JCE
The Diffusion Game - Using Symbolic Mathematics Software to Play the Game on a Large Scale©
W. Tandy Grubbs
Department of Chemistry
Stetson University
DeLand, FL 32720
United States
mail to: william.grubbs@stetson,edu



Abstract
The primary goal of the activities in this document is to observe how the statistical 'microscopic' behavior of individual particles ultimately determines a certain 'macroscopic' behavior in a large system. Diffusion provides a simple example; a particle on one side of a container, through random kinetic collision events, is either kicked to the opposite side of the container or remains on its current side (assuming the container is split into two halves). This behavior is simulated here for a large number of particles by using a Mathcad random number generator. An interative process is carried out whereby a random integer is generated during each step for each particle, and the particle is moved to the other side if a certain pre-selected outcome is obtained. By carrying out the simulation in Mathcad, one can easily alter the ultimate number of steps in the simulation, the number of particles in the simulation, and the 'probability criteria' that is used to determine whether a particle switches sides. The outcome of these simulations are analyzed within the context of equilibrium and non-equilibrium states, entropy maximization, and Fick's law of diffusion, reinforcing one's understanding of the microscopic origin of these phenomena.This Mathcad document is designed for student use in a Junior-Senior level physical chemistry course. Students should have had at least one year of calculus and physics, as well as an introductory knowledge of thermodynamics. While not necessary, it will also be helpful if students are familiar with concepts such as equilibrium and non-equilibrium states, the statistical origin of entropy, and Fick's law of diffusion. Some basic Mathcad skills are assumed (how to enter and solve equations, both numerically and symbolically, as well as the ability to graph functions). This document requires Mathcad 11 or higher.
Commentary
Editor's Commentary
Keywords
Audiences: Upper-Division Undergraduate
Pedagogies: Computer-Based Learning
Domains: Physical Chemistry
Topics: Mathematics / Symbolic Mathematics, Statistical Mechanics, Transport Properties
Documents
File NameDescriptionSoftware TypeSoftware Version
diffusion.mcd JCE Computational Document. Mathcad 11 and higher Mathcad 11
diffusion.pdf Read-Only Document
JCE JCE Subscribers only: name and password or institutional IP number access required.
Citations
Grubbs, W. T. J. Chem. Educ. 2006, 83, 1727.
Comments to: wgrubbs@stetson.edu
©Copyright 2006 Journal of Chemical Education