3 / dt k2
Can you explain the dependence of the order of
the surface catalyzed reaction of partial
pressure of the adsorbing species?
6
Inhibition or poisoning of a surface catalyzed
reaction can occur when two or more species
compete for the same surface sites. Consider the
platinum surface catalyzed decomposition of
ammonia Pt (s) NH3
(g) -----gt 1/2 N2 (g) 3/2 H2 (g) that is
poisoned by the molecular hydrogen product, but
not by molecular nitrogen. Once H2 has been
formed, it can compete with NH3 for sites on the
Pt surface
Since the partial pressure of the poison H2, as a
product of this reaction, increases with the
extent of the reaction, the reaction is said to
be autoinhibited. Examining the adsorption -
desorption equilibrium for the ammonia we
have k1, NH3 PNH3 ( 1 - qNH3 - qH2 )
k-1, NH3 qNH3 which with an analogous
expression for H2 can be solved for the fraction
of the surface covered by ammonia qNH3 KNH3
PNH3 / ( 1 KNH3 PNH3 KH2 PH2 ) What is
the analogus expression for the adsorption -
desorption equilibrium for the molecular
hydrogen qH2 ?
7
The rate of the autoinhibited surface catalyzed
decomposition of ammonia can thus be written
rate - d PNH3 / d t k2 qNH3 k2
KNH3 PNH3 / ( 1 KNH3 PNH3 KH2 PH2
) What would the rate law be, if the molecular
hydrogen product is either strongly adsorbed or
present at high partial pressure?
8
Hydrogen is known to poison the unimolecular
decomposition of ammonia on platinum J. Chem.
Soc., 1271114 (1925) Pt (s)
NH3 (g) -----gt 1/2 N2 (g) 3/2 H2
(g) 1138 oC The total pressure in this
reaction system was followed as a function of
time time (sec) total pressure (mm
Hg) 10 228 60 256 120 272 240 289
360 300 720 320 Assuming that the species
follow Langmuir adsorption isotherms, that
molecular nitrogen is not adsorbed, and that
molecular hydrogen is much more strongly adsorbed
than ammonia a. calculate how the total pressure
would be expected to vary with time. b. Treat
any constants in the theorectical expession as
parameters and vary them to obtain the best fit
with the experimental data. c. On the same
graph plot the experimental data and the best
fit theoretical curve. d. Do you think that
the Langmuir adsorption isotherm provides an
adequate model in this case?