Article pubs.acs.org/jchemeduc
Beyond the Syllabus: Using the First Day of Class in Physical Chemistry as an Introduction to the Development of Macroscopic, Molecular-Level, and Mathematical Models Chrystal D. Bruce* Department of Chemistry, John Carroll University, University Heights, Ohio 44118, United States ABSTRACT: The initial interaction among student, instructor, and content on the first day of class is critical in setting the stage for the remainder of the semester. While many students would like to ease into the semester, experienced faculty realize that the first day of class provides a one-time opportunity to shape the students’ first impression of a subject area. In this paper, a process is outlined for introducing the physical chemistry course in such a way that students expect that much of the course will be about developing models to describe physical and chemical processes and that those models may be macroscopic, molecular-level, or mathematical in nature.
KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Analogies/Transfer, Computer-Based Learning, Theoretical Chemistry
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Successful students are those who learn to transition between thinking about a system macroscopically, at the molecular level, and mathematically.2 Although there are some excellent resources available for physical chemistry course design,3−7 the question of how to engage students in these important endeavors from the beginning has not been well addressed. Online resources do not fill this gap in the literature; attempts at exhaustive searches yielded little except a few forum posts.8,9 Perhaps the reboot of JCE Online as JCE ChemEd Xchange will remedy that. As it stands, there are high school chemistry teacher blogs10,11 and both college-level teaching12 and science research-oriented blogs,13 but very little specifically discussing the teaching of physical chemistry courses. Michelle Francl-Donnay is perhaps the most notable exception with an average of twenty posts per year from 2006 to 2011 and podcasts of her lectures for her quantum mechanics course.14 There are physical chemistry courses available as taped lectures through iTunes and individual university Web sites, including the MIT OpenCourseWare.15 However, the classes that are currently available begin by jumping right into the lecture material with perhaps a few brief statements as to the relevance of the course to the real world. While recognizing that these examples do not provide a complete picture of how physical chemistry is taught in institutions across the world, they are the images of physical chemistry classroom instruction that are currently easily accessible to faculty gathering information on course design.
very semester begins with the same question: how do I introduce the field of physical chemistry to students to convey (1) its relevance, (2) what makes it distinct, and (3) what they will need to do to be successful during the semester? The first day of class is critical in setting the expectations of the course, and it is important to do more than “go over the syllabus”. Within my allotted fifty minutes of their day, I want to show the students why I love physical chemistry and how they can be successful in a course with the reputation of being quite challenging. Like most faculty, I have attempted to accomplish this task in a variety of ways. In recent years, though, I have discovered a first-day-of-class routine that I find particularly beneficial in introducing the idea that, as David Ball states in his textbook Physical Chemistry,1 “One of the goals of physical chemistry is to develop models that explain the behavior of chemical phenomena.” Throughout the physical chemistry course, students will be asked to develop models for a variety of systems. Those models may be macroscopic, molecular-level, or mathematical. In some cases, such as various methods for arriving at the ideal gas equation, students will find that approaching a problem from all three of these perspectives yields the same conclusion. This simple example illustrates the fundamental relevance and innate beauty of physical chemistry. Appreciation of the beauty of physical chemistry is strengthened by success in the course, and students who succeed in physical chemistry are the ones who become proficient in identifying the limitations of certain models and determining ways to compensate, perhaps by approaching the problem from a different perspective. © 2013 American Chemical Society and Division of Chemical Education, Inc.
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Getting students to think critically about the process of developing a model on the first day of class introduces them to much of what the rest of the semester (or year) will involve.
K−12 educators have long recognized the importance of the initial interaction among teacher, student, and content, as well as the effects that this initial encounter have on the remainder of the course.16 Recently, Anderson et al.17 have written an excellent review of first-day activities in college classrooms in fields such as sociology, recreation and leisure studies, philosophy, and history. They conclude that, although students may prefer to be dismissed early after reviewing the syllabus, “The messages you convey on the first day should align with the concepts and content you address throughout the remainder of the semester and should be designed to introduce multiple aspects of the class to students... The first day presents an opportunity. It is too important to serve merely as a chance to ease into the semester. It should be as challenging and pedagogically sound as any other class day.” Perhaps the thought has been that physical chemistry students are a captive audience; it is too late to change majors, so instructors just jump right in and see what happens. Although it may be true that upper-level science majors are stuck with taking a pchem class of some sort, I would prefer for students to get a taste of what it is about this subdiscipline that attracted me so strongly: the way physical chemistry can provide explanations for physical behavior from the macroscopic, molecular-level, and mathematical perspective. I want to start that process on the very first day of class.
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A Comfortable Model: An Ideal Gas
After a discussion about the validity and appropriateness of a good model, the students are ready to consider an example in physical chemistry. Because this course begins with thermodynamics, good models to discuss are those for ideal and real gases. As the students will learn in more detail as the semester progresses, the pressure of a gas provides a nice tool for discussing each approach: macroscopic, molecular-level, and mathematical. The students are comfortable with the macroscopic determination of pressure; they understand that the measured pressure results from collisions of the gas particles with the walls of the container (molecular-level approach); and they know at least one equation of state for calculating pressure at a given temperature, volume, and amount (mathematical approach). In the terminology that Johnstone2 uses, the students’ working memory is not overloaded because they are processing new information in the context of information stored in long-term memory. To provide a more explicit demonstration of the molecularlevel approach and to introduce a new mathematical approach, using the projector system the students are shown a freely available molecular dynamics simulation software program (Virtual Substance19) with a simple, intuitive interface. The goal in introducing this program is to provide a visualization tool for studying mathematically accurate models of particle− particle interactions for gases. In the Virtual Substance program, the user selects a gas (He, Ne, Ar, Kr, Xe, or userdefined) to model, the boundary conditions to use (fixed walls or periodic boundary conditions), and a potential energy function for calculating particle−particle interactions (Figure 1). The program’s output, including kinetic energy, potential
PROCEDURE
Introducing Model Development
The applications of physical chemistry are often in the development of models. As the students are new to physical chemistry, their model-development assignment on the first day of class is relatively simple: propose a T-shirt design for the chemistry department. This task was adapted from a presentation by Jodye Selco at the 242nd ACS National Meeting,18 who uses part of the first day of class to have her students discuss how they would design a napkin given varying resources and requirements. With the T-shirt design, the students were required to list all the factors that would need to be considered in designing a shirt to sell to science students. Some of the items they included were color, logo, fabric, font, and price. After discussing why they made some of their choices in each category for a few minutes, they were asked how some of those selections might change if the T-shirt was not for students, but only for chemistry faculty. They reported that their decisions were made based on the limitations of resources and the preferences of the audience. This class was small enough (7 students in this case) that the students worked as one group, but in larger courses, students could work together in small groups for the 5 min this process takes. But what does this have to do with physical chemistry? The thought process for designing a T-shirt and building a macroscopic, molecular-level, or mathematical model in physical chemistry are, perhaps surprisingly, rather similar. Computational resources determine how appropriate a given system is for ab initio calculations. Various topics in thermodynamics, kinetics, statistical mechanics, and quantum mechanics require considering under what conditions certain assumptions are valid. As part of designing a T-shirt, the students made assumptions that may or may not be valid: can faculty really afford higher-grade fabric than our students? Or would a navy shirt really sell more easily than a neon yellow shirt? So much of science is about asking the right questions.
Figure 1. Screen capture of Virtual Substance model setup parameter screen. 128 argon atoms will be modeled as an ideal gas (no potential) using periodic boundary conditions. The molecular dynamics simulation has not been conducted at this point.
energy, temperature, pressure, and volume, will be used to relate microscopic and mathematical models to the thermodynamic topics studied in class. Although most students are comfortable with the concept of intermolecular interactions, very few have encountered the idea of a mathematical expression for those interactions prior to a physical chemistry course. The first day of class is a good time to discuss such an important concept, but first the students are asked to recall what they know from general chemistry: according to kinetic-molecular theory, an ideal gas has no 1181
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discussions of internal energy, heat capacity, and kineticmolecular theory.
intermolecular interactions. With some guidance, the students predict that an ideal gas has no potential energy of interaction and recognize the implication that the total energy is equal to the kinetic energy. That idea will resurface in the first-day discussion and later in the course. After developing a model, Virtual Substance is used to run a molecular dynamics (MD) simulation. The parameters for that simulation are shown in the top, left side of Figure 2. For those
Expanding the Model: A Real Gas
Up to this point, the class has been operating on basic ideas from general chemistry; reminding students of what they already know can be an effective way to activate their prior knowledge. However, it is time to move beyond their introductory-level understanding of gas behavior by considering real gases. What makes something a real gas? What assumptions have been made in defining the ideal gas that has been modeled thus far? The students are quick to declare that real gases have volume and intermolecular interactions, but they are not exactly sure how to incorporate those factors into the discussion of potential energy, so a diagram of the Lennard-Jones (6,12)
Figure 2. Screen capture of Virtual Substance run dynamics parameter screen. The molecular dynamics simulation has been conducted on 128 argon atoms behaving as an ideal gas at a target temperature of 298 K and molar volume of 1.0 L/mol for 20000 steps at 1.0 fs per step. The simulation output is in the lower left of the screen. Figure 3. Lennard-Jones potential (eq 1). The parameters for argon were used in generating this plot: σ = 0.338 nm and ε/kB = 123 K.
readers unfamiliar with the technique, a classic MD simulation starts with an initial set of coordinates and velocities (in this case, obtained from the desired temperature) and integrates over Newton’s equations of motion to obtain a time-dependent trajectory for the particles in the simulation using the potential energy of interaction that is defined by the user. The integration time step and length of the simulation are also selected by the user. The example illustrated in Figure 2 is the second of two 20 ps simulations (20,000 steps at an integration time set of 1 fs; The total time is 40 ps). The update interval is how often the numerical values of the output are captured. The lower left panel shows the instantaneous (sample column) and average (average column) values of the temperature, pressure, volume, total energy, and kinetic energy as well as the total simulation time (2 × 20 ps simulations in this case). The students are always curious about the difference between the instantaneous and average values, and that is an important conversation to have while the simulation is running. The algorithm for controlling the temperature (and pressure in a constant-pressure simulation) results in fluctuations in these values throughout the simulation, although the average value is relatively close to the target value set by the user. Students are also fascinated to watch the atoms bounce around the screen, and, if periodic boundary conditions have been chosen, pass through the wall of the box and re-enter on the other side. After the simulation is complete, the students do a quick calculation of the pressure predicted by the ideal gas equation using the average temperature during the course of the simulation and compare that to the numerical value of the pressure in the average column. The agreement is quite good, and the longer the simulation runs, the closer the average value is to the value given by the ideal gas law. It is also apparent that the values of the kinetic energy and total energy are equal; the students record that numerical value from the average column, which is (3/2)RT, along with the average temperature for later
potential is sketched (Figure 3) on the board along with its mathematical expression ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ V (r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝r⎠ ⎦ ⎣⎝ r ⎠
(1)
where V is the potential energy as a function of internuclear separation, r, σ is the distance at which the potential is zero, and ε is the well-depth at the minimum potential, as indicated in Figure 3. Although the Lennard-Jones (6,12) potential is not a complex equation in physical chemistry, it can be slightly intimidating to students on the first day of class. However, it is important that the students understand that the multitude of mathematical expressions they will encounter during the semester have meaning and often provide a concise way of clarifying relationships between physically important properties. In this case, the sigma and epsilon parameters give the equilibrium separation distance (re = 21/6σ) and the relative strength of the interaction (ε). On the sketch of the potential function, we see how these quantities manifest themselves as the location and depth of the minimum on the potential well. The final portions of this equation to consider are the power terms. Why the particular choice of (σ/r)12 and −(σ/r)6? The students are asked to recall functions y = 1/x and y = −1/x and sketch them on their papers. When they finally decide what those functions are, they consider 1/r12 and −1/r6, shown in Figure 4. Then they can compare these new sketches to the sketch of the Lennard-Jones potential. Combining multiple representations of this function (an equation and a plot) strengthens the students’ understanding of the distance dependence of intermolecular interactions and how those are modeled mathematically. It is relatively straightforward at this point to 1182
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Figure 4. Plots of the functions y = 1/r12 (left) and y = −1/r6 (right).
identify the portions of the Lennard-Jones potential that arise from the 1/r12 term and those that arise from the −1/r6 term. This conversation lays the foundation for talking about distance dependence of intermolecular interactions and attractive and repulsive components of those interactions as well as providing the students with confidence that they have the abilities necessary to overcome the mathematical challenges in physical chemistry by applying what they already know. Finally, Virtual Substance can be used to run a simulation of a real gas using the Lennard-Jones (6,12) potential, as seen in Figure 5. Before clicking “run simulation”, the students are
Figure 6. Screen capture of the output portion of the Virtual Substance run dynamics parameter screen. The molecular dynamics simulation has been conducted on 128 argon atoms behaving as a Lennard-Jones gas at a target temperature of 298 K and molar volume of 1.0 L/mol for 20000 steps at 1.0 fs per step. The simulation output is in the bottom half of the screen.
interactions (the −an2/V2 term), the students connect another mathematical model (van der Waals equation) for real gas behavior to the macroscopic variable of pressure and the atomic-level observation of the particles colliding with each other and the walls of the container (Virtual Substance simulation). The students are assigned to calculate the pressure predicted by the van der Waals equation of state as a homework problem. Finally, it is important to note that there is a nonzero value for the potential energy during the real gas simulation, and it is a negative number meaning that we are in the region where the attractive portion of the potential is dominant.
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Figure 5. Lennard-Jones potential selected for modeling a real gas using Virtual Substance.
First Class
At this point the fifty minutes of class time is up (a general time table for the class is shown in Table 1), but the students have
asked to predict the pressure that Virtual Substance will calculate for a real gas. Will it be higher, lower, or equal to that of an ideal gas under these temperature and molar volume conditions? What impact does accounting for intermolecular interactions have on the macroscopic property of pressure? Students make predictions on their own papers, and then the simulation is conducted. The process for running the simulation is the same as that for the ideal gas, although the real time necessary for the calculation is noticeably longer, albeit still a short amount of time on a modern computer. This is an opportunity to talk to students about the cost associated with various computational models and how chemists make decisions to balance need and expense. The results of the real gas simulation are shown in Figure 6. The first result to discuss is the pressure: it is lower than that of an ideal gas under these same conditions. The students in the class with good chemical intuition and maybe a bit more memory of their general chemistry course have usually made the correct prediction. Volunteers within that subset of students can be asked to share their reasoning with the rest of the class. For those who did not make the correct prediction, I remind them of the single expression they learned for calculations involving real gases in general chemistry: the van der Waals equation of state. P=
nRT an2 − 2 V − nb V
DISCUSSION
Table 1. Timeline for the First Class Activity
Time Allotted/min
Brief overview of course policies (syllabus) T-shirt design discussion Ideal gas discussion and simulation Real gas discussion and simulation
10 5 10 20
been introduced to some of the most fundamental ideas of physical chemistry: (1) the importance of accurate models, (2) the importance of critically evaluating those models by considering their limitations, (3) the centrality of energy (its origin, distribution, and transfer) to chemically relevant questions, and (4) the skill of approaching a problem by thinking about it macroscopically, at the molecular level, and mathematically. My hope is that, by introducing the course this way, I have begun to convey the relevance of physical chemistry, how it is distinct from other upper-level chemistry courses they have taken, and what skills they will need to develop to be successful. There are many other ways to introduce students to the core ideas of physical chemistry, depending on the goals of the course. I have been using Virtual Substance in my class for many years, and so I like to introduce it early. Examples of other ways to incorporate this software program into the physical chemistry curriculum are available online20 or in Chapter 11 of Advances in Teaching Physical Chemistry.4 Other
(2)
Viewing this equation as a heuristic correction for the fact that real gases have volume (the V − nb term) and intermolecular 1183
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student learning. A question on the first exam is included that asks the students to use the van der Waals equation to calculate the pressure for a real gas, compare the pressure they calculated to that given by the ideal gas law, determine whether the attractive or repulsive part of the potential is dominant, and predict the relative magnitudes of the van der Waals a and b parameters for a series of real gases. The manner in which physical chemistry faculty present material and assess the students to gauge their learning is important to the future of the field. I hope this example provides some ideas for new and current physical chemistry faculty as yet another way to engage students in our chosen subdiscipline.
physical chemistry faculty members incorporate other software programs into their courses and would be able to suggest ways to introduce these fundamental ideas using those programs. Many faculty members who teach quantum mechanics in the first semester rather than thermodynamics will start the course with an introduction to energy distributions among states and statistical thermodynamics. The concepts of energy distribution and computer modeling presented here are relevant to a quantum first approach as well. Maintaining the First-Day Excitement
Faculty members have to find what works best for them and their students, but I hope that this example encourages other physical chemistry faculty to think about what is most important in our courses and how to engage our students in those somewhat complex ideas. That challenge begins on the first day of class and continues throughout the semester. As students encounter new topics, the macroscopic, molecularlevel, and mathematical models are discussed. A few specific examples that are appropriate for a thermodynamics course are listed in Table 2. This is not intended to be an exhaustive list but rather some suggestions for maintaining these connections throughout the semester.
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Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS I would like to thank my wonderful students and colleagues over the years. I would also like to thank John Papanikolas for introducing me to Virtual Substance.
Table 2. Brief List of Topics in the Physical Chemistry Curriculum Where the Connections between Macroscopic Behavior, Molecular-Level Models, and Mathematical Expressions Are Easily Observed Topic Joule−Thompson coefficients Two-component phase equilibria Chemical potential Ion activity
Macroscopic Application Preparation of liquid nitrogen Azeotropes, distillation Colligative properties Ionic strength, activity
Molecular-Level Model Attractive and repulsive intermolecular forces Dynamic equilibrium, intermolecular forces Disruption of bulk properties Solvation shells
AUTHOR INFORMATION
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Mathematical Expression
REFERENCES
(1) Ball, D. W. Physical Chemistry; Brooks-Cole: Pacific Grove, CA, 2003. (2) Johnstone, A. H. You can’t get there from here. J. Chem. Educ. 2010, 87, 22−29. (3) Deckert, A. A.; Nester, L. P.; DiLullo, D. An example of a Guided-Inquiry, Collaborative, Physical Chemistry Laboratory Course. J. Chem. Educ. 1998, 75, 860−863. (4) Advances in Teaching Physical Chemistry; Ellison, M. D., Schoolcraft, T. A., Eds.; Washington, DC: American Chemical Society/Oxford University Press, 2007. (5) Hahn, K. E.; Polik, W. F. Factors Influencing Success in Physical Chemistry. J. Chem. Educ. 2004, 81, 537−572. (6) Shields, G. C. The Physical Chemistry Sequence at Liberal Arts Colleges. J. Chem. Educ. 1994, 11, 951−953. (7) Hinde, R. J.; Kovak, J. Student Active Learning Methods in Physical Chemistry. J. Chem. Educ. 2001, 78, 93−99. (8) Chronicle of Higher Education. http://chronicle.com/forums/ index.php/topic,40820.0.html (accessed Jun 2013). (9) Virtual Inorganic Pedagogical Electronic Resource. https://www. ionicviper.org/forum-topic/cool-first-day-activities (accessed Jun 2013). (10) Crazy Chemistry Teacher: recording my explosions in the classroom. The First Day. http://crazychemteacher.wordpress.com/ 2008/01/07/the-first-day/ (accessed Jun 2013). (11) Chemistry Chris: Navigating my way through a chemical world. http://chemistrychris.wordpress.com/ (accessed Jun 2013). (12) Weimer, M. The Teaching Professor Blog. http://www. facultyfocus.com/topic/articles/teaching-professor-blog/ (accessed Jun 2013). (13) http://scientopia.org/blogs/ (accessed Jun 2013) and http:// scienceblogs.com/ (accessed Jun 2013) host many science bloggers, but there are countless others in many fields, including chemistry. (14) Francl-Donnay, M. The culture of chemistry. http:// cultureofchemistry.fieldofscience.com/ (accessed Jun 2013). (15) MITOpenCourseWare. http://ocw.mit.edu/index.htm (accessed Jun 2013) NOTE: As of fall 2012, there are no Massive Online Open Courses (MOOCs) for physical chemistry, although analytical and organic chemistry courses are being offered by Coursera.
μJT = (∂T/ ∂P)H Henry’s law, Raoult’s law μ(x,T) = μ° + RT ln x Debye− Hückel equations
This constant reminder of the applications of physical chemistry keeps the students from becoming so focused on the math that they forget what a derivative means or what information is obtained when they integrate an equation. I usually finish the semester with Debye−Hückel theory, which provides a nice bookend to the opening day activity described here. We have progressed from ideal gases to aqueous ionic solutions and have considered a variety of macroscopic, molecular-level, and mathematical models along the way. Assessment
Appropriate assessment of student learning is an important tool for educators at all levels of instruction. In my courses, each class is begun with a “warm-up” activity: a handwritten problem projected for the students to see using the document camera. When students enter class, they immediately begin working the problem, and I walk around the classroom checking their work. On the second day of class, my warm-up activity asks students to predict the relative magnitude of the van der Waals a and b parameters for a variety of gases and to explain the connection between the van der Waals equation and the Lennard-Jones potential. This activity is a nice way to refresh the students’ memory of the previous class and prepare them for the second day’s class. A pretest with the same questions could be given at the start of the first day of class for a clearer assessment of 1184
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(16) Wong, H. K. Wong, R. T. The First Days of School: How to be an Effective Teacher. Harry K. Wong Publications: Mountain View, CA. 1998. (17) Anderson, D. M.; McGuire, F. A.; Cory, L. The first day: It happens only once. Teach. Higher Educ. 2011, 16, 293−303. (18) Selco, J. Teaching Physical Chemistry as a Modeling Course. American Chemical Society 242nd National Meeting, Denver, CO, Aug 28 to Sept. 1, 2011. (19) Papanikolas, J. Virtual Substance. To download the software, go to http://www.unc.edu/∼jpapanik/VirtualSubstance/VGMain.htm (accessed Jun 2013). (20) Papanikolas, J. Virtual Substance. For additional virtual experiments, go to http://www.unc.edu/∼jpapanik/ VirtualSubstance/Experiments/ExpIndex.htm (accessed Jun 2013).
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