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Reactions and Kinetics
Session Overview
| Modules | Reactions and Kinetics |
| Concepts | chemical kinetics: the rate equation, order of reaction, and rate laws for zeroth, first, and second order reactions, temperature dependence of rate of reaction, catalysts, Fick’s first law and steady-state diffusion |
| Keywords | steric hindrance, cisplatin, first-order, second-order, zero-order, half-life, radioactive decay, reaction rate, chemical kinetics, rate of reaction, products, reactants, rate constant, rate equation, activation energy, Arrhenius equation, activated complex, decomposition reaction, nuclear decay, linearizing function, least-squares fitting, integral method, differential method, catalysis, reaction coordinate diagram, adsorb, desorb, selectivity, catalyst, inhibitor, diffusion, mass transport, mass flow rate, flux, Fick’s first law, concentration gradient, diffusivity, concentration profile, oxidation, reduction |
| Chemical Substances | dinitrogen pentoxide (N2O5), nitrogen dioxide (NO2), oxygen gas (O2), nitric oxide (NO), cisplatin (PtCl2(NH3)2), water (H2O), chloride (Cl-), uranium-238 (238U), thorium-234 (234Th), helium (4He), carbon monoxide (CO), carbon dioxide (CO2), carbon (C), silicon (Si), boron (B), diborane (B2H6), hydrogen gas (H2), octane (C8H18), platinum (Pt), palladium (Pd), rhodium (Rh) |
| Applications | cisplatin, radiocarbon dating, automobile catalytic converter, semiconductor wafer doping (Pentium), Hindenburg fire, corrosion prevention in automobile engines |
Prerequisites
Before starting this session, you should be familiar with:
- Session 22: Introduction to Kinetics (second part)
- Derivative and integral notation, logarithms, fitting a curve to data
- Doping of semiconductors and thermal excitation (Session 14)
Learning Objectives
After completing this session, you should be able to:
- Compare the nature of reactions with first-order and second-order rates.
- Given a set of data about a reaction, calculate the reaction rate, activation energy, reaction order, and/or rate constant, and derive a general expression for the concentration over time.
- Sketch an energy-level diagram for a reaction, labeling key features.
- Describe the properties and behavior of an effective catalyst.
- Calculate the concentration profile in a doped semiconductor wafer using Fick’s first law.
Reading
Archived Lecture Notes #8 (PDF), Sections 4-7
Archived Lecture Notes #9 (PDF), Section 1
| Book Chapters | Topics |
|---|---|
| [Saylor] 10.7, “The Kinetic Molecular Theory of Gases.” | Molecular description of gases; Boltzmann distributions; the relationships between pressure, volume, and temperature; diffusion and effusion; rates of diffusion or effusion |
| [Saylor] 14.1, “Factors That Affect Reaction Rates.” | Concentration effects; temperature effects; phase and surface area effects; solvent effects; catalyst effects |
| [Saylor] 14.2, “Reaction Rates and Rate Laws.” | Reaction rates; rate laws |
| [Saylor] 14.3, “Methods of Determining Reaction Orders.” | Zeroth-order reactions; first-order reactions; second-order reactions; determining the rate law of a reaction |
| [Saylor] 14.4, “Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders.” | Graphing reaction concentration data to show reaction orders and rate constants; typical graphs for zeroth-, first-, and second-order reactions |
| [JS] 5.1, “Thermally Activated Processes.” | Arrhenius equation; activation energy; Maxwell-Boltzmann distribution; process mechanisms and rate-limiting steps |
| [JS] 5.2, “Thermal Production of Point Defects.” | Activation energy of vacancies vs. interstitials; Arrhenius plot; thermal expansion |
Lecture Video
Resources
Lecture Summary
First-order chemical reactions (e.g. decomposition of cisplatin, N2O5; radioisotope decay) have concentration-independent rates, which is sometimes expressed as the half-life. Second-order rates (e.g. decomposition of NO2) are inversely proportional to concentration. To determine the order and rate constant of an unknown system, integral and differential methods can be used to linearize experimental data measuring concentration over time. Catalysts affect reaction rates by adsorbing, aligning, or otherwise physically manipulating reactants, changing the activation energy of a reaction. Reaction rates are also limited by mass transport of reactants and products. In solids, atoms move via diffusion, driven by concentration gradients, as described by Fick’s first law; the proportionality constant in this case is D, the diffusivity.
Homework
Homework Problems
| [saylor] Sections | Conceptual | Numerical | Application |
|---|---|---|---|
| [Saylor] 14.3, “Methods of Determining Reaction Orders.” | none | 1, 2 | none |
| [Saylor] 14.4, “Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders.” | none | 2 | none |
| [Saylor] 14.5, “Half-Lives and Radioactive Decay Kinetics.” | none | 1, 3, 4 | none |
| [Saylor] 14.9, “End-of-Chapter Material.” | none | none | 11 |
For Further Study
Supplemental Readings
Fick, Adolf. “Ueber Diffusion.” Annalen der Physik 170 (1855): 59-86. (Note: this article is in German.)
People
Culture
Lauper, Cyndi, and Rob Hyman. “Time After Time.” She’s So Unusual. Performed by Cyndi Lauper. Epic Records, 1984.
Lennon, John, and Paul McCartney. “Baby You Can Drive My Car.” Rubber Soul. Performed by The Beatles. EMI, 1965.
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| 5.60 Thermodynamics and Kinetics | MIT OpenCourseWare | Undergraduate (elective) | Lecture 30: Introduction to Reaction Kinetics |
| Diffusion | DoITPoMS | Undergraduate | |
| Diffusion | Connexions | Undergraduate |
Session Overview
| Modules | Reactions and Kinetics |
| Concepts | diffusion: Fick’s first law and steady-state diffusion, dependence of the diffusion coefficient on temperature and atomic arrangement, Fick’s second law and transient-state diffusion, error function solutions to Fick’s second law |
| Keywords | error function, diffusion, mass transport, mass flow rate, flux, Fick’s first law, concentration gradient, diffusivity, concentration profile, rate of ingress, jump frequency, Debye frequency, activation energy, barrier energy, vacancy formation, atom migration, melting point, substitutional atom, interstitial atom, self-diffusion, random walk, equilibrium, diffusion coefficient, surface diffusion, grain boundary, bulk diffusion, effusion, Fick’s second law, permeability, ideal gas law, normal distribution, void fraction, steady-state, transient, heat transfer |
| Chemical Substances | cobalt-60 (60Co), cobalt-59 (59Co), lead (Pb), aluminum (Al), gold (Au), silver (Ag), copper (Cu), iron (Fe), graphite, carbon (C), calcia (CaO), zirconia (ZrO2), hydrogen (H), manganese (Mn), fused silica (SiO2), borosilicate glass (SiO2+B2O3), soda-lime glass (SiO2+Na2O+CaO), lead borate (PbO+B2O3), borate (B2O3) phosphate (P2O5), platinum (Pt) |
| Applications | doping of semiconductors, oxygen sensor for catalytic converters, outgassing, drying |
Prerequisites
Before starting this session, you should be familiar with:
- Crystal lattice structures and point defects (Session 15 through Session 20)
- Thermal excitation and the Maxwell-Boltzmann distribution (Session 14)
- Activation energy, Fick’s first law (Session 23)
- Basic differential equations and calculus
Learning Objectives
After completing this session, you should be able to:
- Sketch the concentration profile as a function of time for simple diffusion situations.
- Describe how diffusion occurs at the atomic level, and identify factors which affect the rate.
- Use Fick’s first and second laws to solve common diffusion problems.
- For a given system, identify some method(s) to increase or decrease the diffusion rate, without adversely affecting other material properties of interest.
- Name 3 industrial applications of diffusion.
Reading
Archived Lecture Notes #9 (PDF)
| Book Chapters | Topics |
|---|---|
| [JS] 5.2, “Thermal Production of Point Defects.” | Activation energy of vacancies vs. interstitials; Arrhenius plot; thermal expansion |
| [JS] 5.3, “Point Defects and Solid-State Diffusion.” | Diffusion and vacancy migration; Fick’s first and second laws; the error function; concentration profiles for common geometries |
| [JS] 5.4, “Steady-State Diffusion.” | Linear solution to diffusion at constant concentration |
| [JS] 5.5, “Alternate Diffusion Paths.” | Bulk, surface, and grain boundary diffusion |
Lecture Video
Resources
Lecture Summary
Last lecture, Prof. Sadoway introduced the concept of diffusion to describe mass transport in solid materials. Thermal vibrations cause atoms to jump randomly through the lattice, so a concentration gradient results in a net flux towards areas of low concentration; at equilibrium, the random motion in one direction equals the motion in the opposite direction, so no net flux occurs. The energy required for this motion depends on specific details of the atomic-level structure, such as: substitutional vs. interstitial travel; number/strength of bonds to break; amount of free volume in close-packed bulk vs. grain boundaries vs. glass with different levels of network formers.
Fick’s first law describes the flux when the concentration gradient is constant (steady-state), while Fick’s second law describes the concentration profile when the gradient changes over time. Prof. Sadoway sketches the steady-state and transient concentration profiles for simple systems, and introduces the error function to describe random walk processes, which follow the normal distribution. Continuing last lecture’s exploration of catalytic converters, he explains how oxygen sensors use diffusion into doped zirconia to monitor the exhaust, giving feedback about the air/fuel ratio to optimize the catalysis.
Homework
For Further Study
Supplemental Readings
Fick, Adolf. “Ueber Diffusion.” Annalen der Physik 170 (1855): 59-86. (Note: this article is in German.)
Carslaw, Horatio S., and John C. Jaeger. Conduction of Heat in Solids. Oxford, England: Clarendon Press, 2004. ISBN: 9780198533689.
People
Culture
Wagner, Richard. “Ride of the Valkyries.” Die Walküre, WWV 86B.
Hornsby, Bruce, and John Hornsby. “The Way It Is.” The Way It Is. Performed by Bruce Hornsby and the Range. RCA, 1986.
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| Diffusion | DoITPoMS | Undergraduate | |
| Diffusion | Connexions | Undergraduate | |
| 1.061/1.61 Transport Processes in the Environment | MIT OpenCourseWare | Undergraduate (elective) / Graduate | Explore lecture notes, animations, and worked examples focusing on environmental systems. |
This self-assessment page completes the Reactions & Kinetics module, and covers material from the following sessions.
- Session 22: Introduction to Kinetics (second half)
- Session 23: Reaction Rates
- Session 24: Diffusion
On this page are a simple weekly quiz and solutions; relevant exam problems and solutions from the 2009 class; help session videos that review selected solutions to the exam problems; and supplemental exam problems and solutions for further study.
Weekly Quiz and Solutions
This short quiz is given approximately once for every three lecture sessions. You should work through the quiz problems in preparation for the exam problems.
Exam Problems and Solutions
These exam problems are intended for you to demonstrate your personal mastery of the material, and should be done alone, closed-book, with just a calculator, the two permitted reference tables (periodic table, physical constants), and one 8 1/2" x 11" aid sheet of your own creation.
After you’ve taken the exam, watch the help session videos below for insights into how to approach some of the exam problems.
Exam Help Session Videos
In these videos, 3.091 teaching assistants review some of the exam problems, demonstrating their approach to solutions, and noting some common mistakes made by students.
Clip 3: Final Exam, Problem 11a
Supplemental Exam Problems and Solutions
These additional exam problems from prior years’ classes are offered for further study.
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