Chemical Kinetics and Reaction Dynamics

Paul L. Houston

• Éditeur: Dover Publications
• Année: 2012
• ISBN:
  9780486131696
• Sujet: Scienze fisiche
• Sous-sujet: Chimica

This text teaches the principles underlying modern chemical kinetics in a clear, direct fashion, using several examples to enhance basic understanding. It features solutions to selected problems, with separate sections and appendices that cover more technical applications.
Each chapter is self-contained and features an introduction that identifies its basic goals, their significance, and a general plan for their achievement. This text's important aims are to demonstrate that the basic kinetic principles are essential to the solution of modern chemical problems, and to show how the underlying question — `How do chemical reactions occur?` — leads to exciting, vibrant fields of modern research. The first aim is achieved by using relevant examples in presenting the basic material, and the second is attained by inclusion of chapters on surface processes, photochemistry, and reaction dynamics.

1

Kinetic Theory of Gases

Chapter Outline

1.1 Introduction

1.2 Pressure of an Ideal Gas

1.3 Temperature and Energy

1.4 Distributions, Mean Values, and Distribution Functions

1.5 The Maxwell Distribution of Speeds

1.6 Energy Distributions

1.7 Collisions: Mean Free Path and Collision Number

1.8 Summary

Appendix 1.1 The Functional Form of the Velocity Distribution

Appendix 1.2 Spherical Coordinates

Appendix 1.3 The Error Function and Co-Error Function

Appendix 1.4 The Center-of-Mass Frame

1.1 INTRODUCTION

The overall objective of this chapter is to understand macroscopic properties such as pressure and temperature on a microscopic level. We will find that the pressure of an ideal gas can be understood by applying Newton’s law to the microscopic motion of the molecules making up the gas and that a comparison between the Newtonian prediction and the ideal gas law can provide a function that describes the distribution of molecular velocities. This distribution function can in turn be used to learn about the frequency of molecular collisions. Since molecules can react only as fast as they collide with one another, the collision frequency provides an upper limit on the reaction rate.

The outline of the discussion is as follows. By applying Newton’s laws to the molecular motion we will find that the product of the pressure and the volume is proportional to the average of the square of the molecular velocity, <v²>, or equivalently to the average molecular translational energy ∈. In order for this result to be consistent with the observed ideal gas law, the temperature T of the gas must also be proportional to <v²> or <∈>. We will then consider in detail how to determine the average of the square of the velocity from a distribution of velocities, and we will use the proportionality of T with <v²> to determine the Maxwell-Boltzmann distribution of speeds. This distribution, F(v) dv, tells us the number of molecules with speeds between v and v + dv. The speed distribution is closely related to the distribution of molecular energies, G(∈) d∈. Finally, we will use the velocity distribution to calculate the number of collisions Z that a molecule makes with other molecules in the gas per unit time. Since in later chapters we will argue that a reaction between two molecules requires that they collide, the collision rate Z provides an upper limit to the rate of a reaction. A related quantity λ is the average distance a molecule travels between collisions or the mean free path.

The history of the kinetic theory of gases is a checkered one, and serves to dispel the impression that science always proceeds along a straight and logical path.² In 1662 Boyle found that for a specified quantity of gas held at a fixed temperature the product of the pressure and the volume was a constant. Daniel Bernoulli derived this law in 1738 by applying Newton’s equations of motion to the m...