Kinetic%20Methods

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Kinetic Methods
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Rates

• 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
  reactions 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

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Rate Laws

• 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 ab
  is referred to as the reaction order.
• The reaction order must always be determined
  experi-
• mentally and may have little to do with the
  molecularity of the reaction, i.e., the balancing
  coefficients.

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Some reaction orders

• 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.

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Pseudo-first-order Kinetics

• It is sometimes possible to use such a great
  excess of one reactant that its concentration
  doesnt 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.

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Analytical Methods

• 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 t0. 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.

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Radiochemical Methods

• 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.

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Radiation

• Alpha particles, helium nuclei, 4He2
• Beta particles, electrons
• Gamma rays, high energy electromagnetic
  radiation, ?
• Radioactive decay follows first order kinetics.
• A ?N and Nt N0e-?t
• where A is activity, ? 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
• ? 0.693/t½

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Neutron Activation Analysis

• 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.

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Neutron Activation Analysis

• The rate of production of radioactive atoms
  depends on several parameters
• Rate FsN
• where F is the neutron flux, s 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 FsN(1-e-?t)
• 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

• 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.

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Isotope Dilution Analysis

• 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)