In the Laboratory
The Iodine Spectrum: A New Look at an Old Topic George Long Department of Chemistry, Indiana University of Pennsylvania, Indiana, PA 15705-1090 Deborah Sauder Department of Chemistry, Hood College, Frederick, MD 21701 George M. Shalhoub Department of Chemistry, LaSalle University, Philadelphia, PA 19141 Roland Stout Department of Chemistry, The University of North Carolina at Pembroke, Pembroke, NC 28372-1510 Marcy Hamby Towns Department of Chemistry, Ball State University, Muncie, IN 47306 Theresa Julia Zielinski* Department of Chemistry, Monmouth University, West Long Branch, NJ 07764-1898; *
[email protected] The Iodine Spectrum: A Classic Physical Chemistry Experiment Determining the spectrum of gas-phase iodine is a classic experiment in the undergraduate physical chemistry laboratory. The iodine experiment, or a similar one using bromine, is described in many physical chemistry laboratory texts and has been the subject of several publications in this Journal (1–7). The strength of this laboratory exercise lies in the ease with which it may be performed and the number of important spectroscopic concepts that may be learned from it. In this paper we describe a set of activities designed to facilitate learning of the concepts addressed when students analyze the iodine spectrum. We use a cooperative learning environment for all activities. The experimental design is appropriate for use in the first undergraduate physical chemistry course that introduces quantum chemistry concepts. Students using these activities should have completed introductory work on the quantum mechanical harmonic oscillator and rigid rotor. They should also have a working knowledge of a symbolic mathematics software package. Experimentally, iodine is easy to work with. It readily sublimes, forming a vapor that has an absorption coefficient high enough to permit measurement of the UV–vis spectrum at room temperature. Furthermore, the vibrational structure of the spectrum is easily resolved using conventional spectrometers (those with resolutions of 0.25 nm or slightly better in the visible region). The spectrum of iodine obtained by students clearly shows several spectroscopic features. The spectrum corresponds to an electronic transition that, with adequate resolution, shows the vibrational progression leading to the dissociation limit and the vibrational progressions emanating from the first two
hot bands. From the spectral data it is possible to determine the dissociation energy, the anharmonicity constant, and the internuclear distance of the I2 molecule. The parameters determined experimentally by students for the excited state along with data from the literature for the ground state permit students to plot the Morse potential diagram for both the ground state and the excited state of I2 (2, 3, 5). This gives students the opportunity to examine the connections between spectroscopic data and the computation of molecular structure parameters (bond lengths in the ground state and excited state); mathematical models (potential energy curves for the ground state and excited state) and experimental spectral features; and the quantization of vibrational and rotational energy levels and the mathematical models obtained from the theoretical treatment of molecular vibrations. In this paper we take a fresh look at the concepts addressed in the study of the I2 spectrum and recast them into a studentcentered perspective. This approach was developed originally to support an online intercollegiate collaborative learning experience for physical chemistry students at geographically dispersed locations (see http:///www.iup.edu/~grlong/i1fac.htm) but it has also been used by Shalhoub in a single-site implementation. This paper does not describe the online experience, but rather presents an alternative way to organize the traditional material, a way that is conducive to student-centered group study or activity-oriented learning (8, 9) whether at a single site or at several linked institutions. The iodine experiment is ideal for this type of innovation because the prelaboratory preparation and postlaboratory data reduction involve many often “tricky” calculations that force students into less productive “plug and chug” work styles in the traditional setting. It is easy for students to fail to gain mastery of the significant scientific concepts and connections as they get wrapped up in calculations that often force them to resort to an algorithmic
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approach for determining the required molecular parameters. Traditional Approaches The traditional iodine experiment is computationally heavy. Students first obtain a spectrum, then often follow carefully constructed instructions for preparing the Birge– Sponer plot, and finally complete the activity by calculating the required molecular parameters. Sometimes they are only required to calculate De, the dissociation energy. At other times they prepare the excited-state Morse potential energy curve after using spectroscopic data to determine the dissociation energy De, the anharmonicity constant ω e χ e , and the Morse anharmonicity coefficient β. In some cases, careful study of the hot bands will provide information on the ground state as well, which, with some data from the literature, allows drawing of the ground-state Morse potential curve. In general, two 3-hour laboratory periods allow enough time for students to complete the measurements and calculations. Two laboratory periods, however, are insufficient for speculation about and reflection on the meaning or accuracy of these measurements and calculations. In some laboratory situations the Birge–Sponer plot and the Morse potential have not been taught in lecture or are not taught in conjunction with this experiment. This leaves the students with an incomplete and fragmented learning experience. We suggest that a more tightly designed guided-inquiry approach will foster greater concept mastery while increasing the efficiency with which students handle the data-reduction aspects of the experiment. The extra time required for students to work through the Mathcad1 templates and to reflect and construct a deeper understanding of the content increases the time required for this experiment to three 3-hour laboratory periods plus an equivalent allocation of homework time. The Conceptual Approach This experiment is concept-rich. Students encounter many separate ideas in the prelaboratory preparation, laboratory measurement, and postlaboratory data analysis periods. An understanding of each concept is required for full appreciation of the significance of the calculations performed. In addition, we wish to encourage effective cooperation among the students, which fosters construction of scientific understanding. Often, for laboratory experiments that require many calculations, student cooperation boils down to division of labor, with little discussion of the concepts under study. Our goal is to get students to discuss the connection between the phenomena observed in the laboratory and the spectroscopic concepts. To this end we chose to divide the laboratory experience into sections and the students into cooperative groups of three or four. Each chemical/spectroscopic content section consisted of a set of concepts called a conceptual “chunk”. We required each group of students to answer all the questions and compete all the activities contained in a chunk of material. At the end the groups shared their results with other groups in the class or, in the case of intercollegiate cooperative learning, with the wider community of interacting distant campus groups via email. Here we present the chunking of the ideas for the experiment and the questions we used to focus student learning. We found that this approach helped students to complete 842
the iodine spectral analysis with substantial improvements in conceptual understanding as determined by the quality of their reports, email discussions (in the case of intercollegiate cooperative learning), and laboratory discussions at each site. Mathcad instructional documents, provided by the faculty, helped the students construct their understanding of the material, decreased the computational burden, and permitted more in-depth and conceptually sophisticated exploration of the various complementary concepts included in this experiment. The full suite of Mathcad documents described in this paper can be found online (10). The Mathcad feature column (11) contains the abstracts describing each document used in this redesigned iodine experiment along with a brief description of how these documents may be used by other instructors. The series of focus questions we used in the project follows. In the case of intercollegiate cooperative learning the focus activities were distributed via a Web site and the students were required to progress linearly through them; the location of the next set of focus questions was withheld until they had successfully completed the current set. The focus activities provided here are essentially the same as those used by the faculty in both an online implementation and a single campus implementation of the “chunked” iodine experiment. Additional details appear with student reactions at the end of this paper.
A. Introduction and Wavelength Range: Focus Activities 1. Consider the chemical iodine. I am sure you have seen iodine before, but if you don’t remember, ask your instructor for a sample. What do you notice? Write a brief statement detailing your observations in your notebook. 2. Decide on a 100-nm range you think is most likely to include the wavelengths at which iodine will absorb.
This introductory activity deals with the properties of iodine. Students within their individual groups had to physically examine iodine, note several physical properties, and discuss several physical chemistry concepts. Some of these ideas are phase changes (in particular sublimation), color of the solid and vapor state, the color of ethanol solutions of iodine, and the metallic luster of the solid state. Faculty can facilitate in this phase by asking questions such as “What is the color of tincture of iodine?” The observations of the various groups may lead to interesting discussions on the effect of state on the spectroscopy of iodine, and the purpose for examining the spectrum in the gas phase, rather than liquid or solid phase. Results of this activity and of the activities that follow were shared with other groups via email or in class discussion. The email sharing triggered release of the next set of focus questions. This preliminary exercise offers an opportunity to uncover misconceptions concerning the physical process of the absorption of light and the relationship between observed color and an absorption spectrum. The intragroup and intergroup discussion provides opportunities to remediate misconceptions and to build or reinforce the links connecting the spectrum to Beer’s law. At this point the idea of an absorption coefficient can be added to the discussion so that the student can begin to appreciate that the absorption coefficient is not only related to the structural characteristics of the molecule but is
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also wavelength dependent. Finally, the introductory material provides the preliminary link between the iodine spectrum and quantum mechanics as the students realize that the absorption is due to an electronic transition of the molecule.
B. Introduction to Potential Energy Surfaces: Focus Activities 1. Prepare a sketch showing the variation of potential energy as a function of inter atomic distance for a diatomic molecule. Where on your potential energy curve is the internuclear distance we traditionally call the “bond length”? Does the bond length change when I2 is electronically excited? If so, how? Explain your reasoning. 2. Would you expect the potential energy curve to be fatter or thinner in the excited state when compared to the ground state? You may need to review your physics notes on the harmonic oscillator and Morse potentials to answer this question. Use Mathcad to construct a document in which you demonstrate your understanding .
This activity asks students to look at the structure of the iodine molecule in terms of the energy of an oscillating system. Here the students may use the harmonic oscillator function but are more likely to use the Morse potential. Although most students will be able to sketch both the Morse potential and harmonic oscillator potential, this is not enough. They must be able to explain the curves and their properties. Teachers can insure this by requiring that students record summaries of their discussions in their notebooks along with annotations of the potential functions that were sketched. For more quantitative work a Mathcad template, MorsePotential.mcd (12), which describes the Morse potential and includes the details of the units used in preparing plots of the Morse potential, may be made available at this time. Using the Mathcad template permits students to interactively explore the behavior of potential energy functions. Completion of the exercises included in the Mathcad template brings this chunk of concepts to closure.
C. The Harmonic Oscillator: Focus Activities 1. Find a mathematical expression (model) for the allowed energy levels of a quantum mechanical harmonic oscillator. 2. Using this model, calculate the ground state and first and second excited vibrational state energies of I2. 3. Calculate the quantity of energy required to excite an I2 molecule from its ground vibrational state to the first excited vibrational state. Repeat the calculation for a transition from the first to the second vibrational excited state. You may use Mathcad for the calculations. 4. Compare this quantity of energy to the quantity associated with a photon of visible light at a wavelength you predicted would be absorbed by I2. What do you notice? 5. Draw the harmonic potential and then draw horizontal lines inside the potential well to illustrate the relative energies associated with the lowest three vibrational energy levels. 6. Find a mathematical equation (model) for the allowed energy levels in a quantum mechanical rigid rotor. 7. Calculate the ground and first and second excited rotational state energies of I2. You may use Mathcad for the calculations. 8. Calculate the quantity of energy required to excite one I2 molecule from its ground rotational state to its first
excited rotational state, and from its first excited rotational state to its second excited rotational state. 9. Compare these energies to the energy required to vibrationally or electronically excite the I2 molecule. What do you notice? Record your observations in your notebook. 10. Add horizontal lines indicating the relative energies of rotation for the I 2 molecule to the harmonic-well picture done previously.
In this section, the students perform calculations using the mathematical models (the harmonic oscillator model and rigid rotor in this case) introduced in a typical undergraduate physical chemistry course. Through the focus questions they are expected to see the relationship between spectra and energy levels. In addition, they are attaching actual numerical values to transitions and comparing the relative magnitudes of rotational, vibrational, and electronic transition energies.
D. The Morse Potential: Focus Activities 1. Look up the equation for the Morse potential and graph it for a diatomic molecule of your choice. What makes the Morse potential more realistic than a harmonic potential? 2. Using Mathcad construct a document in which you can examine how changing each parameter in the Morse potential function changes the shape of the potential energy curve. If you already did this as part of the work you did with MorsePotential.mcd template, then summarize your findings in your notebook. 3. Determine (or look up) the mathematical expression that gives the allowed vibrational energy levels for the Morse potential. 4. Draw horizontal lines representing the relative energies of the lowest three vibrational levels on one of your Morse potential curves. How do these compare to the energy levels in the harmonic function you prepared in the previous section?
The purpose of this activity is to require that students construct a solid understanding of the Morse potential before they apply it directly to the spectrum of iodine. We want them to realize that the Morse potential, while being more realistic than the harmonic oscillator model, is still a model and has limitations. By varying the parameters in the functions they discover the significance of each parameter with respect to the shape of the potential curve. Students will find that construction of their own Morse potential diagrams is easy after using the Morse potential Mathcad document MorsePotential.mcd (12).
E. Predicting the Spectrum: Focus Activities 1. Draw the harmonic potential-energy function for the first electronic excited state of iodine. Place this drawing on the same page as the one you prepared for the ground electronic state. Include vibrational and rotational energy levels as you did for the ground electronic state. Note that the first excited state of iodine is a bonding state with a typical potential energy minimum. The antibonding states (those with no minimum) exist, but are inaccessible in this experiment. 2. Using the vibrational and rotational levels you drew on the harmonic potentials, draw vertical lines from at least three vibronic levels in the ground electronic state to vibronic levels in the excited electronic state to
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In the Laboratory illustrate allowed visible transitions. What is the significance of having the electronic transitions represented by vertical lines? 3. Consider two transitions that start at the same vibrational level, but different rotational energy levels. Then consider two transitions that start at the same rotational energy level, but different vibrational energy levels. Are you going to be able to distinguish between absorptions involving different vibrational energy levels of iodine using your spectrophotometer? Are you going to be able to distinguish between absorptions involving different rotational energy levels of iodine using your spectrophotometer? What did you need to know about your spectrometer in order to answer these questions? 4. Sketch the vibrational wave functions for a few vibrational states onto your ground and excited potential energy functions. Examine the sketches. Starting at the ground state and the functions vertically above it in the excited state, where will significant overlap of the ground and excited state wave functions occur? How do you think these overlaps might affect the intensities of the transitions? Examine all the possible pairs of overlaps of functions in the ground state with those in the excited state. Which transitions would you expect to have the greatest intensity?
Once the students achieve an understanding of the Morse potential, they can use this model to predict a spectrum for iodine. Here is where they start making the connections between theory and experiment. In particular, they begin to understand how the limitations in resolution of their spectrophotometer will affect the quality of the structural information they can gather. For example, students should recognize that a 0.25-nm resolution instrument will not allow them to resolve rovibronic transitions, but will allow the observation of vibronic transitions. They should also recognize that the vibronic lines will become unresolvable as the vibronic transition energies increase, and approach the dissociation limit. Lastly, they should recognize that the most intense absorption band will not be the transition from the v′′ = 0 vibrational level in the ground electronic state to the v′ = 0 vibrational level in the excited electronic state. This provides insight that is important for students to have before they take the spectrum. Although students may not have had explicit instruction in transition moments or Franck–Condon factors at this point, they can, through discussion, uncover the principles involved in terms of overlap of the wave functions. Student answers at this point will be qualitative but focus activity 4 in the following section prepares them for the more quantitative work they will meet later.
F. Line Intensities and Hot Bands: Focus Activities 1. Think back to your general, organic, or analytical course and identify three factors that affect the intensity of an absorption feature. 2. Each of the vibrational peaks emanating from v′′ will have a different intensity. Explain why the intensities of the vibrational bands differ. 3. How would you estimate the number of I2 molecules with v′′= 0, v′′ = 1, and v′′ = 2 (in the ground electronic state) in your I 2 sample? 4. Spectral bands that are due to transitions from vibrational states with v greater than 0 are called “hot bands”. Why ? Predict the frequencies of the first few hot-
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band transitions originating from v′′ = 1 and v′′ = 2. Will these absorptions be greater or weaker in intensity than the absorptions emanating from the v′′ = 0 vibrational state ? Explain.
In this section, students link their early understanding of absorption spectroscopy, which is largely from a quantitative point of view, to the structure of the absorption spectra. The focus activities guide them through the process of predicting the absorption frequencies of individual vibronic transitions and require that they discuss the properties of the molecule in terms of the fundamental theories that explain the differences in the absorption frequencies. In particular, the students will need to recognize that the population of the ground vibrational states is governed by the Boltzmann equation. Up to this point students have not explicitly considered the contribution of the Franck–Condon factors when predicting a spectrum. Consequently, the students may predict qualitative relative intensities of the hot bands, but will not be able to predict the relative intensity differences within a specific progression. In our scheme, Franck–Condon factors are addressed after the spectrum is obtained, first to provide a further question for the students, and also to enhance the discussion of the calculation of the Re value for the excited state of iodine. However, the section concerning the Franck–Condon factors could easily be inserted here. G. The Birge–Sponer Plot Spectra obtained by the students are analyzed using a Birge–Sponer extrapolation to obtain the dissociation energies (Do and De ), the anharmonicity constant (ω e χ e ), and the fundamental vibrational frequency of the excited state (ω e ). Additional calculations permit students to extract the Morse potential anharmonicity factor β from the data. Details of these calculations are discussed elsewhere (1–4 ) and in the Mathcad documents BirgeSponer.mcd (13) and Iodine Spectrum.mcd (14 ). For the Birge–Sponer analysis we do not include specific focus questions here. Rather, a series of guided-inquiry questions are embedded in a Mathcad document (13) that we distributed to the students. The Mathcad template is designed to illustrate the Birge–Sponer extrapolation and some of the mathematical underpinnings of this method. The document builds on the MorsePotential.mcd template and extends the material to include explicit discussion of the excited state of a diatomic molecule. Built-in redundancies between the two documents reinforce learning of the core concepts. After the students complete the BirgeSponer.mcd document they work through the final data analysis for their own data using the IodineSpectrum.mcd document (14 ). The document may appear to complete the data analysis with little input from the students. However, this is not the case. Throughout the IodineSpectrum.mcd document, there is an integrated explanation of the spectroscopic concepts, the Mathcad techniques used, and questions that focus thinking about the scientific or mathematical concepts involved in the data analysis. The work in the IodineSpectrum.mcd document builds and reinforces concepts learned using the previously introduced Mathcad documents in this series. Performing the requisite calculations is simplified using an equation engine such as Mathcad. Instructors must at this point gauge the pedagogical advantages of having students perform the calculation de novo vis à vis the time saved by using a prepared computer worksheet. Our approach uses the
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additional time gained with a prepared worksheet to allow students to consider the conceptual aspects of the experiment given in sections A–F above as focus activities. Inclusion of the computer worksheets allows the study of additional spectra and more in-depth treatment of the spectroscopic concepts, including extension to otherwise neglected topics such as Franck–Condon factors.
use of Mathcad documents up to and including those in this section systematically build an integrated web of spectroscopic concepts through repetition and increasing mathematical rigor. Students start with simple hand-drawn sketches and proceed to quantitative Morse potential diagrams based on data from the literature. The cycle of learning reaches closure in the next section.
H. Franck–Condon Factors: Focus Activities
I. Drawing the Potential Well: Focus Activities
1. Using your knowledge of harmonic-oscillator wave functions, draw a sketch of the probability of finding the I2 oscillator at the various displacements available to it. It is best if you superimpose the probability picture on the Morse potential diagram you drew earlier. At what displacement are you most likely to find an I2 oscillator when it is in its ground vibrational state? At what displacement are you most likely to find an I2 oscillator in v′′ = 2? In v′′ = 5? 2. Consider the Franck–Condon principle. What does it say? If you apply it to any iodine molecule that is absorbing a visible photon, what does it imply about the positions of the I 2 nuclei after photon absorption compared to their relative positions before the photon absorption? 3. Using your data for the wavelength of the maximum absorption of iodine and your understanding of Franck– Condon factors and the Franck–Condon principle, calculate the value for R e of the excited electronic state of iodine.
Perhaps the calculation of Re, equilibrium internuclear distance for the excited state of iodine, is the most difficult task for the students. In this calculation, described in detail by D’alterio et al. (2), the students use the wavelength for the maximum absorption of the iodine, the Re value for the ground state (taken from the literature), and the previously determined values for β and De for the excited state to solve the Morse equation for the excited state Re. This procedure causes confusion if the students do not understand what values are being substituted into the Morse equation and why. It is imperative for the students to discuss Franck–Condon factors and the Franck–Condon principle, and to use graphical representations to observe the overlaps of the wave functions of different states and to relate these overlaps to the intensity of the absorption spectrum. Here is a place to introduce the idea that the equilibrium bond length of the excited state, depending on the nature of the orbitals for each state, may be longer or shorter than the ground state. From this perspective the calculation of Re is somewhat more easily understood. Students learn about the Franck–Condon factors primarily by using the FranckCondonBackground.mcd (15 ) and the FranckCondonComputation.mcd documents (16 ). These documents allow them to explore the concept of overlap of wave functions using harmonic-oscillator wave functions, to compute Franck–Condon factors, and finally to use Franck–Condon factors to simulate an absorption spectrum. The connection between the overlap of the wave function of the ground state with that of the excited state and the intensity of the bands that appear in a spectrum becomes very clear as it builds on the foundation set through focus questions presented earlier in this paper. No focus questions are included here for the reader. Both Franck–Condon Mathcad documents are rich with exercises and opportunities for students to practice concepts and extend ideas learned in previous Mathcad documents and focus activities. Each set of focus questions and the integrated
1. Use your experimentally determined values (De, Re, and β) to plot the Morse potential for the excited state of iodine. On the same graph, plot the Morse potential for the ground state of iodine using parameters found in the literature. If you completed these plots as part of your work with the IodineSpectrum.mcd document, then use the results along with the MorsePotential.mcd document as a model to build your own personalized Mathcad document for the plots. 2. How reliable are your calculated values? If your spectrometer resolution were twice its actual value, how would your calculated parameters change?
Students may use a prepared Mathcad document (12, 13) to generate the Morse potential diagram, or they may create their own Mathcad document. By comparing the ground and excited-state potentials on the same plot students can explore the consequences of adding small variations to the various experimental parameters, β, Re, and De. In fact, it is possible for them to go as far back as the experimentally determined spectra and view the differences in the results of the Morse potential. This provides a compelling demonstration of the link between spectroscopic data and structural parameters of molecules. At this point in the experiment the students have come full circle from the initial sections where predictions of spectra were made. It is now possible for the students to reevaluate their predictions and understand their implications in light of observed spectra. It is here that closure and increased mastery of the concepts are achieved. In the Laboratory The chunks of focus activities and the five Mathcad documents presented in this paper form a suite of integrated yet independent units. We used the Mathcad documents in the order presented, namely, MorsePothential.mcd, BirgeSponer.mcd, IodineSpectrum.mcd, FranckCondonBackground.mcd, and FranckCondonComputation.mcd. This order brings students through a set of learning scenarios that includes detailed unit analysis and plotting of the Morse potential, examination of the mathematical models used to discuss bonding, determination of the Morse potential function parameters for the excited state of iodine, and analysis of the UV–vis spectrum for iodine. The entire sequence of lessons is brought to closure through use of the FranckCondonBackground.mcd and FranckCondonComputation.mcd documents. All the Mathcad documents can be found at the JCE Internet site (17 ). The Mathcad feature column (11) provides a description of each document and its precise location at JCE Internet. Students use the Mathcad document along with the focus questions to guide them sequentially through the chunks of material. There was no looking ahead or skipping. Group work keeps students moving at a steady pace so that all activities
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are completed by diligent students within three 3-hour laboratory periods plus an equivalent segment of time on homework. Students have access to various resources for completing the focus questions and laboratory work. They use laboratory textbooks, instrument manuals, computer manuals, Mathcad templates, their lecture textbooks, articles from the Journal of Chemical Education, teachers’ notes, and any other references that are available in the library. Some students, through independent reading motivated by the focus questions, jump quickly through levels of sophistication. These students tend to lead the others in class as they work through the focus questions. The structure of the activities does not and should not inhibit independent study. While students work through the focus activities and Mathcad templates or obtain the experimental spectrum, the instructor interacts with them as for a normal laboratory exercise. Questions are answered as needed but in such a way that students are encouraged to grow scholastically. When necessary, probing questions direct students to a line of thought that might let them uncover the answers to the focus questions and the questions in the Mathcad templates. Every effort is made to avoid giving students answers. Each instructor who participated in this project used a personal style of interaction with students; there was no instructional recipe. The methods and materials described here are suitable for a wide variety of classroom and laboratory situations. They form a framework that can be individualized to a large variety of classroom situations and pedagogical styles. Results: Student and Faculty Reactions This project was carried out at several different institutions as part of an ongoing construction of a learning community of teachers and students through linking of their geographically dispersed physical chemistry classes (18). While the project was designed specifically to facilitate interaction among groups of students at different institutions, the design is also appropriate for encouraging group and individual student discussion within one class. Instructors who used the experimental design described here noticed substantial in-class cooperation. One of us (GL) who has used this laboratory experiment several times noticed a substantial decrease in the anxiety of the students towards the experiment and an improvement in the quality of laboratory reports. The other learning-community faculty (coauthors of this paper) reported similar results. The faculty coauthor (GS) who used this project with a set of four groups in one class noted that students learned and retained more of the basic concepts of spectroscopy because there was significant interaction and discussion among the groups. The students’ perception of online intercollegiate implementation of the iodine project was positive. The activity chunks were distributed at fixed intervals, approximately one chunk of questions every two to three days, in order to foster a common timetable across participating institutions. Although some students objected that this fractured the project too much and delayed progress, most liked the organizational structure. At the same time students found this structure to be more useful than that found in traditional laboratory experiences. They believed that they wasted less time floundering over the calculations. We are using this information and feedback from other online collaborative 846
projects to design future learning activities that facilitate selfpaced passage through a guided inquiry process designed to promote concept mastery of experiment and theory, interaction within collegial groups, interaction among collegial groups within one class, and interaction among groups across campuses. All the intracollegiate (LaSalle University) and most of intercollegiate groups completed the guided inquiry iodine project (19) in a 3-week laboratory time segment. The students spent additional time, at least the equivalent of their scheduled laboratory time, on the project. Only one laboratory period was required for the measurement of the spectrum. Other time was spent answering the focus questions, working through the Mathcad documents, completing data analysis, and preparing the folio of materials or group project report to be submitted to the instructors. The availability of a Mathcad template (14) facilitated the iodine spectrum data analysis. The experimental results obtained by the students were in good agreement with literature values, as is typically the case for this experiment. The structure of this project was planned as a mechanism to overcome some of the problems associated with the asynchronous delivery of material across several campuses, as noted for earlier online activities (20, 21). Some faculty may find the “chunking” of activities and the use of focus questions inappropriate for junior and senior college students. We do not agree with this position. First, there is enough rich material for students to master in a carefully structured learning scenario that the added burden of deciphering a tightly and concisely written laboratory text is not necessary. Second, providing students with a clear guide to the thought processes, spectroscopic concepts, and the intertwining of the spectroscopic concepts with mathematical models provides them with a script that they can use to create their own learning guides. Third and most important, the chunking and guided-inquiry approach significantly facilitates learning and mastery of the material, as demonstrated by the quality of student reports and discussion. Providing students with well-crafted learning materials and guides to learning allows them to construct a stronger scientific conceptual framework on which to build future learning after they leave our classrooms. Acknowledgments We thank Erica Harvey, Fairmont State University, and Kevin Lehmann, Princeton University, for constructive comments that led to the final versions of this paper and the Mathcad documents described here. Note 1. Mathcad is a registered trademark of Mathsoft, Inc., One Kendall Square, Cambridge, MA 02139.
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