Analytical Chem istry - DePauw University

566 Analytical Chemistry 2.0For a monoprotic weak acid, the equationfor a HA is+[ HO ]3α HA=+[ HO ] + K3 aProblem 10.6 in the end of chapter problemsasks you to explore this chemicallimitation to Beer’s law.Problem 10.7 in the end of chapter problemsask you to explore the effect of polychromaticradiation on the linearity ofBeer’s law.Another reason for measuring absorbanceat the top of an absorbance peak is thatit provides for a more sensitive analysis.Note that the green calibration curvein Figure 10.24 has a steeper slope—agreater sensitivity—than the red calibrationcurve.Because HA is a weak acid, the value of a HA varies with pH. To holda HA constant we buffer each standard to the same pH. Depending on therelative values of a HA and a A , the calibration curve has a positive or anegative deviation from Beer’s law if we do not buffer the standards to thesame pH.In s t r u m e n t a l Limitations t o Be e r’s La wThere are two principal instrumental limitations to Beer’s law. The first limitationis that Beer’s law assumes that the radiation reaching the sample is ofa single wavelength—that is, that the radiation is purely monochromatic.As shown in Figure 10.10, however, even the best wavelength selector passesradiation with a small, but finite effective bandwidth. Polychromatic radiationalways gives a negative deviation from Beer’s law, but the effect issmaller if the value of e is essentially constant over the wavelength rangepassed by the wavelength selector. For this reason, as shown in Figure 10.24,it is better to make absorbance measurements at the top of a broad absorptionpeak. In addition, the deviation from Beer’s law is less serious if thesource’s effective bandwidth is less than one-tenth of the natural bandwidthof the absorbing species. 5 When measurements must be made on a slope,linearity is improved by using a narrower effective bandwidth.Stray radiation is the second contribution to instrumental deviationsfrom Beer’s law. Stray radiation arises from imperfections in the wavelengthselector that allow light to enter the instrument and reach the detectorwithout passing through the sample. Stray radiation adds an additionalcontribution, P stray , to the radiant power reaching the detector; thusP + PA =−log TP + Pstray0 strayFor a small concentration of analyte, P stray is significantly smaller than P 0and P T , and the absorbance is unaffected by the stray radiation. At a higherconcentration of analyte, however, less light passes through the sample and5 (a) Strong, F. C., III Anal. Chem. 1984, 56, 16A–34A; Gilbert, D. D. J. Chem. Educ. 1991, 68,A278–A281.1.21.0absorbance0.80.60.4absorbanceFigure 10.24 Effect of the choice ofwavelength on the linearity of a Beer’slaw calibration curve.0.20.0400 450 500 550 600 650 700wavelength (nm)concentration