Unit 15. Integral 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.

Like Unit 14, Unit 15 considers the situation where the model for a set of kinetics experiments takes the form of a differential equation. This happens when kinetics data for a single reaction are generated using either a batch reactor or a plug flow reactor. In Unit 15, the differential equation is first solved analytically to obtain an algebraic equation. At that point, the fitting process again becomes the same as that described for a CSTR in Unit 13. This integral data analysis approach is generally more accurate and therefore preferred for the analysis of kinetics data from batch reactors and PFRs.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 15 Informational Reading (.pdf)
  • Example 15.1 (.pdf)
  • Example 15.2 (.pdf)
  • Example 15.3 (.pdf)
  • Example 15.4 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 15 Informational Video (.mov)
  • Example 15.1 Video (.mov)
  • Example 15.2 Video (.mov)
  • Example 15.3 Video (.mov)
  • Example 15.4 Video (.mov)
• Reference Files:
  • Unit 15 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • 15_How_To_1.pdf - How to test a rate expression using integral data analysis and linear least squares
  • 15_How_To_2.pdf - How to test a single parameter rate expression using integral data analysis
  • Example_15_1.m - MATLAB file used in the solution of Example 15.1
  • Example_15_2.m - MATLAB file used in the solution of Example 15.2
  • Example_15_3.m - MATLAB file used in the solution of Example 15.3
  • Example_15_4.m - MATLAB file used in the solution of Example 15.4

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
  • 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_15_1.m - MATLAB file used in the solution of Activity 15.1
    • Activity_15_2.m - MATLAB file used in the solution of Activity 15.2
• Alternative Questions (.pdf) that could be used in a pre-class quiz

Practice Problems

1. Repeat any problem from Unit 14 using an integral data analysis.

2. Suppose you are studying the kinetics of the gas phase condensation, reaction (2a), using a 600 cm³ perfectly mixed batch reactor. In one experiment you charged the reactor with 2.3 atm of A and 2.0 atm of B (no Z was initially present) at 300 K and then recorded the total pressure as a function of time. The resulting data are presented in this Table (.xlsx file). For this one set of experimental data, does the rate expression given in equation (2b) provide an adequate description of the reaction kinetics? If so, what is the best value for the rate coefficient, and what is the uncertainty in that value?

(Problem Statement as .pdf file)

3. Suppose you are studying gas phase reaction (3a) using a laboratory PFR with an inside diameter of 2.2 cm and a length of 30 cm. The reactor operates isothermally, at steady state and at constant pressure. A series of experimental runs were made at 723 K using different combinations of feed flow rate and reactor pressure. In each run, the feed consisted of pure A and the mole fraction of A was measured at the reactor outlet. The experimental data are presented in this Table (.xlsx file). Determine whether the reaction rate can be accurately modeled using the rate expression given in equation (3b), and if it can, compute the best value for the rate coefficient along with its uncertainty.

(Problem Statement as .pdf file)

4. Suppose that the liquid-phase Diels-Alder combination of cyclopentadiene (A) and benzoquinone (B), reaction (4a), was studied in the liquid phase using a 2 gal perfectly mixed batch reactor. The temperature was constant and the same in all of the experiments. In any one experiment the reactor was charged with known concentrations of A and B and the concentration of A was measured after a known reaction time. Using the resulting data, in this Excel© file, determine whether the rate expression in equation (4b) accurately predicts the reaction kinetics. If it does, determine the best value for the rate coefficients, including 95% confidence limits.

(Problem Statement as .pdf file)

5. Suppose that the gas phase decomposition of A, reaction (5a), was studied in an isothermal, isobaric, steady-state PFR. In every experiment the temperature was 675 K, the pressure was 1 atm, and the feed was pure A, an ideal gas. The space time was varied from one experiment to the next, and the fractional conversion of A was measured. Using the resulting data, in this Excel© file, determine whether the rate expression in equation (5b) accurately predicts the reaction kinetics. If it does, determine the best value for the rate coefficient, including 95% confidence limits.

(Problem Statement as .pdf file)