1. Reaction Sequences - Catalytic Cycles
Catalyzed reactions do not proceed in a single elementary step, but through a sequence of steps (many of which are speculative).
The observed behaviour of a catalytic process represents the overall kinetics of the reaction sequence.
Open Reaction Sequences
When a reaction sequence generates products through reactive intermediates that are not reproduced in any step, the sequence is said to be open.
Consider the decomposition of ozone:
Since the reactive intermediate O is not reproduced, this is considered an open sequence.
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2. Catalytic Reaction Sequences
Closed Reaction Sequences
A closed reaction sequence is one in which an active centre is reproduced to generate a cyclic reaction pattern.
If CS represents an active site on the surface of a solid catalyst:
we have a closed reaction sequence.
Catalytic Reactions - are closed sequences whose active centres are provided by a separate entity called the catalyst which in principle has a long lifetime
Chain Reactions - are closed sequences whose active centres are generated within the system itself and survive only during a limited number of cycles.
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3. Consecutive Elementary Reactions
When proposing a reaction sequence, or mechanism, it is important to derive a rate expression that can be tested against experimental data. If we consider the simplest elementary sequence:
the question is how would reaction products evolve from a system that abides by this mechanism?
The differential equations governing the rate of formation and/or decomposition of the components of the system are:
For A,
For B,
For C,
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4. Integration of these ordinary differential equations gives:
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5. If r2 is “quick” (k2 = 2 k1) If r2 is “fast” (k2 = 10 k1)
Quite different kinetic behaviour is observed if the decomposition of B (r2) is rapid, relative to the decomposition of A (r1).
In this example, rate comparisons are made on the basis of first-order rate constants i.e. k2 relative to k1
If r2 is “quick” (k2 = 2 k1) If r2 is “fast” (k2 = 10 k1)
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6. Steady-State Approximation
The steady-state hypothesis (SSH) is an important technique of applied chemical kinetics.
If an intermediate compound in a reaction sequence is very reactive, its concentration reaches a plateau after a short period, called the relaxation time.
The analytical expression of the SSH: the derivative with respect to time of the concentration of reactive intermediates is equal to zero.
If compound B was highly reactive, meaning k1/k20, our rate expressions would reduce to:
which can be solved to yield:
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7. Catalytic Reaction Sequences - SSH
Steady-State Hypothesis
In a sequence of elementary steps going through reactive intermediates, the rates of the steps in the sequence are equal.
In our consideration of the sequence ABC, the SSH applied to B reduced the rate expressions to:
This suggests that the rate of decomposition of A (-d[A]/dt) equals the rate of formation of C (d[C]/dt) when the intermediate is sufficiently reactive.
CHEE 323
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8. Catalytic Sequences: Steady State Approximation
Example 1-1 of Gates illustrates the catalytic decomposition of ozone by chlorine. k1 k2
From a design perspective, we are interested in the overall rate of reaction and its dependence on concentration, temperature and [catalyst].
This is a more complex problem than the elementary reaction case, because sequential reactions contribute to the overall process.
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9. Catalytic Sequences: Steady State Approximation
The rates of the constituent reactions are:
To derive an expression for the overall reaction rate that this sequence supports, we start with component material balances:
Note that this is a system of coupled, ordinary differential equations
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10. Catalytic Sequences: Steady State Approximation
Solving this system of equations is greatly simplified if the SSH is applicable.
In this example, suppose that Cl. and ClO are sufficiently reactive such that their concentration is expected to be constant.
Applying the SSH to Cl• yields:
from which the concentration of the intermediate is derived:
(the same expression is derived from treating [ClO] with the SSH)
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11. Catalytic Sequences: Steady State Approximation
Using [Cl.] in the rate expressions r1 and r2 yields:
Given that reactions 1 and 2 proceed
through the same reactive intermediates,
the SSH results in these rates being equal.
In this example, the overall rate of reaction,
r3, is that of both r1 and r2 providing that
the SSH applies.
However, this expression is unsatisfactory
for design purposes, given that Cl• and ClO
are unlikely to be measurable quantities. k1 k2
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12. Catalytic Sequences: Steady State Approximation
Our rate expressions remain a function of an intermediate, [ClO]. Since we typically have no measure of this quantity, we should express the rate in terms of the total concentration of catalyst, [Cl]T.
Substituting for [Cl]T yields:
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J.S. Parent