The most commonly employed standardization method uses one or more external standards containing known concentrations of analyte.

**External Standards**

The most commonly employed standardization method
uses one or more **external
standards **containing known
concentrations of analyte.
These standards are identi-
fied as external standards because
they are prepared
and analyzed separately from the samples.

A quantitative determination using a single
external standard was
described at the beginning
of this section, with *k *given
by equation 5.3. Once standardized, the concentration of analyte,
*C*_{A}, is given as

5.4

A multiple-point external standardization is accomplished by
constructing a calibration curve, two examples of which are shown in Figure 5.3. Since this is
the most frequently employed method
of standardization, the
resulting relation- ship often is called a **normal calibration curve. **When the calibration curve is a linear
(Figure 5.3a), the
slope of the
line gives the
value of *k. *This
is the most
de- sirable situation since
the method’s sensitivity remains constant throughout the standard’s concentration
range. When the calibration curve is nonlinear, the method’s sensitivity is a function of the analyte’s concentration. In Figure
5.3b, for example, the value of *k *is greatest
when the analyte’s concentration is small and decreases continuously as the amount
of analyte is increased. The
value of *k *at any point along the calibration curve is given by the slope at that point. In
either case, the calibration curve
provides a means
for relating *S*_{samp} to the ana- lyte’s concentration.

An external standardization allows a related
series of samples
to be ana- lyzed using a single calibration curve. This is an important advantage in labo- ratories where many samples
are to be analyzed or when the need for a rapid throughput of samples is critical. Not surprisingly, many of the most com- monly encountered quantitative analytical methods are based
on an external standardization.

There is a serious limitation, however, to an external standardization. The relationship between *S*_{stand} and *C*_{S} in equation 5.3 is determined when the analyte is present in the external
standard’s matrix. In using an exter- nal
standardization, we assume
that any difference between the matrix
of the standards and the sample’s
matrix has no effect on the value of *k. *A proportional determinate error is
introduced when differences between the two matrices cannot be ignored. This is shown
in Figure 5.4,
where the re-
lationship between the signal and the amount of analyte is shown for both the sample’s matrix and the
standard’s matrix. In this
example, using a normal calibration curve results in a negative
determinate error. When matrix problems are expected, an effort is made to match the
matrix of the standards to that of the sample.
This is known as **matrix matching. **When the sample’s
matrix is unknown,
the matrix effect
must be shown
to be negligi- ble, or an alternative method
of standardization must
be used. Both
approaches are discussed in the following sections.

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