Nonlinear Fits of Standard Curves: A Simple Route to Uncertainties in Unknowns

Carl Salter
Department of Chemistry, Moravian College, Bethlehem, PA 18018-6650
Robert de Levie
Department of Chemistry, Bowdoin College, Brunswick, ME 04011
J. Chem. Educ., 2002, 79 (2), p 268
DOI: 10.1021/ed079p268
Publication Date (Web): February 1, 2002

Abstract

A simple nonlinear least-squares method is described that permits direct least-squares fitting to the data of a standard curve to obtain the unknown concentration and its associated uncertainty. This procedure uses the unknown concentration as a parameter of the fit, so that it and its uncertainty are obtained immediately, bypassing the need to compute a propagation of interdependent uncertainties. Examples of the procedure, as implemented on Excel, are given for a standard additions analysis and for an analysis based on a standard calibration curve.

Keywords (Audience):

First-Year Undergraduate / General

Keywords (Domain):

Analytical Chemistry

Keywords (Subject):

Chemometrics

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This article has been cited by 4 ACS Journal articles (4 most recent appear below).

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      How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually ...

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      A laboratory exercise in quality assurance (QA) of analytical chemistry is presented. Quality assurance is considered by students to be difficult, and it is also a demanding subject to the teachers, owing to the multitude of methods available to the ...

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    Design of an Excel Spreadsheet To Estimate Rate Constants, Determine Associated Errors, and Choose Curve's Extent

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    • Design of an Excel Spreadsheet To Estimate Rate Constants, Determine Associated Errors, and Choose Curve's Extent

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      Journal of Chemical Education2006 83 (12), 1879

      In this article we wish to present a new Microsoft Excel spreadsheet design that enables a prompt calculation of rate constant values (k) and associated errors and also addresses less common features such as the choice of experimental curve's extent. The ...

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    A Global Least-Squares Fit for Absolute Zero

    Carl Salter
    Journal of Chemical Education2003 80 (9), 1033
    • A Global Least-Squares Fit for Absolute Zero

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      Journal of Chemical Education2003 80 (9), 1033

      A simple, nonlinear least-squares method is described that permits gas thermometry data to be fitted directly to absolute zero. This nonlinear method can be implemented using Solver in Excel, and unlike other linear methods previously reported, it is ...

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History

  • Received: August 03, 2009

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