Characters” in General Chemistry - American Chemical Society

Feb 9, 2011 - Chemistry: Can Creating a Sense of Narrative in the ... By student numbers, ..... Number,. Energy. Levels, and. Orbitals. Quantum number...
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In the Classroom

Bringing Out the “Main Characters” in General Chemistry: Can Creating a Sense of Narrative in the Classroom and for the Textbook Aid Long-Term Memory? Junyoung Chang Hankuk Academy of Foreign Studies, Mohyun-myun, Yongin, Gyunggi-Do 449-854, Republic of Korea David Churchill* KAIST-Chemistry, Guseong Dong, Daejeon 305-701, Republic of Korea; *[email protected]

Much has been written about general chemistry (GENCHEM), including articles published in this Journal (1-4). By student numbers, it is a behemoth introductory course, even at medium-sized universities. The unwieldy size also relates to the accompanying commercial written materials. Obviously, much is contained in a modern standard general chemistry text that routinely exceeds 1000 pages.1 The collegiate textbook for any class is intended as the main resource; it is meant to guide in the organized learning process. But, to make the contents of a major tome digestible and better connected, new in- and out-of-class strategies are important to consider. The topic of how overall student's performance (and thus learning) in such large enrollment classes can be improved by various in- and out-of-class methods and exercises has been considered by this Journal. Another difficult topic to address is students' long-term retention of concepts and facts learned, for example, in a general chemistry (GENCHEM) course. The bulkiness of texts has been addressed practically by the appearance of some more concise texts in recent years (e.g., the Siska or ACS texts; see refs 5 and 6). The connection between memory and the narrative approach has been previously considered in the psychology literature (7-10) and will not be treated here. Moving from one chapter to the next in GENCHEM, the choppiness and disjointedness is unavoidable because of the wide coverage of topics. If an instructor does embrace the facts of excessive book size and the concern for long-term student retention of information (far beyond the final exam time), perhaps a narrative approach could be considered as a theoretical new way forward; such an approach has, to the best of our knowledge, not been considered by this Journal in article form previously. Design and Methods Main and Connectivity Characters Importantly, a better chance for long-term memory of the material might be gained by a narrative approach. A narrative quality that has us longing to watch the next TV drama episode, or unable to put a novel down, could conceivably somehow be employed when approaching the task of instructing a GENCHEM course. In fact, what is more gripping in a movie or novel than to have effective character development? But which “characters” might exist in GENCHEM? And how can we make the jump from the realm of rigid hard science to the media of fiction that is quite a different mode of communication 408

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altogether? In essence, we could focus on the most commonly occurring compound or concept. This could be assigned as the “main character”.2 Thus, the main character would be a single molecule or concept that could be the center of discussion, action, and development in each chapter. While this is only theoretical, this approach can be “food for thought” and later considered to be partially or completely adapted by high school and university instructors alike. In the first place, let us assume that the most commonly occurring compound in GENCHEM is H2O. The molecule H2O could be made to stand as the center for discussion. Water is ubiquitous, but could it be discussed in every chapter and serve effectively as a thread to attach the chapters together? (See Table 1.) Other possible main characters that might serve the intended use and are discussed herein are “energy quantization” in chemistry and “electrons” (taken collectively). (See Tables 2 and 3, respectively.) Figure 1 shows a scheme animation flowchart of these three “characters” that can be developed during a GENCHEM course. These are by no means the only possible ones, but seem to fit well into the intended theoretical thrust. Let us consider each of these three “characters” in turn below. Water (H2O) as a Character In Table 1, we can start our discussions with water in the textbook of D. D. Ebbing (4th ed.; see ref 11). In the introductory Chapter 1, water is exemplified as a molecule having three commonly encountered states: solid, liquid, and gas. Through this conceptual starting point (and development of “character”), we are expected to forecast the states of matter in both the physical and chemical senses (that is, water is connected to larger principles). In Chapter 2, water is viewed as a molecule consisting of H and O atoms. In addition, two ions that can be derived from water are also explained: OH- and H3Oþ. This explanation of water (development of character) can lead us toward an understanding of atomic theory and the resultant structures of molecules and ions (connection to larger principles). Reactions involving water as a medium or reagent give us an idea how reactions can proceed (Chapter 3). Chapter 4 displays a reverse view of the molecule compared to that found in Chapter 2: water can be obtained by the reaction of hydrogen and oxygen (development of character). As a result, we can obtain information on how this “character” is connected to the larger concepts of molecular composition, concentration,

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Solubility and Complex-Ion Equilibria

Thermodynamics and Equilibrium

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Nuclear Chemistry

Metallurgy and Chemistry of the Main-Group Metals

Chemistry of the Nonmetals

The Transition Elements

Organic Chemistry

Biochemistry

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Electrochemistry

Acid-Base Equilibria

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Chemical Equilibrium; Gaseous Reactions

Molecular Geometry and Chemical Bonding Theory

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Rates of Reaction

Ionic and Covalent Bonding

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15

Electron Configurations and Periodicity

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14

Quantum Theory of the Atom

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Chemical Reactions: Acid-Base and Oxidation-Reduction Concepts

Thermochemistry

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13

The Gaseous State

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Solutions

Calculations with Chemical Formulas and Equations

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Chemical Reactions: An Introduction

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States of Matter: Liquids and Solids

Atoms, Molecules and Ions

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11

Chemistry and Measurement

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Chapter Number and Title

Water vapor, and comparison with other gases

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Old definition of carbohydrates as carbonic compounds to react with water

Addition reaction of ethylene with H2O to form ethanol

Bonding of Fe(II) ion to 6 molecules of H2O to give the Fe(H2O)62þ complex

Dissolution of carbon dioxide in water to form an aqueous solution of carbonic acid

Reaction of metal- or nonmetal oxides with water to give basic or acidic solutions

Photosynthetic reaction of CO2 and H2O to produce glucose and O2 (isotopically labeled)

Voltaic cell connected by a salt bridge in an aqueous solution

Phase transition of water between ice, liquid water and steam

Quantitative analysis of water solubility of compounds

Ionization of water and aqueous solution of acids or bases

Biochemical compounds: structures/properties

Functional groups in organic chemistry and their interconversion

Metal complex formation and coordination chemistry

Physical and chemical properties of nonmetals

Composition of metal oxides; concept of acidity-basicity; electron configuration of metals

Isotopic atoms as radioactive tracers

Electrochemical phenomena and electrolysis

Enthalpy, entropy, free-energy, and the thermodynamical laws

Factors governing the solubility

Relative strengths of acidity/basicity and titration of acids/bases

Reaction rate laws and mechanism Setting up of chemical equilibrium and change of the equilibrium constant

Decomposition of hydrogen peroxide into water and oxygen

Acid-base and oxidation-reduction concepts

Hydronium, hydroxide species, amphiphilicity, etc.; comparison with other common species Reaction of CO and H2 to produce CH4 and H2O, and its reverse reaction

Solubility, solution processes, and colligative properties

Aqueous solutions; beginnings of a collective treatment; community of molecules (stemming from Ch 9, also)

Phase transitions and their diagrams

The VSEPR model, valence bond theory, and molecular structure

Molecular geometry of H2O, dipole moment; arrangements of H2O in different forms of ice Ice, water, steam and comparison with those states for a few other molecules

Bond types, their strengths, and energies

Acidity-basicity

Fundamentals of quantum mechanics

Energy involved in reactions and the laws of thermodynamics

Gas laws, pressure, and stoichiometry of gaseous state

The O-H bond; hydrogen bonding; how this dipole-dipole type leans to ionic bonding

Oxides of main group elements to react with water

The hydrogenic orbital

The burning of things to give water as a by-product

Composition of molecules, concentration, and quantitative analysis

Reaction media and the concept of acids-bases

Reactions involving H2O and/or aqueous solutions Reaction of hydrogen and oxygen to produce water

Physical and chemical states in a general sense Atomic theory and atomic/molecular structures

H and O atom; H2O molecule; Hþ, OH-, H3Oþ ions

How “Character” Connects to Larger Concepts

Water state: solid (ice), liquid (water), and gas (steam)

How “Character” Develops Chapter by Chapter

Table 1. Development of H2O as a Main Character in Chapters of Ref 11

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Orbitals and Chemical Bonding II: The Molecular Orbital Model and Molecular Energy Levels

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Spontaneity of Chemical Reactions

Free Energy and Chemical Equilibrium

Electrochemistry

States of Matter and Intermolecular Forces

Rates and Mechanisms of Chemical Reactions

The Nucleus

The Transitions Metals

The Chemistry of Carbon

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Energy Changes in Chemical Reactions

Orbitals and Chemical Bonding I: The Valence Bond Model and Molecular Geometry

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Valence Electron Configurations, Periodicity, and Chemical Behavior

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Properties of Gaseous and the Kinetic Molecular Theory

Atoms with Many Electrons and the Periodic Table

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Wave Mechanics and the Hydrogen Atom: Quantum Number, Energy Levels, and Orbitals

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Molecular Motion and Sepctroscopy

The Quantum Revolution: The Failure of Everyday Notions to Apply to Atoms

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Physical Principles Underlying Chemistry

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Chapter Number and Title

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Diels-Alder reaction dictated by reactants' frontier orbitals

Magnetic properties of transition metal complexes defined by their specific spin states

Nuclear magnetic resonance from elements having specific nuclear spins

Correlation of specific energy disposal of early and late energy barriers to vibrational and translational energy

Band theory of metals resulting from the energy quantization of orbitals

Relationship between discrete values of ionization voltage and certain number of electrons being transferred

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Common quantization both in electrons and nucleus

Channeling available energy into specific degrees of freedom to give non-statistical energy distribution

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Macroscopic observations vs microscopic reversibility Equilibrium dependence on various environments

Entropy of a perfect crystal at 0 K is zero

Microscopic molecular motion and macroscopic energy transfer

How continuous velocity distribution is related to energy quantization

Certain types of molecular motions resulting from the energy quantization

Molecules having specific energy and resonance phenomena

Different magnetic properties in certain isoelectronic molecules

Electron sharing in Lewis covalent bonding; electronegativity; chemical reactions

Prediction of chemical properties: ionization energy, electron affinity, and atomic radius

Specification of the energy and wave functions

Energy quantization as a powerful tool to solve many scientific conundrums in early 20th-century science

Hint from macroscopic observations to delve into subatomic structure

How “Character” Connects to Larger Concepts

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Heat capacities resulting from molecular motion having specific values

Maxwell-Boltzmann velocity distribution

Relationship between number of degrees of freedom and allowed mode of molecular motion

Linear combination of atomic orbitals leading to bonding and antibonding molecular energy levels

Specific types of hybridization resulting from energy quantization

Only certain types of electron sharing for the formation of covalent bonds

Specific electron spins allowing only certain electron configurations

Quantum numbers

Nature making a jump

Laws of definite proportions and multiple proportions are a kind of macroscopic quantization restraint

How “Character” Develops Chapter by Chapter

Table 2. Development of Energy Quantization as a Main Character in Chapters of Ref 5

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In the Classroom Table 3. Development of Electrons as a Main Character in Some Chapters of Ref 6 Chapter Number and Title

How “Character” Develops Chapter by Chapter

How “Character” Connects to Larger Concepts

Negatively charged particles consisting of atoms

Role of electrons in various physical and chemical behaviors

1

Water: A Natural Wonder

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Aqueous Solutions and Solubility

Bonding and nonbonding electrons

Electron transfer for the formation of bonds

3

Origin of Atoms

Atomic numbers and spectroscopy

Electron numbers and electronic transition

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Structure of Atoms

Quantum model of atoms

Origin of periodicity and electron configuration

5

Structure of Molecules

Lewis structures of molecules and resonance structures

Electrons in chemical bonding

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Chemical Reactions

Relationship between electron affinity and acidity/basicity

Electron transfer in chemical reactions

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Chemical Energetics: Enthalpy

Energy involving in bond formation and breaking

Electron transfer in bond breaking and making

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Reduction-Oxidation: Electrochemistry

Electron transfer in oxidation-reduction

Applications in electrochemical processes

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Reaction Pathways

Radioisotopes decaying to other isotopes by emitting electrons

Reaction progress and rate laws

Figure 1. Flowchart of three possible “characters” in subsequent chapters that can be developed during a general chemistry course. The two graphics are clip art figures from Microsoft Office Powerpoint 2007.

and quantitative analysis. Water vapor is viewed as a representative example of matter in the gaseous state, conveniently leading to a discussion of “gas laws” in Chapter 5. By analyzing the energy involved in the oxidation of organic molecules to produce CO2 and water, laws of thermodynamics are introduced in Chapter 6. Although a direct usage of water is not seen in Chapter 7, fundamentals of quantum mechanics are introduced by discussing hydrogenic orbitals. In Chapter 8, reactions of oxides of main

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group elements with water allows for a further development of water as a “character”; this is shown to reveal the concept of acidity and basicity (connection to larger concepts). In Chapter 9, the hydrogen bonding of H2O is a central point. (The general-organic-biochemistry textbook by James Armstrong uses the hydrogen bond effectively throughout his book in the fashion described here; see ref 12.) This also serves as a lead-in to a consideration of the types, strengths, and energies of

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bonds in general (connection to larger concepts). The molecular geometry of H2O was used for the generalization into VSEPR, valence bond theory; the resulting prediction of molecular structures is found in Chapter 10. Three states of H2O (ice, water, and steam) exemplify phases whose transitions clearly diagrammed in Chapter 11 are extraordinarily central and important. Also, the monumental “quirk” that water melts when compressed can serve as additional development of water as a “main character”. Properties of aqueous solutions are used to describe solubility, solution processes, and colligative actions in Chapter 12. The hydronium and hydroxide ions are the central species for introducing Brønstead-Lowry acid-base theory and the oxidation-reduction concept (Chapter 13). The mention of the quantitative analysis of decomposition of hydrogen peroxide into water and oxygen serves as an entrance for the student to learn how to obtain reaction rate laws and mechanisms in Chapter 14. A description of both forward and reverse reactions of CO and H2 to produce CH4 and H2O was employed in Chapter 15; this sets the stage for the concept of chemical equilibrium and the change in the equilibrium constant. Once again, as in Chapters 8 and 13, the ionization of water and analysis of aqueous solution of acids and bases were used critically for the cementing the concept of acidity-basicity and their relative strengths of these species, and the titration of acids and bases in Chapter 16. Quantitative analysis of the solubility of compounds in water is connected to the factors governing solubility in Chapter 17. The phase transition of water is the basis for the introduction of thermodynamic concepts that include: (i) enthalpy; (ii) entropy; (iii) free-energy; and (iv) their laws (and equations) in Chapter 18. The voltaic cell connected by a salt bridge requires an aqueous solution, thus serving as a prominent example of the electrochemical process, as described in Chapter 19. The photosynthetic reaction of CO2 and H2O to give glucose and O2 that was deliberately isotopically labeled was used for the introduction of isotopes and radioisotopes in nuclear chemistry (Chapter 20). Understanding of metal oxides and nonmetal oxides, and their interconversions in aqueous solutions was the basis for the electron configuration of metals and nonmetals, and their various chemical properties, including acidity-basicity (Chapters 21 and 22). Aqua complexes of transition metals were used for the basis of coordination chemistry in Chapter 23. The addition reaction of ethylene and water provides a foothold for introducing the principles of reactivity in organic chemistry (Chapter 24). In a different light, carbohydrates are formally composed of carbonic compounds and water and stand as a major class of biomolecules (Chapter 25). These examples describe how H2O can serve to interconnect many GENCHEM concepts and thus serve as a “main character” for the GENCHEM audience for a given textbook. Energy Quantization In this section, instead of following the development of a chemical species, we can track the development of something more abstract. Table 2 shows the narrative approach using “energy quantization”, which serves as our second example; herein, the Siska text was used (5). “Energy quantization” was chosen because, in contrast to the water molecule used in Table 1, it is interesting to see how an essential (albeit, abstract) model, can be considered throughout GENCHEM. Further, this concept is especially central for quantum chemistry. Although it was not explicitly presented, the laws of definite and multiple proportions can be regarded as a macroscopic quantization that does not have 412

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arbitrary numbers (Chapter 1). Chapters 2 and 3 contain the central idea and introduction of energy quantization (character development) and the resultant quantum chemistry (connection to larger ideas). Specific electron spins and the resultant electron configuration of atoms are the result of energy quantization (Chapter 4). The quantization concept was applied to bond formation, allowing for only certain types of electron sharing between atoms to be possible (Chapter 5). Hybridization and the molecular orbital model are additional examples derived from energy quantization (Chapters 6 and 7, respectively). The concept of the allowed number of degrees of freedom is closely related to the energy quantization in molecular motions (Chapter 8). In contrast to the development above, in the next few chapters there is a shift in the character development. The Maxwell-Boltzmann distribution of gas particle velocity allows us to consider how energy quantization in subatomic units can be connected to the continuous parameters in macroscopic molecular assemblies (Chapter 9). The same argument can be applied to the discussion of energy changes in: (i) chemical reactions (Chapter 10); (ii) entropy (Chapter 11); and (iii) Gibbs free energy (Chapter 12). Because electrochemistry deals with electrons being transferred in a chemical processes, discrete values of ionization voltage can be related to a macroscopic view of matter (Chapter 13). Band theory discussed in Chapter 14 is directly related to the requisite energy quantization of orbitals for individual atoms. A specific disposal of energy barriers in chemical reactions can be related to the given degrees of freedom in vibrational and translational energy (Chapter 15). Nuclear magnetic resonance discussed in Chapter 16 is the result of the certain allowed nuclear spin states. Magnetic properties of transition metals are defined by their specific electronic spin states (Chapter 17). Lastly, stereochemical outcomes of concerted pericyclic organic transformations (e.g., the Diels-Alder reaction) can be interpreted by the interaction of certain frontier orbitals that arise from the quantization of energy (Chapter 18). “Electrons” Taken Collectively as a Main Character In the third and last descriptive section here, we will consider “electrons” as a collective entity and track how these subatomic particles appear through the chapters of GENCHEM; through their being mentioned interactively they can be developed as a “main character”. Table 3 shows the development and connectivity that is offered by “electrons” through the use of ref 6. It was anticipated to be interesting to see how various physical and chemical aspects unfold here, because all chemical reactions can be ultimately interpreted as electron transfer processes. In addition, almost all chemical and physical properties of compounds are closely and intrinsically related to each other by their constituent electrons. Chapter 1 introduces electrons and their roles in various chemical and physical behaviors. Bonding and antibonding electrons are described in Chapter 2; the transfer of electrons for the formation of bonds is also discussed. Electron numbers and electronic transitions are a main topic in Chapter 3. Quantum theory and electron configurations, as well as periodicity, are discussed in Chapter 4. Valence electrons play a key role also in the discussions of Lewis molecular structures and of resonance (Chapter 5). The introduction of electron transfer is a crucial point at which to consider the underpinnings of chemical reactions (Chapter 6) and related energy involved in those processes (Chapters 7, 8, and 9). Electrochemical processes such as oxidation and reduction are a direct result of the

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In the Classroom

transfer of electrons (Chapter 10). Reaction pathways can be traced by incorporating isotopic labeling atoms that involve electron transfer, thereby allowing the formulation of rate laws to be possible (Chapter 11). Can Long-Term Memory Be Aided This Way? Now we can summarize by considering how this narrativetype style might aid in memory of the litany of concepts and ideas for GENCHEM. In Table 1, water was used as an example for this purpose. The choice of H2O as a main character is thought to be a wise one. Water is familiar and interesting to all, and has many unique and unusual properties; it is omnipresent in GENCHEM applications. It also fits well paired with “electrons” as a secondary character in terms of hydrogen bonding, coordination chemistry (electron pair sharing), polar covalent bonding, oxidation-reduction chemistry, Lewis acids and bases, and so on. Water also has many applications to everyday life and to important general topics such as pollution, wastewater treatment, acid rain, global warming, and rising water levels. Instructors and practitioners already call vertical chemical groups families, so it would be easy to extend the main character's family to H2S, H2Se, H2Te, as well as nearby neighbors of CH4, NH3, and HF in terms of periodic trends, exceptions, and other approaches to the theme. With respect to water and the chosen Ebbing textbook (11), numerous concepts were introduced by using water as a key component for the introduction. For instance, reactions of chemical compounds with water were used for the concept of composition of molecules, acidity-basicity, thermodynamic laws, and rate laws. On the other hand, decomposition and structure of water were the basis of atoms, molecular interactions, and structural formations. In addition, physical properties of water were used importantly in determining various chemical and physical aspects such as solubility, acidity, and intermolecular interactions. The same strategy mentioned above was also used with respect to energy quantization and electrons. The former was chosen because it was anticipated that a new concept of energy quantization and its connections made in relation to other traditional chemistry would be interesting to a GENCHEM audience. In addition, “electrons” were chosen because they are not only a constituent of atoms, but also the (formal) atom-toatom transfer of valence electrons dictates chemical reactions in general. As can be seen in Table 2, although energy quantization was introduced as a new concept in quantum mechanics, the idea is now adapted in explaining various chemical behaviors and structural elucidation of molecules. Likewise, electrons have become a key character for describing physical transformations and chemical reactivities, as well as properties of chemical compounds (Table 3). Through this “main character” approach, one molecule or a set of molecules can be appreciated from many angles. Such a treatment might be an effective way of understanding the corpus of GENCHEM deeply, and over a long time; with such depth, assignments could be made such as a long essay that could be easily prepared about it, without the use of detailed reference materials. This might help improve the level of interest in the GENCHEM classroom in general.3 This approach has not been formally tested, however. We will coordinate with high school and university classes to propose that this approach be incorporated into the curriculum in a trial fashion. Along with control groups, the future learning-outcome data obtained will hopefully clearly indicate that this approach has merit.4

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Conclusions A new approach for teaching general chemistry recommends using a narrative style in which the same chemical item or concept is iteratively discussed from chapter to chapter. This method may allow for continuity between the seemingly unrelated chapters in the routinely large GENCHEM text. This more interesting “narrative” presentation might be remembered by the students for longer durations (from GENCHEM 1 to 2 or possibly years later). At an anecdotal level, we can say that material is often forgotten quickly, that is, GENCHEM I concepts are not remembered for GENCHEM II. Repetition is a reliable way to teach, learn, and understand something. This approach would not really take time away from other things. The support for the narrative approach aiding long-term memory has been the subject of certain articles in the psychology arena. There might also be some further connections that can be made into the field of psychology.5 Specifically, “H2O”, “energy quantization”, and “electrons” are considered as three such “characters.” How these “characters” are developed and connected to larger principles throughout all chapters in several standard chemistry books is presented. Various parallels with characters in fiction books can be made, and various modifications (inclusions and omissions) from the specific plan outlined can be made conveniently by the intended chemistry instructor. As a result, each character is iteratively discussed in each chapter from a different view, depending on the emphasis of the chapter. Three contemporary GENCHEM texts were used, but there is, in fact, no limit to which text is used or perhaps which “character” is exploited (ammonia and HF could have been used perhaps equally as well as H2O was). Simply, the unraveling of water's characteristics, and a focused development of its understanding through as many facets as there are units in the course, may be an effective and enjoyable approach to learning the subject. Acknowledgment D.C. would like to thank KAIST for financial support, his department for continued encouragement, and his students for quiet enlightenment. Notes

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1. On the other hand, the old texts like that authored by Sienko and Plane, for example, did not seem to have this problem; they were designed and praised for their conciseness (13). 2. This will allow us to avoid spending hundreds of hours listing which molecules appear how frequently in all ∼20þ chapters of any one of the numerous freshman texts. To determine which molecule is in fact most frequently mentioned (and perhaps, best qualified) in the text, captions, marginal glosses can be made simply by an electronic search. An analysis of frequency versus chapter can be easily determined and graphed via spreadsheet programs. 3. This narrative concept could be employed in many kinds of classrooms. Other possibilities might exist here; different molecule “main characters” can be introduced each semester. Alternatively to picking only one “main character”, we could consider a small group of related molecules. As characters relate to each other in a book, so might molecules be discussed by how they interact or react. Obviously, different small sets of molecule characters can give rise to interesting new interconnections

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by way of the stylized class discussion. Furthermore, this concept could be expanded or adapted to various degrees. Each class session could focus on the main character (there could be supporting actors and actresses as well). How the students have grown to understand more about “him or her” could be a subject of writing assignments. Printed media could be adapted (texts), and the lecture (slide) presentation itself could be tailored in this way. New written resources can also be adapted to this style. This method gives the instructor a natural progression, and allows for consideration of an alternate chapter order. Lastly, there is of course some opportunity to incorporate humor.6 4. Future efforts will include applying this in chemistry high school and college courses using control groups as well to get some quantitative information. Also, seeing as this is a preliminary “map”, the real syllabus might be modified slightly or adapted. One can measure the long-term retention by test questions or surveys. Individuals could agree to be polled much later, or the students could not be told they would much later be asked again. The same assignments and tests (exercises, problems) used in the class could appear again. A festival or homecoming could be arranged whereupon old course material could be once again given to the students so to allow for an anonymous study in the spirit of improving the curriculum and student academic performance. 5. One reviewer of this manuscript suggested that literature that discusses the hierarchical theories of the Swiss-born developmental psychologist Jean Piaget can be consulted. Specifically, the final stage, named the formal operational stage (fourth stage), of Piaget's theory relates to ages 11 and above, during which abstract reasoning is developed. This may be useful to determine what young minds can handle in progression from practical experiential knowledge to abstract theoretical knowledge such as what was mentioned herein. 6. As presented here, there is leeway for this approach to include humor to any extent (minor or major). If we consider a novel or

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motion picture narrative analogy, we could have the genre of comedy instead of that of action. Specifically, the joke about the dangers of dihydrogen monoxide (water) and its social consequences is always a popular spoof, and proof of the students own competences.

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