Theresa Julia Zielinski
An Introduction to Mathcad
Theresa Julia Zielinski, Monmouth University
Arthur Ferguson, Worcester State College
Sidney H. Young, University of South Alabama
This document provides a tutorial for Mathcad vs 8, 2001i, and 11.
A Summary of Statistical Thermodynamic Calculations JCE
Theresa Julia Zielinski, Monmouth University
Sidney H. Young, University of South Alabama
In this document students can explore the full set of statistical thermodynamic calculations leading to the prediction of the heat capacity at constant volume from the translational, rotational, vibrational, and electronic partition functions. An extension of the calculation of the thermodynamic properties of a molecule is made to predict the equilibrium constant of the dissociation of N2. The document concludes with the study of the NO molecule which has a low lying electronic energy level.
CP, ΔCP , ΔrH, S, ΔrS, and ΔrG as a function of T: N2, H2 and NH3
Theresa Julia Zielinski, Monmouth University
An introduction to thermodynamic calculations leading to a calculaton of the equilibrium constant for a gas phase reaction.
Computing a Flame Temperature
Theresa Julia Zielinski, Monmouth University
Joseph H. Noggle (1936 - 1998), Monmouth University
Mathcad document that allows students to learn how to compute adiabatic flame tempertures.
Computing Enthalpies of Reaction
Theresa Julia Zielinski, Monmouth University
A symbolic mathematics document to provide hands on practice for computing heats of reaction and heat of reaction as a function of temperature given a constant value for Cp.The thermodynamic data required for a large variety of reactions is provided in the file ThDATA.xls.
Conventional Entropies and the Third Law of Thermodynamics JCE
Theresa Julia Zielinski, Monmouth University
Todd M. Hamilton, Georgetown College
After fitting a polynomial to heat capacity as a function of temperature data, students calculate the standard molar third law entropy for a solid, a liquid, and a gas.
Diffusion: A Brief Overview
Theresa Julia Zielinski, Monmouth University
An introduction to diffusion concepts using Fick's Laws.
Exploring Orthonormal Functions JCE
Theresa Julia Zielinski, Monmouth University
A Mathcad template that provides students with quided inquiry practice with orthonormal functions.
Exploring the Harmonic Oscillator Wave Function Components JCE
Theresa Julia Zielinski, Monmouth University
A Mathcad template that provides students with guided inquiry practice with harmonic oscillator wave functions.
Exploring the Morse Potential JCE
Theresa Julia Zielinski, Monmouth University
The goal of the 'Exploring the Morse Potential' document is to provide hands on practice with the Morse potential energy function and the units used for calculating this potential. In the document is a step-by-step description of how to create the Morse potential function for HCl.
Finding Molecular Vibrational Frequencies from HCl to SO2 JCE
Franklin M.C. Chen, University of Wisconsin-Green Bay
Theresa Julia Zielinski, Monmouth University
Students learn about finding molecular vibrational frequencies through normal mode analysis and numerical solutions for simple molecule such as HCl and more complicate molecules such as CO2 and SO2. Topics such as displacement coordinates, internal coordinates, symmetry coordinates, and their relationship are developed.
Fitting a Polynomial to CP vs. T for Ag
Theresa Julia Zielinski, Monmouth University
This document demonstrates the method of fitting a polynomial of any reasonable power to a set of data and provides an example of how to use matrix methods to solve simultaneous equations in physical chemistry.
Introduction to Franck-Condon Factors JCE
Theresa Julia Zielinski, Monmouth University
George M. Shalhoub, La Salle University
The background document contains a very brief introduction to Franck-Condon factors through a sequence of guided inquiry type exercises. Students use potential energy diagrams for a diatomic molecule to examine a transition from a ground electronic state to an excited electronic state including consideration of the vibrational levels of each state. The overlap of vibrational wave functions introduces Franck-Condon factors. All of the exercises in this document are done with pencil and paper as preparation for more detailed work to be done in the companion computational document The Franck-Condon Factors.
Introductory Explorations of the Fourier Series JCE
Theresa Julia Zielinski, Monmouth University
A Mathcad template that provides students with quided inquiry practice using a Fourier series expansion.
Modeling Chemical Bonds with a Mathematical Function
Theresa Julia Zielinski, Monmouth University
Mathcad documents providing a framework for exploration of basic harmonic oscillator concepts used as a model for the chemical bond. The treatment is classical Hooke's Law as used in Molecular Mechanics.
Nonlinear regression: Kinetics of sucrose inversion*
Theresa Julia Zielinski, Monmouth University
An introduction to nonlinear curve fitting using data using first order data. Explorqtion of the basic concepts of ploting data, writing the fitting function, estimating the fitting parameters and then finding the best fit parameters by minimizing the sum of the squares of the deviations (SSD) between the fitting function and the data.SSD from before and after obtaining the optimum parameters are compared. The document concludes withcalculation of residuals and a plot of residuals to demonstrate that points lie between. ? 2 sigma.
Numerical Solution of Second Order Differential Equations
Theresa Julia Zielinski, Monmouth University
Danny G. Miles, Jr., Mount St. Mary's University
In this document students can explore using numerical methods for solving second order differential equations. Students are expected to apply the method to the quantum mechanical oscillator and explore the properties of the resulting solutions.
Particle-in-a-Box Dynamics JCE
Theresa Julia Zielinski, Monmouth University
David M. Hanson, State University of New York at Stony Brook
This Mathcad document explores the time-dependent quantum mechanics for a particle-in-a-box using guided inquiry and the animation tools of the software.
Playing with Waves
Theresa Julia Zielinski, Monmouth University
A Mathcad template that provides students with quided inquiry practice to learn about wave behavior. This documents serves as a review and extends the lessons to include creation of left and right moving waves, standing waves from traveling waves and the Euler relation.
Real Gases: Defining the Standard State and Quantifying Deviations from Ideality
Theresa Julia Zielinski, Monmouth University
Joseph H. Noggle (1936 - 1998), Monmouth University
This document has four parts. In part 1 is an exploration of the PV behavior of gases using the Redlich-Kwong equation. Part 2 determines the energy required to raise the temperature of a sample of a gas and also explores the mathematical definition of the standard state the imperfection concept to account for real properties of a gas. In part 3 is the calculation of the temperature drop and the Joule-Thomson inversion temperature for the expansion of a SO2 gas.
Rotational States of Carbon Monoxide JCE
Theresa Julia Zielinski, Monmouth University
David M. Hanson, State University of New York at Stony Brook
This Mathcad document develops the components that contribute to the observed rotational absorption spectrum of CO.
Steepest Descents: Finding the Minimum in a Function
Theresa Julia Zielinski, Monmouth University
Jeffry D. Madura, Duquesne University
An introduction to the method of Steepest Descents for finding a minimum in a function. Countour maps are developed and search variables explored. A set of exercises using the 2-D Rosenbrock function, whichcontains a minimum that lies at the bottom of a banana shapedvalley completes the set of interactive exercises.
The Autocatalytic Reaction
Theresa Julia Zielinski, Monmouth University
An introduction autocatalytic reactions and the use of the Runge-Kutta method for finding numerical solutions to sets of coupled chemical reactions. This document can serve as one component in a series of studies on the standard chemical kinetics systems found in most standard physical chemistry texts.
The Iodine Spectrum JCE
George Long, Indiana University of Pennsylvania
Theresa Julia Zielinski, Monmouth University
The goal of this document is to present a systematic development of the relationship between spectroscopic experiments and the determination of molecular bond lengths in the excited state of diatomic molecules for which a high resolution vibronic spectrum is available. This document can serve as a template for students to use for data analysis of the UV-vis spectrum of I2 or other diatomic gases.
The Joule-Thomson Effect and Enthalpy for SO2*
Theresa Julia Zielinski, Monmouth University
An introduction to thermodynamics of real gases, computing imperfection functions, Joule-Thomson coefficients, and Joule-Thonson inversion temperatures.
Using Mathcad in Physical Chemistry - Calculus
Theresa Julia Zielinski, Monmouth University
R. D. Poshusta, Washington State University
Provides a set of documents to help students learn the fundamental operations of Mathcad. Basic usage, algebra, solving equations, graphing functions, arrays, and matrices are the topics covered. The templates are easy for students to use.
Using Mathcad in Physical Chemistry - Introductory Exercises
Theresa Julia Zielinski, Monmouth University
R. D. Poshusta, Washington State University
Provides a set of documents to help students learn the fundamental operations of Mathcad. Basic usage, algebra, solving equations, graphing functions, arrays, and matrices are the topics covered. The templates are easy for students to use.
van der Waals and Redlich Kwong: Fitting Two Parameter Equations to Gas Data
Theresa Julia Zielinski, Monmouth University
The Mathcad document given here is a highly annotated application of non-linear curve fitting for determining the a and b parameters for the van der Waals and Redlich-Kwong equations. The document goes through the development of the sum of squares of deviations SSD, applies the Levenberg-Marquradt to minimize the SSD and then uses the F-test to determine the equation that best represents the data. The determination of the standard deviation of the fitting parameters is done through the explicit construction and inversion of the Hessian matrix.
Vibronic Spectra of Diatomic Molecules and the Birge-Sponer Extrapolation JCE
Theresa Julia Zielinski, Monmouth University
George M. Shalhoub, La Salle University
The goal of this document is to examine the potential energy curve for both the ground and excited state of an electronic transition in order to set the stage for a Birge-Sponer determination of the Do and De dissociation energies of the excited state of a diatomic molecule from experimental UV-vis spectral data. After using this document students will be able to: explain the relationship between the potential energy curves for excited and ground states in a molecule; explain the significance of each parameter in a Morse potential energy function; and use a Birge-Sponer plot to determine dissociation energy of an electronic excited state of a diatomic molecule. IodineSpectrum.mcd, is the companion template for the analysis of the UV-vis spectrum of a diatomic molecule.