D. Harvey - Modern Analytical Chemistry (794078), страница 34

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“Planning and Analysis ofResults of Collaborative Tests” published in Statistical Manual of theAssociation of Official Analytical Chemists, Association of OfficialAnalytical Chemists: Washington, DC, 1975.1400-CH05 9/8/99 3:58 PM Page 1045ChapterCalibrations, Standardizations,and Blank CorrectionsIn Chapter 3 we introduced a relationship between the measured signal,Smeas, and the absolute amount of analyteSmeas = knA + Sreag5.1or the relative amount of analyte in a sampleSmeas = kCA + Sreag5.2where nA is the moles of analyte, CA is the analyte’s concentration, k isthe method’s sensitivity, and Sreag is the contribution to Smeas fromconstant errors introduced by the reagents used in the analysis. Toobtain an accurate value for nA or CA it is necessary to avoiddeterminate errors affecting Smeas, k, and Sreag. This is accomplished bya combination of calibrations, standardizations, and reagent blanks.1041400-CH05 9/8/99 3:58 PM Page 105Chapter 5 Calibrations, Standardizations, and Blank Corrections5A Calibrating SignalsSignals are measured using equipment or instruments that must be properly calibrated if Smeas is to be free of determinate errors.

Calibration is accomplishedagainst a standard, adjusting Smeas until it agrees with the standard’s known signal.Several common examples of calibration are discussed here.When the signal is a measurement of mass, Smeas is determined with an analytical balance. Before a balance can be used, it must be calibrated against a referenceweight meeting standards established by either the National Institute for Standardsand Technology or the American Society for Testing and Materials. With an electronic balance the sample’s mass is determined by the current required to generatean upward electromagnetic force counteracting the sample’s downward gravitational force.

The balance’s calibration procedure invokes an internally programmedcalibration routine specifying the reference weight to be used. The reference weightis placed on the balance’s weighing pan, and the relationship between the displacement of the weighing pan and the counteracting current is automatically adjusted.Calibrating a balance, however, does not eliminate all sources of determinateerror. Due to the buoyancy of air, an object’s weight in air is always lighter than itsweight in vacuum. If there is a difference between the density of the object beingweighed and the density of the weights used to calibrate the balance, then a correction to the object’s weight must be made.1 An object’s true weight in vacuo, Wv, isrelated to its weight in air, Wa, by the equation 11 Wv = Wa × 1 + – × 0.0012 Do Dw where Do is the object’s density, Dw is the density of the calibration weight, and0.0012 is the density of air under normal laboratory conditions (all densities are inunits of g/cm3).

Clearly the greater the difference between Do and Dw the more serious the error in the object’s measured weight.The buoyancy correction for a solid is small, and frequently ignored. It may besignificant, however, for liquids and gases of low density. This is particularly important when calibrating glassware.

For example, a volumetric pipet is calibrated bycarefully filling the pipet with water to its calibration mark, dispensing the waterinto a tared beaker and determining the mass of water transferred. After correctingfor the buoyancy of air, the density of water is used to calculate the volume of waterdispensed by the pipet.EXAMPLE 5.1A 10-mL volumetric pipet was calibrated following the procedure just outlined,using a balance calibrated with brass weights having a density of 8.40 g/cm3.

At25 °C the pipet was found to dispense 9.9736 g of water. What is the actualvolume dispensed by the pipet?SOLUTIONAt 25 °C the density of water is 0.99705 g/cm3 . The water’s true weight,therefore, is 11 Wv = 9.9736 g × 1 + – × 0.0012 = 9.9842 g 0.99705 8.40 1051400-CH05 9/8/99 3:58 PM Page 106106Modern Analytical Chemistryand the actual volume of water dispensed by the pipet is9.9842 g= 10.014 cm 3 = 10.014 mL0.99705 g/cm 3If the buoyancy correction is ignored, the pipet’s volume is reported as9.9736 g= 10.003 cm 3 = 10.003 mL0.99705 g/cm 3introducing a negative determinate error of –0.11%.Balances and volumetric glassware are examples of laboratory equipment.

Laboratory instrumentation also must be calibrated using a standard providing aknown response. For example, a spectrophotometer’s accuracy can be evaluated bymeasuring the absorbance of a carefully prepared solution of 60.06 ppm K2Cr2O7 in0.0050 M H2SO4, using 0.0050 M H2SO4 as a reagent blank.2 The spectrophotometer is considered calibrated if the resulting absorbance at a wavelength of 350.0 nmis 0.640 ± 0.010 absorbance units. Be sure to read and carefully follow the calibration instructions provided with any instrument you use.5B Standardizing MethodsThe American Chemical Society’s Committee on Environmental Improvement defines standardization as the process of determining the relationship between themeasured signal and the amount of analyte.3 A method is considered standardizedwhen 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 byconsidering the chemical and physical processes responsible for the signal.

Unfortunately, such calculations are often of limited utility due either to an insufficientlydeveloped theoretical model of the physical processes or to nonideal chemical behavior. In such situations the value of k must be determined experimentally by analyzing one or more standard solutions containing known amounts of analyte. Inthis section we consider several approaches for determining the value of k.

For simplicity we will assume that Sreag has been accounted for by a proper reagent blank,allowing us to replace Smeas in equations 5.1 and 5.2 with the signal for the speciesbeing measured.5B.1 Reagents Used as StandardsThe accuracy of a standardization depends on the quality of the reagents and glassware used to prepare standards. For example, in an acid–base titration, the amountof analyte is related to the absolute amount of titrant used in the analysis by thestoichiometry of the chemical reaction between the analyte and the titrant. Theamount 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 beno better than the accuracy to which the titrant’s concentration is known.primary reagentA reagent of known purity that can beused to make a solution of knownconcentration.Primary Reagents Reagents used as standards are divided into primary reagentsand secondary reagents. A primary reagent can be used to prepare a standard containing an accurately known amount of analyte.

For example, an accurately weighedsample of 0.1250 g K2Cr2O7 contains exactly 4.249 × 10–4 mol of K2Cr2O7. If this1400-CH05 9/8/99 3:59 PM Page 107Chapter 5 Calibrations, Standardizations, and Blank Correctionssame sample is placed in a 250-mL volumetric flask and diluted to volume, the concentration of the resulting solution is exactly 1.700 × 10–3 M. A primary reagentmust have a known stoichiometry, a known purity (or assay), and be stable duringlong-term storage both in solid and solution form. Because of the difficulty in establishing the degree of hydration, even after drying, hydrated materials usually arenot considered primary reagents. Reagents not meeting these criteria are called secondary reagents. The purity of a secondary reagent in solid form or the concentration of a standard prepared from a secondary reagent must be determined relativeto a primary reagent.

Lists of acceptable primary reagents are available.4 Appendix 2contains a selected listing of primary standards.Other Reagents Preparing a standard often requires additional substances that arenot primary or secondary reagents. When a standard is prepared in solution, for example, a suitable solvent and solution matrix must be used. Each of these solventsand reagents is a potential source of additional analyte that, if unaccounted for,leads to a determinate error.

If available, reagent grade chemicals conforming tostandards set by the American Chemical Society should be used.5 The packaginglabel included with a reagent grade chemical (Figure 5.1) lists either the maximumallowed limit for specific impurities or provides the actual assayed values for the impurities as reported by the manufacturer. The purity of a reagent grade chemicalcan be improved by purification or by conducting a more accurate assay. As discussed later in the chapter, contributions to Smeas from impurities in the sample matrix can be compensated for by including an appropriate blank determination in theanalytical procedure.107secondary reagentA reagent whose purity must beestablished relative to a primary reagent.reagent gradeReagents conforming to standards set bythe American Chemical Society.Figure 5.1Examples of typical packaging labels fromreagent grade chemicals.

Label (a) providesthe actual lot assay for the reagent asdetermined by the manufacturer. Note thatpotassium has been flagged with an asterisk(*) because its assay exceeds the maximumlimit established by the American ChemicalSociety (ACS). Label (b) does not provideassayed values, but indicates that thereagent meets the specifications of the ACSfor the listed impurities. An assay for thereagent also is provided.(a)(b)© David Harvey/Marilyn Culler, photographer.1400-CH05 9/8/99 3:59 PM Page 108108Modern Analytical ChemistryPreparing Standard Solutions Solutions of primary standards generally are prepared in class A volumetric glassware to minimize determinate errors. Even so, therelative error in preparing a primary standard is typically ±0.1%.

The relative errorcan be improved if the glassware is first calibrated as described in Example 5.1. Italso is possible to prepare standards gravimetrically by taking a known mass of standard, dissolving it in a solvent, and weighing the resulting solution. Relative errorsof ±0.01% can typically be achieved in this fashion.It is often necessary to prepare a series of standard solutions, each with a different concentration of analyte. Such solutions may be prepared in two ways. If therange of concentrations is limited to only one or two orders of magnitude, the solutions are best prepared by transferring a known mass or volume of the pure standard to a volumetric flask and diluting to volume.

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