3.091SC | Fall 2010 | Undergraduate

Introduction to Solid State Chemistry

Reactions and Kinetics

23. Reaction Rates

« Previous | Next »

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


Before starting this session, you should be familiar with:

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.


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


Lecture Slides (PDF - 1.4MB)

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.


Problems (PDF)

Solutions (PDF)

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.)


Adolf Fick

Thomas Graham


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  

« Previous | Next »

Course Info

As Taught In
Fall 2010
Learning Resource Types
Course Introduction
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos
Problem Sets
Exam Materials