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Product No. 99814 Supplementary Print Price: FREE with membership
 

Calibration and the Law of Mass Action

Yves Nievergelt


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.

| ©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 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