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Calibration and the Law of Mass Action
Yves Nievergelt

Mathematics Topic: Calculus, Modeling, Statistics 
Application Areas: Chemistry, Weighted leastsquares 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. 

 ©2015 by COMAP, Inc.  UMAP Journal 36.1  31 pages 
Students studying statistics, numerical analysis, calculus,
chemistry, or any other science using measured
data.

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 Ostwaldâ€™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 ODDNUMBERED EXERCISES
STATISTICAL APPENDIX
REFERENCES
ACKNOWLEDGMENTS
ABOUT THE AUTHOR



