## 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 (N_{2}O_{5}), nitrogen dioxide (NO_{2}), oxygen gas (O_{2}), nitric oxide (NO), cisplatin (PtCl_{2}(NH_{3})_{2}), water (H_{2}O), chloride (Cl^{-}), uranium-238 (^{238}U), thorium-234 (^{234}Th), helium (^{4}He), carbon monoxide (CO), carbon dioxide (CO_{2}), carbon (C), silicon (Si), boron (B), diborane (B_{2}H_{6}), hydrogen gas (H_{2}), octane (C_{8}H_{18}), 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

> Download from iTunes U (MP4 - 225MB)

> Download from Internet Archive (MP4 - 225MB)

### Resources

### Lecture Summary

**First-order** chemical reactions (e.g. decomposition of cisplatin, N_{2}O_{5}; radioisotope decay) have **concentration-independent** rates, which is sometimes expressed as the **half-life**. **Second-order** rates (e.g. decomposition of NO_{2}) 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 |