252
6 Quantitative Aspects of Analytical Chemistry
I 6.1.5 Quantitation Methodologies
There is no universally accepted classification of quantitation methodologies. That
depicted in Fig. 6.2 compiles the more commonplace, basically in terms of foundation and method calibration approach, which leads to an immediate distinction
between calculable and relative methods as per ISO Guide 32. This section provides a general discussion of the two that is expanded in subsequent sections.
A calculable method is a method that yields a result from computations based
on the laws that govern chemical and physical parameters, which materialize in
mathematical formulae that involve both constants (e.g. atomic weights) and
measurements made during the eMP such as the weight of the aliquot subjected
to the process, titrant volume, precipitate weight, etc. These are all potential
primary methods (see Fig. 8.7).A distinction can be made here between absolute
methods that use no analytical chemical standard (e.g. a pure substance, a standard sample) to produce the results and absolute methods involving analytical
standards, which use an analytical chemical standard not containing the
analyte. Titrimetries and isotope dilution mass spectrometry are two typical
examples of the latter type.
Worthy of special note among calculable methods are stoichiometric methods,
which rely on calculations based on the stoichiometric coefficients - and on atomic
weights, which are chemical standards - of the chemical reaction on which the
measuring process relies; the reaction can be of the heterogeneous (precipitation in
gravimetry and titrimetry) or homogeneous type (solution titrimetry). Isotope
dilution mass spectrometry is a non-stoichiometric absolute methodology.
A relative method is a method that relies on a comparison of measurements of
the (treated or untreated) sample with those provided by a set of analytical
chemical standards from which a result can be derived without the need for
calculations based on physical or chemical theories.
Relative methods can be classified into two groups. Interpolation methods use
instruments where the signal is unequivocally related to the analyte concentration and the relationship materializes in a "calibration curve", the ideal form of
which is a straight line (one resulting from a linear relationship). Such a
relationship is established by having the instrument process analytical standards (either pure or mimicking the composition of the sample in method
calibration). There should thus be no differences in matrix between the sample
and the set of standards; otherwise, such differences should affect the signal. The
analyte concentration is determined by interpolating the sample signal into the
calibration curve. Typical examples include photometric, fluorimetric, atomic
absorption spectrophotometric and polarographic methods.
The other type of relative method, the comparative method, compares the
sample signal with those produced by sample standards of similar composition
(usually CRMs) containing the analyte (preferably at a variable concentration).
As a rule, they are used when the instrument response depends not only on the
analyte concentration but also on the sample matrix. These methods are usually
employed in CMPs based on the direct insertion of (solid) samples (X-ray
fluorescence spectroscopy included). While previous equipment calibration is
not essential here, it invariably leads to improved results.
6 Quantitative Aspects of Analytical Chemistry
I 6.1.5 Quantitation Methodologies
There is no universally accepted classification of quantitation methodologies. That
depicted in Fig. 6.2 compiles the more commonplace, basically in terms of foundation and method calibration approach, which leads to an immediate distinction
between calculable and relative methods as per ISO Guide 32. This section provides a general discussion of the two that is expanded in subsequent sections.
A calculable method is a method that yields a result from computations based
on the laws that govern chemical and physical parameters, which materialize in
mathematical formulae that involve both constants (e.g. atomic weights) and
measurements made during the eMP such as the weight of the aliquot subjected
to the process, titrant volume, precipitate weight, etc. These are all potential
primary methods (see Fig. 8.7).A distinction can be made here between absolute
methods that use no analytical chemical standard (e.g. a pure substance, a standard sample) to produce the results and absolute methods involving analytical
standards, which use an analytical chemical standard not containing the
analyte. Titrimetries and isotope dilution mass spectrometry are two typical
examples of the latter type.
Worthy of special note among calculable methods are stoichiometric methods,
which rely on calculations based on the stoichiometric coefficients - and on atomic
weights, which are chemical standards - of the chemical reaction on which the
measuring process relies; the reaction can be of the heterogeneous (precipitation in
gravimetry and titrimetry) or homogeneous type (solution titrimetry). Isotope
dilution mass spectrometry is a non-stoichiometric absolute methodology.
A relative method is a method that relies on a comparison of measurements of
the (treated or untreated) sample with those provided by a set of analytical
chemical standards from which a result can be derived without the need for
calculations based on physical or chemical theories.
Relative methods can be classified into two groups. Interpolation methods use
instruments where the signal is unequivocally related to the analyte concentration and the relationship materializes in a "calibration curve", the ideal form of
which is a straight line (one resulting from a linear relationship). Such a
relationship is established by having the instrument process analytical standards (either pure or mimicking the composition of the sample in method
calibration). There should thus be no differences in matrix between the sample
and the set of standards; otherwise, such differences should affect the signal. The
analyte concentration is determined by interpolating the sample signal into the
calibration curve. Typical examples include photometric, fluorimetric, atomic
absorption spectrophotometric and polarographic methods.
The other type of relative method, the comparative method, compares the
sample signal with those produced by sample standards of similar composition
(usually CRMs) containing the analyte (preferably at a variable concentration).
As a rule, they are used when the instrument response depends not only on the
analyte concentration but also on the sample matrix. These methods are usually
employed in CMPs based on the direct insertion of (solid) samples (X-ray
fluorescence spectroscopy included). While previous equipment calibration is
not essential here, it invariably leads to improved results.