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Mathcad in the Chemistry Curriculum
Theresa Julia Zielinski Monmouth University West Long Branch, NJ 07764-1898
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Goals and Objectives for Student Mathcad Activities One of the requirements for developing a Mathcad document for publication in this Journal is that the document contain clear goals and objectives. The design of goals and objectives, however, is not something with which most teaching chemists are facile. One reason is that dictionaries indicate that these terms are interchangeable by using each term in the definition of the other. Pedagogically, goals and objectives are different. A goal is the reason we write teaching materials; it is what we want to do for the students through a particular activity or lesson. An objective, on the other hand, states clearly what we want the students to do after they complete a particular activity and is driven by the goal we set for that activity. In this brief essay I will give examples of goals and objectives from the Mathcad documents presented in this issue of the Mathcad in the Chemistry Curriculum column. Hal Harris in his “Carnot Cycle” document writes his objectives with the expectation that students, after completion of the document, will be able to identify the variables that affect the efficiency of the Carnot cycle and complete an analysis of a real gas as the operating gas of a Carnot engine. This pair of objectives contrasts with the six goals he sets for the activity. In the goals, Harris includes things like gaining an understanding of the steps in the cycle, investigating the efficiency of the process, observing what happens when a real gas is used as the working fluid with an equation of state other than the ideal gas law, and investigating the effect of non-ideal gas parameters on the behavior of a real gas equation. Although Harris has written several goals and only two objectives, the distinction is clear between the two terms. The objectives are clearly what students are supposed to do or complete while engaged in a process of learning through a Mathcad document. The important difference between a goal and objective is the action word in the sentence stating the objective. The Mathcad document created by W. Tandy Grubbs, “Variational Methods Applied to the Particle in a Box”, further illustrates the use of action words in objectives and the teacher’s purpose in writing the document. Grubbs’s goal is that the user will gain a familiarity with the variational method. His objectives are what he expects students to do. He asks them to be able to explain the principles, select appropriate functions and boundary conditions, use appropriate trial functions, estimate the accuracy of a trial function, and improve the accuracy of a trial function by using a linear combination of trial functions. “Relating Qualitative Analysis to Equilibrium Principles” by Glenn V. Lo is the first Mathcad document intended for the general chemistry laboratory course that has been published in this column. Lo has one goal: to relate students’ laboratory experience to the theory for ion separation taught in the lecture course. He does this by providing students with a template that they use to complete assignments. The objectives for the students are to estimate the amount of ion 1556
that is removed from solution and to explain the significance of pH for the precipitation of ions. Notice the action words, estimate and explain, in the objectives. The student document is incomplete and the structure of this incomplete document supports the beginning student in completing the goal of the instructor and developing the skills to achieve the objectives. Lo also states that his objectives are performance objectives. Performance is the key to a good objective. An objective should state how we expect the students to perform after they complete an activity we design. The three Mathcad documents presented in this column have a mix of traditional directed instruction and interactive components for students to use to hone their skills. The emphasis on active learning is an important aspect of any Mathcad document. The Mathcad documents included in this column are written for Mathcad2000, Mathcad8, or Mathcad6.0. Users should check their manuals for detailed instructions regarding some Mathcad operations. Only for the Carnot document is there a significant difference between version 6 and higher versions in the graphics display. The Carnot Cycle: CarnotVDW2000.mcd, CarnotVDW8.mcd, CarnotVDW6.mcd
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Harold H. Harris, Department of Chemistry, University of Missouri–St. Louis, St. Louis, MO 63121;
[email protected] With this Mathcad document students investigate the Carnot cycle with numerical calculations on an ideal, monatomic gas. They discover the consequences on the net work and the thermodynamic efficiency of changing variables such as the pressure to which expansion occurs, and the working temperatures of the process. Especially informative are indicator diagrams in color that illustrate the work associated with each step of the cycle. Pressure versus volume is integrated 2·106 1.8·106 1.6·106 1.4·106
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1.2·106 1·106 8·105 6·105 4·105 0.001
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V12 The shaded area represents the work done on the gas during expansion. It is calculated numerically using “the trapezoid rule”.
Journal of Chemical Education • Vol. 78 No. 11 November 2001 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources
using the trapezoid rule, and compared to exact calculations. A much more challenging problem is to repeat the calculation, using a real gas equation of state. The van der Waals model of methane is thoroughly illustrated as an example; the instructor can decide how much of this help would be provided to students. Student groups might be assigned different gases or different equations of state with as much of the van der Waals development provided as is appropriate for the course and the students. Variational Methods Applied to the Particle in a Box: Variational2000.mcd, Variational6.mcd
W Relating Qualitative Analysis to Equilibrium Principles: Qual6.mcd and Qual6a.mcd W
W. Tandy Grubbs, Department of Chemistry, Stetson University, DeLand, FL 32720;
[email protected] Glenn V. Lo, Department of Physical Sciences, Nicholls State University, Thibodaux, LA 70310;
[email protected] A Mathcad instructional document is presented that allows students to explore the variational method, an approximate method (based upon the variation theorem) that is commonly used in commercial software packages to estimate the energies of real chemical systems. The use of this method involves supplying an initial guess about the form of a wave function for a particular system and then calculating the energy on the basis of this trial function. Excellent estimates for energy can be obtained if the selected trial function is suitably flexible. The variational method is used here to estimate the energy levels of a well-known model system, the particle in a one-dimensional box, where exact expressions
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Ψ(l,x) 1.5 1.0
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Comparison of a trial function with the ground state particle-in-abox wave function prior to application of the variation method.
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are available for the energies and wave functions. By practicing the variational method on a known system, students explore the factors that govern the accuracy of the estimated energy and thereby gain an appreciation and confidence in the variational method that is difficult to obtain in any other fashion. Exercises are included throughout the document that allow students to practice the numerical methods and to try the variational method using a wide range of trial functions. These documents are suitable for use in a physical chemistry course.
Qualitative analysis in the general chemistry laboratory provides an excellent opportunity to help students make connections between ionic equilibrium topics covered in the lecture course and physical reality. Although laboratory manuals generally provide ample discussion of the equilibrium principles upon which the procedures are based, students’ attention tends to be focused mostly on techniques, the reactions involved, and physical observations. A lack of understanding of the underlying principles often results in students being unable to make simple modifications to the procedure. This Mathcad document is intended to be used in a prelab activity for qualitative analysis experiments (based on modules ANAL364-366 of the Modular Laboratory Program in Chemistry, Palmyra, PA 17078), which are done toward the end of the general chemistry laboratory course at Nicholls State University. Mathcad is introduced at the beginning of the course and is routinely used throughout the semester for data analysis; handouts for these activities are available at http://chem.nicholls.edu/mathcad. The students are therefore quite competent in Mathcad by the time this activity is conducted. Students are given an incomplete Mathcad document (Qual6.mcd), which they complete as they explore the subject. An exemplary, completed document is available for instructors (Qual6a.mcd).
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