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99814 |
Supplementary Print |
Price:
FREE with membership |
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Calibration and the Law of Mass Action
Yves Nievergelt
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Mathematics Topic:
Calculus, Modeling, Statistics |
Application Areas:
Chemistry, Weighted least-squares linear regression |
Prerequisites:
Linear inequalities, summation notation, and calculus,
including substitutions for integrations of integral
powers. Several exercises refer to weighted leastsquares
techniques as developed in Nievergelt [2014],
and the Appendix refers to tables and equations from
that source. |
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| ©2015 by COMAP, Inc. | UMAP Journal 36.1 | 31 pages |
Students studying statistics, numerical analysis, calculus,
chemistry, or any other science using measured
data.
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This Module shows how methods for various analyses
of data reduce to the calculation of a weighted mean
to minimize a weighted sum of squares. Applications
include Wilhelm Ostwald’s calibration of a laboratory
instrument called an azotometer, mathematical modeling
of chemical reactions, and test of the chemical Law
of Mass Action.
Table of Contents
1. INTRODUCTION
2. CALIBRATING AN AZOTOMETER WITH MATHEMATICAL MODELS
2.1 Collecting Data from Controlled Experiments
2.1.1 Constant Excess in Readings from the Azotometer
2.1.2 Proportionality in Readings from the Azotometer
2.1.3 Systematic Excess in the Readings from the Azotometer
2.2 Fitting Mathematical Models to the Data
3. TESTING THE LAW OF MASS ACTION WITH MATHEMATICAL MODELS
3.1 Modeling Bimolecular Reactions
4. SOLUTIONS TO ODD-NUMBERED EXERCISES
STATISTICAL APPENDIX
REFERENCES
ACKNOWLEDGMENTS
ABOUT THE AUTHOR
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