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, CA, is given as
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 Ssamp 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 Sstand and CS 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.