Unit 16. Numerical Data Analysis

This website provides learning and teaching tools for a first course on kinetics and reaction engineering. The course is divided into four parts (I through IV). Here, in Part II of the course, the focus is on chemical reaction kinetics, and more specifically, on rate expressions, which are mathematical models of reaction rates. As you progress through Part II, you will learn how rate expressions are generated from experimental kinetics data.

Part II of the course concludes with Section C which describes how to test a rate expression (Section A) using experimental data (Section B). The testing of a rate expression entails its substitution into the model for the experimental reactor and the subsequent fitting of that model to the experimental data. The end result will reveal whether the selected rate expression offers a sufficiently accurate representation of the rate of the reaction under consideration. If it does, the fitting process also will yield the best values for the parameters that appear in the selected rate expression.

In Units 13 through 15 the models for the kinetics experiments were linearized, after which they were fit to experimental data using linear least squares. Unit 16 shows how non-linear models for kinetics experiments can be fit to experimental data without linearizing them. It also describes how to fit models that involve differential equations without first analytically solving them to obtain an algebraic model equation. Instead, the differential equations are solved numerically at the same time the model is being fit to the data. Finally, Unit 16 presents an introduction to the analysis of kinetics data where more than one chemical reaction is taking place.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 16 Informational Reading (.pdf)
  • Example 16.1 (.pdf)
  • Example 16.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 16 Informational Video (.mov)
  • Example 16.1 Video (.mov)
  • Example 16.2 Video (.mov)
• Reference Files:
  • Unit 16 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_16_1.m - MATLAB file used in the solution of Example 16.1
  • Example_16_2.m - MATLAB file used in the solution of Example 16.2

Teaching Resources

• Archive (.zip) - Contains all teaching resources listed below for this unit
• Sample Class
  • Online Pre-class Quiz (.pdf file)
  • Redacted slides to make available to students before class
    • Keynote 09
    • PowerPoint
  • Other files to make available to students before class
    • 16_Activity_1.pdf - handout for Activity 16.1
    • 16_Activity_2.pdf - handout for Activity 16.2
  • Class Lesson Plan (.pdf)
  • Complete slides to make available to students after class
    • Keynote 09
    • PowerPoint
  • Other files to make available to students after class
    • Activity_16_1.m - MATLAB file used in the solution of Activity 16.1
    • Activity_16_2.m - MATLAB file used in the solution of Activity 16.2

Practice Problems

1. Repeat any problem from Unit 13, 14 or 15 using numerical least squares for the data analysis.