# 5.S: Standardizing Analytical Methods (Summary)

In a quantitative analysis we measure a signal, Stotal, and calculate the amount of analyte, nA or CA, using one of the following equations.

$S_\ce{total} = k_\ce{A}n_\ce{A} + S_\ce{reag}$

$S_\ce{total} = k_\ce{A}C_\ce{A} +S_\ce{reag}$

To obtain an accurate result we must eliminate determinate errors affecting 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 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, including external standards, the method of standard addition and internal standards. The most common strategy is a multiple-point external standardization, resulting in a normal calibration curve. We use the method of standard additions, in which known amounts of analyte are added 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 can provide 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, can be used.

## 5.7.1 Key Terms

 external standard internal standard linear regression matrix matching method of standard additions multiple-point standardization normal calibration curve primary standard reagent grade residual error secondary standard serial dilution single-point standardization standard deviation about the regression total Youden blank unweighted linear regression weighted linear regression

ve the actual values for the three replicate measurements. In place of the actual measurements, we just enter the average signal three times. This is okay because the calculation depends on the average signal and the number of replicates, and not on the individual measurements.

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