Unit 9. Homogeneous and Enzymatic Catalysis

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.

This first section of Part II of the course focuses upon the selection of an equation to be tested as a rate expression. The equation to be tested can be chosen simply for its mathematical convenience. Alternatively, theory can be used to select the mathematical form of the equation to be tested. For some reactions, theory can be applied directly. In other cases the reaction must be described in terms of a group of reactions that comprise what is known as a reaction mechanism. In the latter case theory can be applied to the reactions in the mechanism which are then combined to get the mathematical form of the equation to be tested.

A mathematical expression for the rate of a non-elementary reaction can be generated from its mechanism, using methods described in the last three units. However, when the reaction mechanism involves charged species, enzymes or homogeneous catalysts, those methods must be modified to account for the conservation of charge or catalyst. This is the subject of Unit 9.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 09 Informational Reading (.pdf)
  • Example 9.1 (.pdf)
  • Example 9.2 (.pdf)
  • Example 9.3 (.pdf)
  • Example 9.4 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 09 Informational Video (.mov)
  • Example 9.1 Video (.mov)
  • Example 9.2 Video (.mov)
  • Example 9.3 Video (.mov)
  • Example 9.4 Video (.mov)
• Reference Files:
  • Unit 9 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_9_4.m - MATLAB file used in the solution of Example 9.4

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
  • Solutions to the in-class activities to make available to students after class
    • Activity 9.1 Solution (.pdf)
    • Activity 9.2 Solution (.pdf)
    • Activity_9_2.m - MATLAB file used in the solution of Activity 9.2
• Alternative Questions (.pdf) that could be used in a pre-class quiz

Practice Problems

1. Setty and Prengle (Ind. Eng. Chem. Fund. 3(4), 300, 1964.) studied reaction (1a) and proposed the mechanism given in reactions (1b) through (1e). The reaction was catalyzed by AlCl₃, which was added to the system by dissolving a known amount of it in nitromethane and injecting the resulting solution. As reaction (1b) indicates, some of the AlCl₃ complexes with the nitromethane, and this complex is the catalytically active entity. Derive an expression for the rate of consumption of hexene on the basis of this mechanism. In doing so, you may assume that nitromethane will always be present in sufficient quantity to permit easy measurement of its concentration.

(Problem Statement as .pdf file)

2. Suppose that enzyme E requires a cofactor, C, in order to catalyze the conversion of its substrate, S, to the product, P. If the overall reaction is given by equation (2a) and the mechanism is given by equations (2b) through (2d) with reaction (2d) being irreversible, derive an acceptable expression for the overall rate of reaction. The free cofactor concentration is easy to measure, so it is acceptable for its concentration to appear in the rate expression.

(Problem Statement as .pdf file)

3. Suppose the combination of substrate A, SA, and substrate B, SB, to form the product P, reaction (3a), is catalyzed by an enzyme, E, according to the mechanism given in reactions (3b) through (3d). Reactions (3b) and (3d) are reversible. Compare the rate expression that results if reaction (3c) is effectively irreversible to the rate expression that results if reaction (3c) is rate-determining.

(Problem Statement as .pdf file)