| dc.description.abstract | A very large effort has been directed towards heterogeneous catalysis and establishing the proper form for equations that express the rate of surface reactions as a function of system variables. These equations range from:
Simple empirical expressions
Forms suggested by reaction stoichiometry and thermodynamics
Complex forms typical of the Langmuir–Hinshelwood hypothesis, extensively studied by Hougen, Watson, and others
Reaction Rate Models
The reaction rate for any heterogeneous catalytic reaction can be expressed by two types of models:
Hougen–Watson Models
Derived from the Langmuir–Hinshelwood theory of adsorption
Rate expression:
r=k?CAm?CBn(1+?KiCi)(1)r = \frac{k \, C_A^m \, C_B^n}{(1 + \sum K_i C_i)} \tag{1}r=(1+?Ki?Ci?)kCAm?CBn??(1)
The denominator expresses competition for active sites by system components, where KiK_iKi? are Langmuir adsorption equilibrium constants.
Exponents mmm and nnn often equal 1/21/21/2 or 222 for dissociative adsorption.
This type of expression is called a Langmuir rate law or Hougen–Watson model.
Power-Function Models
Rate expression:
r=k?CAm?CBn(2)r = k \, C_A^m \, C_B^n \tag{2}r=kCAm?CBn?(2)
Rate Constants
The rate constants in Equations (1) and (2) are not those of unique elementary processes but can usually be represented by the Arrhenius equation:
k=A?exp?(?ERT)(3)k = A \, \exp\left(-\frac{E}{RT}\right) \tag{3}k=Aexp(?RTE?)(3)
where:
AAA = pre-exponential factor
EEE = apparent activation energy
RRR = gas constant
TTT = temperature
Assumptions in Kinetic Relations
In deriving kinetic relations of type (1), several assumptions are made regarding elementary steps. Ignoring transport processes, the steps include:
Adsorption of reactants
Surface reaction of adsorbed molecules
Desorption of products
Independent mass transfer studies show that concentration gradients across the gas film are negligible. Since diffusional steps are not rate-controlling, the remaining steps to examine are adsorption, surface reaction, and desorption.
Case Study: Hydrogenation of Aniline to Cyclohexylamine
Several models were postulated, and rate expressions developed based on combinations of the following factors:
Hydrogen adsorption state: Molecular (I) or atomic (II)
Mode of hydrogen addition: Simultaneous (A) or stepwise (B)
Adsorption sites:
Both reactants on the same active site
Aniline in gas phase, hydrogen adsorbed
Hydrogen in gas phase, aniline adsorbed
Rate-controlling steps considered:
(a) Adsorption of hydrogen
(b) Adsorption of aniline
(c) Desorption of cyclohexylamine
(d) Surface reaction
Combination of these factors produced 34 rate expressions. Reverse reaction (cyclohexylamine ? aniline) was neglected as thermodynamically insignificant. By-products (dicyclohexylamine, phenylcyclohexylamine, ammonia) were considered only in adsorption terms.
Model Evaluation
Least-squares analysis compared experimental data with developed rate equations.
The model with smallest standard deviation and non-negative constants was considered most probable.
Observations:
No single model gave positive constants at all temperatures.
After neglecting adsorption constants for by-products, some models gave positive constants, but different equations worked for different temperatures.
Models with positive constants at all temperatures lacked a definite trend in adsorption equilibrium constants with respect to temperature.
Conclusion
It is not possible to correlate the data using a single Hougen–Watson type rate expression for a single reaction that is part of a complex heterogeneous reaction occurring on the catalyst surface. | |
