Reaction Kinetics 3

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Reaction Kinetics (3)
Physical Chemistry

• Xuan Cheng
• Xiamen University

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Physical Chemistry
Reaction Kinetics
Determination of the Rate Law
1. Half-life method
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Physical Chemistry
Reaction Kinetics
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Physical Chemistry
Reaction Kinetics
Determination of the Rate Law
2. Powell-plot method
(17.50)
the fraction of A unreacted
For n ? 1
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Physical Chemistry
Reaction Kinetics
Determination of the Rate Law
For n ? 1
For a given n, there is a fixed relation between
? and ? for every reaction of order n.
Plot ? versus log10? for commonly occurring
values of n to give a series of master curves.
(Fig. 17.6)
The Powell-plot method requires the initial
investment of time needed to make the master
plots.
Table 17.1 gives the data needed to make the
master plots.
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Physical Chemistry
Reaction Kinetics
Determination of the Rate Law
3. Initial-rate method
Measure r0 for two different initial
concentrations A0,1 and A0,2 while keeping
B0, C0, fixed.
The ratio of initial rates for runs 1 and 2
? can be found
The orders ?,? can be found similarly
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Physical Chemistry
Reaction Kinetics
Determination of the Rate Law
4. Isolation method
Make initial concentrations of reactant A much
less than the concentrations of all other
species B0 gtgt A0, C0 gtgt
A0,
The rate law becomes
Where j is essentially constant.
The reaction has the pseudo-order ?.
The orders ?,? can be found similarly.
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Physical Chemistry
Reaction Kinetics
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Physical Chemistry
Reaction Kinetics
Rate Laws and Equilibrium Constants for
Elementary Reactions
Show that for a reaction that takes place in a
sequence of steps, the overall equilibrium
constant is a product of ratios of the rate
constants for each step.
It is sufficient to consider a reasonably general
but simple two-step reaction sequence, such as
(second-order in each direction, k1, k-1)
(first-order forwarded, second-order reverse, k2,
k-2)
(overall)
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Physical Chemistry
Reaction Kinetics
Rate Laws and Equilibrium Constants for
Elementary Reactions
At equilibrium, all the reaction are individually
at equilibrium, and setting the net rates each
equal to zero gives
The equilibrium constant of the overall reaction
is therefore
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
The Rate-Determining-Step Approximation
The reaction mechanism is assumed to consist of
one or more reversible reactions that stay close
to equilibrium during most of the reaction,
followed by a relatively slow rate-determining
step, which in turn is followed by one or more
rapid reactions.
The number of molecules that react in an
elementary step
The molecularity of the elementary reaction
unimolecular
bimolecular
trimolecular (termolecular)
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
For the consecutive unimolecular reactions
Suppose now that
Then whenever a B molecule is formed it decays
rapidly into C.
reduces to
The formation of C depends on only the smaller of
the two rate constants
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
The Steady-State Approximation
Assumes that during the major part of the
reaction, the rates of change of concentrations
of all reaction intermediates are negligibly small
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
C is formed by a first-order decay of A, with a
rate constant k1, the rate constant of the
slower, rate-determining step.
The same result as before, but obtained much more
quickly.
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Consider the following mechanism composed of
unimolecular reactions
D is rapidly formed from C
(the rate-determining step)
is slower than
remains close to equilibrium
is not in equilibrium
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Example 17.4
The rate law for the Br--catalyzed aqueous
reaction
is observed to be
(17.55)
A proposed mechanism is
rapid equilib.
slow
(17.56)
fast
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Example 17.4
Deduce the rate law for this mechanism and relate
the observed rate constant k in (17.55) to the
rate constants in the assumed mechanism (17.56)
(1)
the rate-determining step
(2)
(3)
The formation of ONBr in (2)
Step (1) is near equilibrium. Equation (17.53)
gives
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Example 17.4
Example 17.5
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
More examples in using the steady-state
approximation
Account for the rate law for the decomposition of
N2O5
on the basis of the following mechanism
First identify the intermediates
NO and NO3
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
According to the steady-state approximation, set
both rates equal to zero
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
The net rate of change of concentration of N2O5 is
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
because
It follows that the reaction rate is
where
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Pre-equilibria
From a simple sequence of consecutive reactions
we now turn to a slightly more complicated
mechanism
Where C denote the intermediate.
This scheme involves a pre-equilibrium, in which
an intermediates is in equilibrium with the
reactants.
A pre-equilibrium arises when the rates of
formation of the intermediate and its decay back
into reactants are much faster than its rate of
formation of products thus, the condition is
possible when kagtgtkb but not when kb gtgtka.
Because we assume that A, B, and C are in
equilibrium.
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Pre-equilibria
We can write
In writing these equations, we are presuming that
the rate of reaction of C to form P is too slow
to affect the maintenance of the pre-equilibrium
(see the following example). The rate of
formation of P may now be written
This rate law has the form of a second-order rate
law with a composite rate constant
where
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Pre-equilibria
Example Analyzing a pre-equilibrium
Repeat the pre-equilibrium calculation but
without ignoring the fact that C is slowly
leaking away as it forms P.
The net rates of change of P and C are
where
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Physical Chemistry
Reaction Kinetics
Reaction Mechanisms
Pre-equilibria
where
When the rate constant for the decay of C into
products is much smaller than that for its decay
into reactants
where
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Physical Chemistry
Reaction Kinetics
Homework
Page 592
Page 593
Prob. 17.28
Prob. 17.39
Prob. 17.29
Prob. 17.52
Prob. 17.33
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Physical Chemistry
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Physical Chemistry
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Physical Chemistry
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Physical Chemistry
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Physical Chemistry
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Physical Chemistry
??(1)?????
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Physical Chemistry
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