Analytical Chem istry - DePauw University

596 Analytical Chemistry 2.0Ac c u r a c yUnder normal conditions a relative error of 1–5% is easy to obtained withUV/Vis absorption. Accuracy is usually limited by the quality of the blank.Examples of the type of problems that may be encountered include thepresence of particulates in a sample that scatter radiation and interferentsthat react with analytical reagents. In the latter case the interferent mayreact to form an absorbing species, giving rise to a positive determinateerror. Interferents also may prevent the analyte from reacting, leading toa negative determinate error. With care, it may be possible to improve theaccuracy of an analysis by as much as an order of magnitude.PrecisionIn absorption spectroscopy, precision is limited by indeterminate errors—primarily instrumental noise—introduced when measuring absorbance.Precision is generally worse for low absorbances where P 0 ≈ P T , and forhigh absorbances when P T approaches 0. We might expect, therefore, thatprecision will vary with transmittance.We can derive an expression between precision and transmittance byapplying the propagation of uncertainty as described in Chapter 4. To doso we rewrite Beer’s law asC =− 1 logT10.22εbTable 4.10 in Chapter 4 helps us in completing the propagation of uncertaintyfor equation 10.22, giving the absolute uncertainty in the concentration,s C , as0.4343 sTs =− ×10.23CεbTwhere s T is the absolute uncertainty in the transmittance. Dividing equation10.23 by equation 10.22 gives the relative uncertainty in concentration,s C /C, assCCs= 0. 4343T logTIf we know the absolute uncertainty in transmittance, we can determine therelative uncertainty in concentration for any transmittance.Determining the relative uncertainty in concentration is complicatedbecause s T may be a function of the transmittance. As shown in Table 10.8,three categories of indeterminate instrumental error have been observed. 12A constant s T is observed for the uncertainty associated with reading %Ton a meter’s analog or digital scale. Typical values are ±0.2–0.3% (a k 1 of±0.002–0.003) for an analog scale, and ±0.001% a (k 1 of ±0.000 01) for12 Rothman, L. D.; Crouch, S. R.; Ingle, J. D. Jr. Anal. Chem. 1975, 47, 1226–1233.T