Unit 7. The Steady State Approximation

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.

An apparent rate expression for a macroscopically observed, non-elementary reaction can be generated if the reaction mechanism is known, as described in Unit 6. The resulting rate expression is of limited utility because it will include concentrations or partial pressures of reactive intermediates, which are very small and challenging to measure. The Bodenstein steady state approximation, presented in this unit, can be used to eliminate the concentration or partial pressure of reactive intermediates from the rate expression. Unit 7 additionally introduces a few other assumptions that can be used to simplify a rate expression derived from a mechanism, provided, of course, that the assumptions are valid.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 07 Informational Reading (.pdf)
  • Example 7.1 (.pdf)
  • Example 7.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 07 Informational Video (.mov)
  • Example 7.1 Video (.mov)
  • Example 7.2 Video (.mov)
• Reference Files:
  • Unit 7 Definitions, Nomenclature and Equations (.pdf)
  • How-To Generate a Rate Expression from a Mechanism (.pdf)

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
  • Activity 7.2 Solution (.pdf) - algebra involved in the solution to Activity 7.2.
• Alternative In-Class Learning Activities
  • Alternative Activity 7.1 (.zip) - an activity where students simulate a reaction mechanism by moving cards from one pile to another and observe the attainment of steady state concentrations of reactive intermediates.

Practice Problems

1. The formation of phosgene appears macroscopically to take place according to reaction (1a) below. It has been suggested that this reaction does not take place at the molecular level, and that instead the actual events taking place are given by reactions (1b), (1c) and (1d). Supposing that reactions (1b) and (1c) are reversible, but reaction (1d) is effectively irreversible, use the Bodenstein steady state approximation to derive a rate expression for reaction (1a). Your resulting rate expression should not contain concentrations or partial pressures of reactive intermediates.

(Problem Statement as .pdf file)

2*. The solution to Example 6.1 claimed that even though unimolecular reactions cannot be elementary, “[in most cases] a unimolecular reaction will obey the rate expression predicted by transition state theory, except at very low pressures.” Example 7.2 validated this statement for a reaction that was unimolecular in both the forward and reverse directions. This problem considers reaction (2a), which is unimolecular in the forward direction, but bimolecular in the reverse direction. According to transition state theory, the rate expression for the rate of reaction (2a) with respect to B would be given by equation (2b).

Suppose that the mechanism for reaction (2a) is given by reactions (2c) and (2d), where an A* represents a collision-activated molecule and M represents a molecule of any type. Note that reaction (2d) is an elementary reaction because it can occur just as written (the reactant has sufficient energy to react). Treating the collision-activated molecule as a reactive intermediate, use the Bodenstein steady state approximation to derive a rate expression for reaction (2a) and show that at high pressures it is equivalent to the transition state rate expression given in equation (2b).

(Problem Statement as .pdf file)

3. Reaction (3a) is non-elementary; it has been proposed to occur via the mechanism consisting of reactions (3b) through (3e). Generate a rate expression for the non-elementary reaction (3a) assuming mechanistic steps (3c) and (3d) to be effectively irreversible.

(Problem Statement as .pdf file)