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The Chemical Educator
ISSN: 1430-4171 (electronic version)
Abstract Volume 20
(2015) pp 206-213
A Gaussian Accommodation of Beer’s Law Deviations
John C. O’C.Young*
Department of Chemistry, Saint Mary’s University, Halifax, Nova Scotia, Canada, B3H 3C3 john.young@smu.ca
Received June 22, 2015. Accepted August 5, 2015.
Published: 20 August 2015
Abstract. Except under extremely deviant conditions, the “standard curve” regressional relationship between optical absorbance and absorbent concentration is shown to exhibit an S-shaped profile of progressively increasing slope up to an inflexion followed by a region of progressively decreasing slope. Applied to this profile, a Gaussian regression procedure is shown to deliver i) a versatile, accurate representation of these sigmoid deviations from the Beer’s Law proportional relationship between absorbance (A) and absorbent concentration (C), namely Ar = a exp[ – {(C – b) / c}2 + d in which a, b, c and d are experimentally determined constants ii) an explicit inversion of this regressional relationship C = b + c sqrt[ ln{ a / (Ar – d)}] which is required to determine the absorbent concentration corresponding to an observed value of absorbance, and iii) an expression for the slope of the regressional relationship dAr / dC = – 2(a / c2) (C – b) exp[ – (C – b)2 / c2 ] as a measure of the sensitivity of the experimental procedure.
Key Words: In the Classroom; physical chemistry
(*) Corresponding author. (E-mail: john.young@smu.ca)
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