In a quantitative analysis we measure a signal, Stotal, and calculate the amount of analyte, nA or CA, using one of the following equations.
Stotal = kAnA + Sreag
Stotal = kACA + Sreag
To obtain an accurate result we must eliminate determinate errors that affect the signal, Stotal, the method’s sensitivity, kA, and the signal due to the reagents, Sreag.
To ensure that we accurately measure Stotal, we calibrate our equipment and instruments. To calibrate a balance, for example, we use a standard weight of known mass. The manufacturer of an instrument usually suggests appropriate calibration standards and calibration methods.
To standardize an analytical method we determine its sensitivity. There are several standardization strategies available to us, including external standards, the method of standard addition, and internal standards. The most common strategy is a multiple-point external standardization and a normal calibration curve. We use the method of standard additions, in which we add known amounts of analyte to the sample, when the sample’s matrix complicates the analysis. When it is difficult to reproducibly handle samples and standards, we may choose to add an internal standard.
Single-point standardizations are common, but are subject to greater uncertainty. Whenever possible, a multiple-point standardization is preferred, with results displayed as a calibration curve. A linear regression analysis provides an equation for the standardization.
A reagent blank corrects for any contribution to the signal from the reagents used in the analysis. The most common reagent blank is one in which an analyte-free sample is taken through the analysis. When a simple reagent blank does not compensate for all constant sources of determinate error, other types of blanks, such as the total Youden blank, are used.
total Youden blank
normal calibration curve
unweighted linear regression
method of standard additions
standard deviation about the regression
weighted linear regression