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Chapter: Modern Analytical Chemistry: Calibrations, Standardizations, and Blank Corrections

Standardizing Methods: Single-Point versus Multiple-Point Standardizations

The simplest way to determine the value of k in equation 5.2 is by a single-point standardization.

Single-Point versus Multiple-Point Standardizations*

The simplest way to determine the value of k in equation 5.2 is by a single-point standardization. A single standard containing a known concentration of analyte, CS, is prepared and its signal, Sstand, is measured. The value of k is calcu- lated as

               5.3

A single-point standardization is the least desirable way to standardize a method. When using a single standard, all experimental errors, both de- terminate and indeterminate, are carried over into the calculated value for Any uncertainty in the value of k increases the uncertainty in the ana- lyte’s concentration. In addition, equation 5.3 establishes the standardiza- tion relationship for only a single concentration of analyte. Extending equation 5.3 to samples containing concentrations of analyte different from that in the standard assumes that the value of k is constant, an as- sumption that is often not true. Figure 5.2 shows how assuming a con- stant value of k may lead to a determinate error. Despite these limitations, single-point standardizations are routinely used in many laboratories when the analyte’s range of expected concentrations is limited. Under these con- ditions it is often safe to assume that k is constant (although this assump- tion should be verified experimentally). This is the case, for example, in clinical laboratories where many automated analyzers use only a single standard.


The preferred approach to standardizing a method is to prepare a se- ries of standards, each containing the analyte at a different concentration. Standards are chosen such that they bracket the expected range for the analyte’s concentration. Thus, a multiple-point standardization should use at least three standards, although more are preferable. A plot of Sstand versus CS is known as a calibration curve. The exact standardization, or calibration relationship, is deter- mined by an appropriate curve-fitting algorithm.* Several approaches to standard- ization are discussed in the following sections.

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