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Excel Tutorial: Using the Least-Squares Method To Calculate Unknown Concentrations and Error
J. J. Harynuk and J. Lam
Department of Chemistry, University of Alberta, Edmonton, AB T6G 2G2, Canada
Cover
July 2009
Vol. 86 No. 7
p. 879

Full Text
It was observed that undergraduate chemistry students lacked the basic skills required to evaluate data, generate a calibration curve using least-squares, and calculate the error in the value that they were reporting in their third-year analytical instrumentation laboratory. Additionally, many students were unable to break a somewhat complex equation down into a series of relatively simple calculations to be performed with a spreadsheet.

To address these problems, an online tutorial was developed. This tutorial guides students through the construction of a spreadsheet that performs least-squares analysis to find the best-fit line through a series of data points. These calculations can be performed automatically in many spreadsheets, but here we use a somewhat longer process. This has two benefits for students: they can see what the high-level functions are doing, and they learn how to translate an equation into a series of calculations that can be implemented with a spreadsheet. After working through the tutorial, the students have constructed a spreadsheet that will serve them throughout the remainder of the semester, and have also gained significant exposure to the use of spreadsheets.

The tutorial comprises several parts. First, there is the Excel tutorial Using the Least-Squares Method To Calculate Unknown Concentrations and Error (Figure 1). This is a Macromedia flash file that can be embedded as an object in any Web-enabled course, and it is easily accessible and functional on common Web browsers on both the PC and Mac platforms. The tutorial runs about 15 minutes.

Figure 1

Figure 1. Screenshot from the MS Excel tutorial Using the Least-Squares Method To Calculate Unknown Concentrations and Error

The second portion is a handout The Calibration Curve that provides some information about types of calibration and also gives a quick overview of the mathematics used in the tutorial.

Sample problem sets with imperfect data (some points saturating detectors, simulation of swapped standard vials, standards prepared at concentrations below the detection limit), a copy of a calibration lab exercise, and an additional instructor handout are also provided to aid instructors in implementing this tutorial in their courses.

Supplement
Find "Using the Least-Squares Method To Calculate Unknown Concentrations and Error" in the JCE Digital Library.
More Information
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Citation
Harynuk, J. J.; Lam, J. J. Chem. Educ. 2009, 86, 879.
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Keywords
Analytical Chemistry; Calibration; Computer-Based Learning; Internet / Web-Based Learning; Laboratory Computing / Interfacing; Laboratory Instruction; Quantitative Analysis; Second-Year Undergraduate; Upper-Division Undergraduate
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History
Created:
Last Updated:
6/1/2009
6/8/2009
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