Unit 4. Reaction Rates and Temperature Effects

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.

Unit 4 begins by describing two ways to define a reaction rate, with respect to a reagent and as a generalized reaction rate. Rate expressions, their sources and the behavior they should display are then considered. Reaction rates depend upon the temperature, and there are a few very common ways in which this temperature dependence is manifested in a reaction rate expression. The last part of the unit presents these common sources and models for temperature dependence. The information presented in this unit appears throughout the remainder of "A First Course on Kinetics and Reaction Engineering;" it is essential that one masters it before continuing in the course.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 04 Informational Reading (.pdf)
  • Example 4.1 (.pdf)
  • Example 4.2 (.pdf)
  • Example 4.3 (.pdf)
  • Example 4.4 (.pdf)
  • Example 4.5 (.pdf)
  • Example 4.6 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 04 Informational Video (.mov)
  • Example 4.1 Video (.mov)
  • Example 4.2 Video (.mov)
  • Example 4.3 Video (.mov)
  • Example 4.4 Video (.mov)
  • Example 4.5 Video (.mov)
  • Example 4.6 Video (.mov)
• Reference Files:
  • Unit 4 Definitions, Nomenclature and Equations (.pdf)
  • How To Generate a Rate Expression (.pdf)
• Other Files:
  • 04_Example_4.xlsx - Excel file used in the solution of Example 4.4
  • 04_Example_6.xlsx - Excel file used in the solution of Example 4.6
  • Example_4_6.m - MATLAB file used in the solution of Example 4.6

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
  • Handouts (.zip) to make available to students before class
  • Class Lesson Plan (.pdf)
  • Complete slides to make available to students after class
    • Keynote 09
    • PowerPoint
  • Learning activity files to make available to students after class
    • Solution (.pdf) - to the in-class Activity 4.2 problem
    • Activity_4_2.m - MATLAB file used in the solution of Activity 4.2
• Alternative Questions (.pdf) that could be used in a pre-class quiz
• Alternative In-Class Learning Activities
  • Alternative Activity 4.1 (.zip) - an activity where students learn about the sources for rate expressions.
  • Alternative Activity 4.2 (.zip) - an activity where students analyze a failed reactor scale-up and determine its cause.
  • Alternative Activity 4.3 (.zip) - an activity where students examine a paper from the literature and evaluate the process used to generate a rate expression.

Practice Problems

1. Consider the representative reaction 2A + B → Y + Z, and answer the questions below. For parts (a) through (f) assume that the rate is to be expressed in units of moles per volume per time.

1. What are the units of the rate coefficient if the rate expression is r = k⋅(C_A)^0.5 and the concentration is in units of mol cm^-3?
2. What are the units of the rate coefficient if the rate expression is r = k⋅(C_A)(C_B) and the concentration is in units of mol L^-1?
3. What are the units of the rate coefficient if the rate expression is r = k⋅(P_A) and the partial pressure is in units of Torr?
4. What are the units of the rate coefficient if the rate expression is r = k⋅(P_A)² (1 - (P_Y)(P_Z)/(K⋅(P_A)²(P_B)), K is the equilibrium constant for the reaction divided by 1 atm, all species can be treated as ideal gases and the partial pressures are in units of atm?
5. If the rate of reaction with respect to Y is 27 mmol cm^-3 s^-1, what is the rate of reaction with respect to A?
6. If the generalized rate of reaction is 35 mmol cm^-3 s^-1, what is the rate of reaction with respect to B?
7. Suppose that glass catalyzes the reaction and the generalized rate was measured in a cylindrical glass reactor that was 10 cm in diameter and 15 cm in axial length. Suppose further that the rate was found to equal 0.2 mmol cm^-2 s^-1. If a poorly trained engineer measured the rate and assumed that it took place homogeneously in the gas phase, what rate with respect to B would that engineer report?

(Problem Statement as .pdf file)

2. Reaction (2a) below takes place in the liquid phase at 60 °C. A glass cylinder, 10 cm in diameter and 15 cm tall was filled to 75% of its capacity and the apparent rate of generation of Z was measured to be 24 mol L^-1 s^-1. Later it was discovered that the reaction was not homogeneous, but instead it was catalyzed by the glass walls of the reactor. Calculate the rate of reaction (1) per unit catalyst surface area with respect to A, B and Z.

(Problem Statement as .pdf file)

3. A reaction was studied at the temperatures listed in the Table below, and at each temperature the value of the first-order rate coefficient was determined. On the basis of the information provided in the table, does the rate coefficient display Arrhenius temperature dependence? If it does, what are the values of the pre-exponential factor and the activation energy?

(Problem Statement as .pdf file)

4*. Suppose that the rate coefficient for the isomerization of α-glucose to β-glucose was measured at several temperatures with the results given in the table below (and in this Excel file (.xlsx)). Determine the Arrhenius parameters, k₀ and E, corresponding to the rate coefficient. Then determine the parameters, k₀, a and E, in equation (4a), which is an alternative to the Arrhenius expression for the temperature dependence of a rate coefficient. Discuss the accuracy of the two models.

(Problem Statement as .pdf file)

5. A batch reaction engineering problem encountered later in the course might read as follows: An adiabatic batch reactor is filled with gas containing 67% A and 33% inert I at 300 K and 3 atm. It is necessary to convert 90 % of the A according to reaction (5a). Reaction (5a) is irreversible, and its rate expression is given by equation (5b). The heat capacities, in cal mol^-1 K^-1, of A, X, Y, and I are 7, 4, 4, and 8, respectively. The heat of reaction (1) is -30000 cal mol^-1 at 298 K. The rate coefficient in equation (5b) is equal to 0.12 h^-1 at 298 K, and the activation energy is 25 kcal mol^-1. Calculate the time required and the final temperature.

In order to solve this problem, you would likely write mole balances and an energy balance. The mole balance on reagent A would include an expression for the rate of reaction (5a) with respect to A, and in that rate expression, the rate coefficient k₁ would be written as an Arrhenius expression. Write the necessary rate expression, inserting the proper values for the pre-exponential factor and activation energy.

(Problem Statement as .pdf file)