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106 Modern Analytical Chemistry

and the actual volume of water dispensed by the pipet is
9 9842 g 3
.
.
= 10 014 cm = 10 014 mL
.
0.99705 g/cm 3
If the buoyancy correction is ignored, the pipet’s volume is reported as
.
9 9736 g 3
.
.
= 10 003 cm = 10 003 mL
0.99705 g/cm 3
introducing a negative determinate error of –0.11%.
Balances and volumetric glassware are examples of laboratory equipment. Lab-
oratory instrumentation also must be calibrated using a standard providing a
known response. For example, a spectrophotometer’s accuracy can be evaluated by
measuring the absorbance of a carefully prepared solution of 60.06 ppm K 2 Cr 2 O 7 in
2
0.0050 M H 2 SO 4 , using 0.0050 M H 2 SO 4 as a reagent blank. The spectrophotome-
ter is considered calibrated if the resulting absorbance at a wavelength of 350.0 nm
is 0.640 ± 0.010 absorbance units. Be sure to read and carefully follow the calibra-
tion instructions provided with any instrument you use.

5 B Standardizing Methods

The American Chemical Society’s Committee on Environmental Improvement de-
fines standardization as the process of determining the relationship between the
3
measured signal and the amount of analyte. A method is considered standardized
when the value of k in equation 5.1 or 5.2 is known.
In principle, it should be possible to derive the value of k for any method by
considering the chemical and physical processes responsible for the signal. Unfortu-
nately, such calculations are often of limited utility due either to an insufficiently
developed theoretical model of the physical processes or to nonideal chemical be-
havior. In such situations the value of k must be determined experimentally by ana-
lyzing one or more standard solutions containing known amounts of analyte. In
this section we consider several approaches for determining the value of k. For sim-
plicity we will assume that S reag has been accounted for by a proper reagent blank,
allowing us to replace S meas in equations 5.1 and 5.2 with the signal for the species
being measured.

5 B.1 Reagents Used as Standards
The accuracy of a standardization depends on the quality of the reagents and glass-
ware used to prepare standards. For example, in an acid–base titration, the amount
of analyte is related to the absolute amount of titrant used in the analysis by the
stoichiometry of the chemical reaction between the analyte and the titrant. The
amount of titrant used is the product of the signal (which is the volume of titrant)
and the titrant’s concentration. Thus, the accuracy of a titrimetric analysis can be
no better than the accuracy to which the titrant’s concentration is known.

Primary Reagents Reagents used as standards are divided into primary reagents
primary reagent
A reagent of known purity that can be and secondary reagents. A primary reagent can be used to prepare a standard con-
used to make a solution of known taining an accurately known amount of analyte. For example, an accurately weighed
concentration. sample of 0.1250 g K 2 Cr 2 O 7 contains exactly 4.249 ´10 –4 mol of K 2 Cr 2 O 7 . If this