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130 Modern Analytical Chemistry

5 E KEY TERMS

aliquot (p. 111) multiple-point standardization (p. 109) secondary reagent (p. 107)
external standard (p. 109) normal calibration curve (p. 109) single-point standardization (p. 108)
internal standard (p. 116) primary reagent (p. 106) standard deviation about the
linear regression (p. 118) reagent grade (p. 107) regression (p. 121)
matrix matching (p. 110) residual error (p. 118) total Youden blank (p. 129)
method of standard additions (p. 110)

5 F SUMMARY

In a quantitative analysis, we measure a signal and calculate the and the use of an internal standard. The most desirable standard-
amount of analyte using one of the following equations. ization strategy is an external standardization. The method of
standard additions, in which known amounts of analyte are added
S meas = kn A + S reag
to the sample, is used when the sample’s matrix complicates the
analysis. An internal standard, which is a species (not analyte)
S meas = kC A + S reag
added to all samples and standards, is used when the procedure
To obtain accurate results we must eliminate determinate errors does not allow for the reproducible handling of samples and
affecting the measured signal, S meas , the method’s sensitivity, k, standards.
and any signal due to the reagents, S reag . Standardizations using a single standard are common, but also
To ensure that S meas is determined accurately, we calibrate are subject to greater uncertainty. Whenever possible, a multiple-
the equipment or instrument used to obtain the signal. Balances point standardization is preferred. The results of a multiple-point
are calibrated using standard weights. When necessary, we can standardization are graphed as a calibration curve. A linear regres-
also correct for the buoyancy of air. Volumetric glassware can sion analysis can provide an equation for the standardization.
be calibrated by measuring the mass of water contained or de- A reagent blank corrects the measured signal for signals due to
livered and using the density of water to calculate the true vol- reagents other than the sample that are used in an analysis. The
ume. Most instruments have calibration standards suggested by most common reagent blank is prepared by omitting the sample.
the manufacturer. When a simple reagent blank does not compensate for all constant
An analytical method is standardized by determining its sensi- sources of determinate error, other types of blanks, such as the
tivity. There are several approaches to standardization, including total Youden blank, can be used.
the use of external standards, the method of standard addition,

5 G Suggested EXPERIMENTS

Experiments Calibration—Volumetric glassware (burets, pipets, and and internal standards are a common feature of many
The following exercises and experiments help connect the material in this chapter to the analytical laboratory.

Standardization—External standards, standard additions,
volumetric flasks) can be calibrated in the manner described
quantitative analyses. Suggested experiments using these
in Example 5.1. Most instruments have a calibration sample
standardization methods are found in later chapters. A good
that can be prepared to verify the instrument’s accuracy and
project experiment for introducing external standardization,
precision. For example, as described in this chapter, a
solution of 60.06 ppm K 2Cr 2O 7 in 0.0050 M H 2SO 4 should
give an absorbance of 0.640 ± 0.010 at a wavelength of
matrix is to explore the effect of pH on the quantitative
analysis of an acid–base indicator. Using bromothymol blue
350.0 nm when using 0.0050 M H 2SO 4 as a reagent
as an example, external standards can be prepared in a pH 9
blank. These exercises also provide practice with using standard additions, and the importance of the sample’s
volumetric glassware, weighing samples, and preparing buffer and used to analyze samples buffered to different pHs
solutions. in the range of 6–10. Results can be compared with those
obtained using a standard addition.