Abstract

The relation between given relative errors in transmittance (<i>T = I/I</i>_o) and absorbance (<i>A</i> = -log <i>T</i>) in photometric analysis is Δ<i>A</i>/<i>A</i> = – (log <i>e</i>)Δ<i>T</i>(10^<i>A</i>/<i>A</i>). (1) If Beer's law holds, the concentration of a substance is given by <i>c</i> = <i>A</i>/<i>ab</i>, where <i>a</i> is its absorptivity at the wave length used and <i>b</i> is the path length; the relative error in the concentration, Δ<i>c/c</i>, is then just Δ<i>A/A</i>. If it is further assumed that the error in measuring the transmittance is independent of <i>T</i> (i.e., that Δ<i>T</i> is constant), then differentiation of Eq. (1) shows that Δ<i>c/c</i> is minimized for <i>A</i> = log <i>e</i> = 0.43, or <i>T</i> = <i>e</i>⁻¹ = 0.37, at which point | Δ<i>c/c</i> | = <i>e</i>Δ<i>T</i> = 2.72Δ<i>T</i>. The minimum is a rather flat one, and the useful analytical range is generally quoted as about 20 to 60 % <i>T</i>.

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