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Quantitative Photometric Analysis Using Absorbance Ratios: Optimizing Peak Transmittances

Volume 26, Number 3 (June 1972) Page 405-406

McDowell, Robin S.

The relation between given relative errors in transmittance (T = I/Io) and absorbance (A = -log T) in photometric analysis is

ΔA/A = - (log eT(10A/A). (1)

If Beer's law holds, the concentration of a substance is given by

c = A/ab,

where a is its absorptivity at the wave length used and b is the path length; the relative error in the concentration, Δc/c, is then just ΔA/A. If it is further assumed that the error in measuring the transmittance is independent of T (i.e., that ΔT is constant), then differentiation of Eq. (1) shows that Δc/c is minimized for A = log e = 0.43, or T = e−1 = 0.37, at which point | Δc/c | = eΔT = 2.72ΔT. The minimum is a rather flat one, and the useful analytical range is generally quoted as about 20 to 60 % T.