Page 125 - Modern Analytical Chemistry

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108 Modern Analytical Chemistry

Preparing Standard Solutions Solutions of primary standards generally are pre-
pared in class A volumetric glassware to minimize determinate errors. Even so, the
relative error in preparing a primary standard is typically ±0.1%. The relative error
can be improved if the glassware is first calibrated as described in Example 5.1. It
also is possible to prepare standards gravimetrically by taking a known mass of stan-
dard, dissolving it in a solvent, and weighing the resulting solution. Relative errors
of ±0.01% can typically be achieved in this fashion.
It is often necessary to prepare a series of standard solutions, each with a differ-
ent concentration of analyte. Such solutions may be prepared in two ways. If the
range of concentrations is limited to only one or two orders of magnitude, the solu-
tions are best prepared by transferring a known mass or volume of the pure stan-
dard to a volumetric flask and diluting to volume. When working with larger con-
centration ranges, particularly those extending over more than three orders of
magnitude, standards are best prepared by a serial dilution from a single stock solu-
tion. In a serial dilution a volume of a concentrated stock solution, which is the first
standard, is diluted to prepare a second standard. A portion of the second standard
is then diluted to prepare a third standard, and the process is repeated until all nec-
essary standards have been prepared. Serial dilutions must be prepared with extra
care because a determinate error in the preparation of any single standard is passed
on to all succeeding standards.

5 B.2 Single-Point versus Multiple-Point Standardizations*

single-point standardization The simplest way to determine the value of k in equation 5.2 is by a single-
Any standardization using a single point standardization. A single standard containing a known concentration
standard containing a known amount of of analyte, C S , is prepared and its signal, S stand , is measured. The value of k is calcu-
analyte.
lated as
S stand
k = 5.3
C S
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
k. Any uncertainty in the value of k increases the uncertainty in the ana-
lyte’s concentration. In addition, equation 5.3 establishes the standardiza-
Assumed
relationship 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-
Signal relationship sumption that is often not true. Figure 5.2 shows how assuming a con-
6
Actual
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-
S stand Concentration ditions it is often safe to assume that k is constant (although this assump-
reported tion should be verified experimentally). This is the case, for example, in
C s clinical laboratories where many automated analyzers use only a single
C A Actual standard.
concentration The preferred approach to standardizing a method is to prepare a se-
ries of standards, each containing the analyte at a different concentration.
Figure 5.2
Standards are chosen such that they bracket the expected range for the
Example showing how an improper use of
a single-point standardization can lead to a
determinate error in the reported *The following discussion of standardizations assumes that the amount of analyte is expressed as a concentration. It
concentration of analyte. also applies, however, when the absolute amount of analyte is given in grams or moles.