Kinetic Methods
Rates
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In order to use a reaction for analytical purposes, the
reaction must have a rate slow enough to measure but
fast enough to get it done in a reasonable time.
There must be some way of monitoring the reaction’s
progress.
The rate law for the reaction must be known.
Rate is defined so as to always be a positive quantity.
Thus for Reactant → Product,
Rate = -d(Reactant)/dt or +d(Product)/dt
Rate Laws
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Reaction rates depend upon reactant concentrations in
often complicated ways.
This is because reactions rarely proceed by one simple
step but rather through several steps.
The dependence of rate on concentration really is a
matter of what is involved in the slowest, or rate
determining step.
If there are several reactants (A, B, etc.) we can write:
Rate = k(A)a(B)b… where the sum a+b+… is referred
to as the reaction order.
The reaction order must always be determined experimentally and may have little to do with the
molecularity of the reaction, i.e., the balancing
coefficients.
Some reaction orders
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Zero order: Rate = k(reactant)0 = constant
This is often characteristic of heterogeneously
catalyzed reactions.
First order: Rate = k(reactant)1
These reactions follow ln(At) = ln(A0) - kt if A
is the reactant. Also, k = 0.693/t½, where t½ is
the half-life of the reaction, the time required
for half the reactant to disappear.
Second order: Rate = k(reactant)2 or k(A)1(B)1.
The first type follows 1/(At) = 1/(A0) + kt.
Pseudo-first-order Kinetics
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It is sometimes possible to use such a great
excess of one reactant that its concentration
doesn’t change during the analysis and thus the
rate depends on only the other reactant. Such
conditions are called pseudo-first-order.
It may even be possible to adjust conditions so
as to make the reaction pseudo-zero-order.
Analytical Methods
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It is possible to use kinetic methods in many different
ways (see diagram in text, p.626).
For example, one can measure the reactant
concentration at some particular time and use the
integrated rate law to calculate what the value was at
t=0. This can sometimes be accomplished by stopping
the reaction chemically to give time to measure (At).
An alternative is to measure the time required for some
amount of reactant to disappear.
Radiochemical Methods
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Isotopes of many elements are radioactive.
Thus the presence of such isotopes makes for a
sensitive way of detecting and quantifying them.
In substances where only very small amounts of
radioactive isotope are present, it is possible to
‘activate’ the sample by bombarding with
neutrons to produce more radioactivity and thus
make the analysis easier.
Radioactive compounds can also be added to
samples to enable one to see how effective
certain transfer procedures are.
Radiation
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Alpha particles, helium nuclei, 4He2+
Beta particles, electrons
Gamma rays, high energy electromagnetic radiation, γ
Radioactive decay follows first order kinetics.
A = λN and Nt = N0e-λt
where A is activity, λ is decay constant (in disintegrations
per unit time), and N is the number of radioactive
atoms. The decay constant is related to half-life by
λ = 0.693/t½
Neutron Activation Analysis
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An analysis method based on bombarding a sample
with neutrons to make it radioactive and then
measuring the disintegrations, generally as gamma
radiation.
The sample is bombarded in a nuclear reactor or with a
slow neutron instrument. It is allowed to ‘cool’ for a
period to make it safe to handle and permit short-term
interferences to decay to background.
The method is applicable to nearly all elements and is a
nondestructive technique.
Neutron Activation Analysis
The rate of production of radioactive atoms depends on
several parameters
Rate = ΦσN
where Φ is the neutron flux, σ is the reaction cross-section
and N is the number of atoms originally present in the
sample.
 The initial radioactivity, A0, after radiation for some time, t,
is given by
A0 = ΦσN(1-e-λt)
 Thus, if one can determine A0, and know the other
parameters, one can calculate N, the number of atoms
present in the sample.
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Isotope Dilution Analysis
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In this technique, a radioactive tracer is added to
an analyte sample.
After the analyte has been treated to isolate it for
final quantification, the radioactivity of the
sample can be used to determine what fraction
of the original analyte was lost in the analytical
process, e.g. precipitation, filtration, or
extraction.
Isotope Dilution Analysis
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A mass, wT, of tracer with known activity, AT, is
added to the unknown mass, wx, of analyte and
the sample is made homogeneous.
If after the analysis it is found that wA grams of
analyte were found, and one finds the activity of
the isolated substance is AA, then following
relationship will hold
AA = AT [wA/(wx +wT)]