Dynamic Reaction Figures: An Integrative Vehicle for Understanding

In the Classroom

Dynamic Reaction Figures: An Integrative Vehicle for Understanding Chemical Reactions Emeric Schultz Department of Chemistry, Bloomsburg University, Bloomsburg, PA 17815; [email protected]

There is a growing recognition that significant effort should be expended to deliver general chemistry in a manner that has a more visible story line. With increased activity and emphasis in this Journal on research in chemical education, there is also an enhanced awareness of how chemistry is learned. Areas in which there are widespread misconceptions and instances in which chemical language or symbolism are confusing to students are being identified and discussed. With the ascendancy of molecular visualization, there is an ongoing discussion of the effectiveness and appropriateness of various “tools” that claim to facilitate student learning. In the author’s view a significant milestone in the re-thinking of general chemistry occurred with the publication of a set of articles from the Task Force on General Chemistry (1–4). In these articles the authors described an approach, employing both the new and the old, that served to “connect” certain physical, chemical, and structural concept areas. Earlier, de Vos et al. detailed an effort to seek a “missing framework” for a coherent conceptual structure for the general chemistry curriculum (5). Subsequent to this Russell et al. described a methodology for simultaneous macroscopic, microscopic, and symbolic approaches that enhance the learning of chemistry concepts (6). Specific articles dealing with misconceptions and chemical language problems have included those detailing the ionization–dissociation concept (7) and the differences in the concepts of valence, oxidation number, and charge (8). A notable effort toward finding a common “framework” for reactions was a set of five articles by de Vos and Verdonk (9–13). In these articles the authors investigated the manner in which students understand the meaning of reactions versus how the chemistry teacher understands reactions. It is useful to set the context for the effort to be described in this communication with a quote from one of these articles: “...we aim at the gradual development of a reaction concept that starts from a very primitive intuitive basis. We confront our students with ever-increasing dosages of experience with the reaction phenomenon, encouraging them to enrich and readjust their original ideas as their knowledge matures” (11). In a later contribution, de Vos and Pilot detail how, in the standard textbook exposition of the content area of acids and bases, little attention is given to this “gradual” development of concepts (including the different ways of viewing acid–base reactions), but rather that various different concepts are mixed together (14). A noteworthy recent contribution to the effort to give students a deeper understanding of the nature of chemical reactions details a method that encourages student decision making in completing chemical reactions (15). In the spirit of these endeavors, this article details the ways in which a highly flexible tool can be used by students to “get” the right chemical equation (in conventional form), as well as a means by which the underlying “mechanism” in a chemical reaction can be highlighted. This way of looking at reactions leads to an integration of certain concept areas into a common framework not normally considered as being connected. The characteristics of 386

what I will refer to as dynamic reaction figures, henceforth DRFs, will be developed by investigating different types of chemical transformations. Some specific applications will be dealt with in detail in individual sections. Other applications will be mentioned, but not detailed. Further details on these applications, as well as the manner in which this approach is presented in a class setting, are provided in the extensive online supplements that accompany this article. Dynamic Reaction Figures: Brønsted–Lowry Acid–Base Chemistry A DRF is a pictorial device that is used to portray chemical and physical events typically presented as chemical equations in linear fashion. It is somewhere between a static chemical equation and a computer animation of the event represented by the equation. Figure 1 shows a DRF of what would be meant by the statement “an acid is a proton donor”. The reactant, HA, ionizes to produce H+, placed in the center of the figure, and the product, A−, placed to the right. In analogy to redox half reactions, this is the acid half reaction of an acid–base reaction. One simply draws an upper semi circle and from the mid point draws a downward arc; arrows are placed at the ends of the lines (reading left to right). Generation of this figure as a computer graphic is trivial; once the figure has been created, any conjugate acid–base pair can be edited into the figure. The characteristics of the base half reaction follows from the definition of a Brønsted base as “a proton acceptor” (Figure 2). In order for the base, B, to go to product, HB+, a proton must

HA

á

Aź

H

Figure 1. Dynamic reaction figure for an acid half reaction.

B

Há

HBá

Figure 2. Dynamic reaction figure for a base half reaction.

Journal of Chemical Education • Vol. 85 No. 3 March 2008 • www.JCE.DivCHED.org • © Division of Chemical Education

In the Classroom

be accepted from some proton donor. The two half reactions can now be combined to give the complete acid–base DRF. Figures 3 and 4 serve to introduce terminology universal to this approach and highlight the donor–acceptor and reactant–product relationships, respectively, in this approach. The only portion common to all hemispheres is the species being transferred. Figure 4 introduces the transfer or molecular decision box, which contains either species transferred across hemispheres (protons, electrons) or species that encounter other species with which potential interactions can occur (and for which decisions have to be made). The transfer option will be discussed now; the decision option will be dealt with later. The correlation between DRFs and conventional formalism for the autoionization of water is shown in Figure 5. In the upper hemisphere water donates a proton and in the lower hemisphere water accepts a proton. The overall reaction is obtained by summing the reactants and products with result given below the figure. The rules are simple and apply in all applications: reactants are species from which lines lead away (reading left to right); products are species at the ends of arrows; and intermediates are species between lines (and therefore do not appear in the overall balanced equation). The DRF for the autoionization reaction of water serves as a starting point for investigating what happens upon the addi-

tion of acidic and basic species. Any species capable of acting as an acid replaces water in the upper donor hemisphere, an H+ is removed, and the conjugate base is placed in the product position of the upper hemisphere. Nothing else changes! The DRF, with the “summed” reaction in conventional form, for a typical weak acid, HCN is given in Figure 6. Use of this approach more clearly demonstrates how an acid species produces “excess” hydronium ion (since it is not at the same time producing hydroxide, but rather the conjugate base of the acid). Secondly, the fact that the lower portion of the figure does not change, no matter what acid is placed in the upper hemisphere, has the pedagogic effect of generalizing the concept of acidity. Instead of the student having the notion that each acid reaction is different, a sense of unification is provided. The way to get the correct overall reaction is menu driven and straight forward: (i) remove an H+ from the acid and write the formula of the conjugate base in the upper hemisphere product position; (ii) add an H+ to the reactant base in the lower hemisphere and write the formula of its conjugate acid in the lower hemisphere product position; and (iii) sum the reactant and product sides to give the overall equation in conventional form. The overlay with Brønsted–Lowry and the notion of conjugate acid–base is direct and simple: acid going to conjugate base (upper hemisphere) as base goes to conjugate acid (lower hemisphere).

Donor Hemisphere HA

ź

Há

B

A

á

H2O H2O

á

H

OHź H3Oá

HB Acceptor Hemisphere

OHź á H3Oá

H2O á H2O Figure 3. Hemisphere definitions of dynamic reaction figure for completed acid–base reaction.

Figure 5. Dynamic reaction figure for autoionization of water.

HCN HA B

Reactants

á

H Molecular Decision or Transfer

Aź

H2O

á

H

CNź H3Oá

á

HB

Products

Figure 4. Other definitions of dynamic reaction figure for completed acid–base reaction.

HCN á H2O

CNź á H3Oá

Figure 6. Dynamic reaction figure for ionization reaction of HCN.

© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 3 March 2008 • Journal of Chemical Education

387

In the Classroom

H2O NH3

Há

OHź

A0

NH4á

B0

OHź á NH4á

H2O á NH3

Figure 7. Dynamic reaction figure for the base ionization of ammonia.

e

Aá á Bź

Figure 9. Dynamic reaction figure for generalized oxidation–reduction reaction.

B

Al

H2O

Há

NH2ź H3O

á

Bź

A0 á B0

A

NH3

Aá

ź

Al3á

3eź 2eź

2 Al

2Brź

Br2

6 3eź

3 Br2

2 Al3á ź

2e 6

6 2Brź

C H2O á NH3

NH2ź á H3Oá

Figure 8. Misconception for base ionization of ammonia demonstrated by dynamic reaction figure.

2 Al 3 Br2

2Al á 3Br2

Similarly when a weak base, ammonia for example, is added to water, the DRF in Figure 7 is obtained. Since ammonia is a base, it is placed as a reactant in the lower hemisphere, the proton is added from water, and the ammonium ion results as a product. The demonstration of excess hydroxide, the generalization of the concept of basicity, and the menu driven aspect described above apply here as well. It is instructive to see what happens when the menu driven algorithm is applied incorrectly by the student. Consider the simple question: Give the equation that would describe what happens when ammonia is added to water. There are only two possible actions a student can take: put NH3 as a reactant in the lower hemisphere (resulting in the correct solution) or put NH3 as a reactant in the upper hemisphere (Figure 8). The result obtained should clearly indicate to most perceptive students that a mistake has been made since the species NH2− is not found in aqueous solutions. Therefore, the student would implement the other option. Dynamic Reaction Figures: Oxidation–Reduction The generalized DRF, with the summed overall reaction, for an oxidation–reduction reaction transferring a single elec388

6eź

2 Al3á 6 Brź

2Al3á á 6Brź

Figure 10. (A) Oxidation and reduction dynamic half reaction figures. (B) Work to balance redox half reactions (C) Completed redox dynamic reaction figure.

tron is given in Figure 9. The next pedagogical development would involve the replacement of these abstract reactant species with elemental species. This approach, in the experience of the author, minimizes common errors encountered in balancing redox equations. The process is again menu driven: (i) oxidation and reduction equations are placed into the upper and lower hemisphere respectively; (ii) the equations are multiplied such that the number of electrons produced matches the number of electrons required; and (iii) the species are summed to give the full redox reaction. The utility of the molecular decision or transfer box in balancing is demonstrated with this typical exercise: Give the balanced net ionic equation for the reaction of aluminum powder with aqueous elemental bromine. [The unbalanced equation may be given: Al(s) + Br2(aq) → Al3+(aq) + Br−(aq)]. The steps involved toward a final solution are shown in the diagrams in Figure 10. The first step (Figure 10A) involves writing the two


In the Classroom

( ) á

Na3PO4(aq)

3 Na Ca(NO3)2(aq)

() PO4

( )

3Ca(NO3)2(aq)

6 2 NO3ź 3 Ca2á ( ) () ź 3Ca2á (aq) á 2PO43 (aq)

Zn(s)

Zn2á

CuSO4(aq)

Figure 13. Solution for balanced molecular equation and for net ionic equation using dynamic reaction figures.

half reactions in dynamic reaction form. The second step (Figure 10B) balances the electrons and all species affected by this balancing. The last step (Figure 10C) connects the two half reactions with the number of electrons transferred and then sums the reactants and the products to give the conventional result. This may appear to some readers to be similar to the very old “bridge” method, a method that this author was not familiar with until it was pointed out by a reviewer. This approach also lends itself nicely to balancing redox reactions in acidic or basic solution. The mechanics of how this is done and some examples are found in the online supplement. Dynamic Reaction Figures: Other Applications DRFs can also be used in balancing other types of equations as well, for instance, in obtaining net ionic equations. Consider the following question: Complete and balance the equation that

Cu2á ( )

() 2eź

SO42ź Cu2á ()

( )

Ca3(PO4)2(s)

ź

( )

6 2 NO3ź 3Ca2á

6NaNO3(aq) á Ca3(PO4)2(s)

??

Figure 14. Initial dynamic reaction figures for eq 2.

()

Figure 12. Balancing in molecular decision box to obtain correct match.

( ) () 6 3 Naá 2 PO43ź

Zn CuSO4(aq)

SO42 ()

6 3 Naá 2 PO43ź

()

( )

Figure 11. Initial molecular decision box for combination of two soluble salts.

2 Na3PO4(aq)

Zn(s)

2 NO3ź Ca2á ()

()

( ) 3ź

( )

Figure 15. Intermediate solution for eq 2 using dynamic reaction figures.

describes the mixing of aqueous solutions of calcium nitrate and sodium phosphate; also give the net ionic equation. One must assume that the student knows the following (or it is provided):

Na3PO4(aq) á Ca(NO 3)2(aq)

(1)

Equation 1 can be completed by using the molecular decision or transfer box in a systematic way. The ions produced from the first species are listed in the upper hemisphere with the cation first and the anion second whereas for the second species the resultant ions are listed in the lower hemisphere with the anion first and the cation second (Figure 11). The task is then to match the charge on the ions by balancing appropriately (Figure 12). The last step involves knowing the facts (solubility rules) and going on to products. The net ionic equation can be obtained directly by going to the box to get the number of each ionic species needed to make the new product (Figure 13). DRFs are especially useful in “forcing” student decision making, a skill we very much want to promote (15). Consider the following incomplete reaction for which the predicted products and perhaps a net ionic equation are desired:

4(aq) Zn(s) á CuSO

(2)

Consider what the student would set up using the technique described in the previous problem; the resulting initial DRF would look like Figure 14. This forces a decision: What should I do with the zinc? Or what is zinc inclined to do? Recognition that zinc is a metal and will give up electrons hopefully leads to Figure 15, which in turn would lead to the recognition that the


389

In the Classroom

two electrons can be transferred to ionic copper to give metallic copper and the equation can then be completed. DRFs work nicely in showing the displacement, replacement, or transfer of chemical “units” from one species to another. Two examples are the replacement of one ligand from a coordination complex by another and the transfer of a phosphate in biochemical phosphorylation reactions. Further detail of both these applications is given in the online supplement.

%Gpb / kJ ATP

ADP Pi

glucose

K ä 8.6 ò 103

DRFs can also be used to provide a “picture” that aids quantitative problem solving. To demonstrate this, and also to indicate the breadth of application of this approach, consider this example from biochemistry. The determination of the overall Gibbs energy change in a biochemical phosphate transfer is typically done in a linear additive fashion. The two linear reactions would typically be extracted from a table of Gibbs energies of hydrolysis, ATP á H2O

á H2O glucose-6phosphate

ADP á Pi

%Gpb 30.5 kJ/mol

glucose á Pi

%Gpb 13.8 kJ/mol

ATP glucose

ADP glucose-6-phosphate

Figure 16. Determination of the Gibbs energy of a biochemical phosphate transfer using a dynamic reaction figure.

H

Cl

Cl H

where Pi is shorthand for phosphate and the Gibbs energy changes are for standard conditions at pH 7. Upon proper summing the overall phosphate transfer reaction is given as: ATP á glucose

ź(ź13.8) ź16.7

The Quantitative Dimension

ź30.5

glucose-6phosphate

O H

H H

H

O H

ADP á glucose-6-phosphate

%Gp 30.5 kJ/mol

ź (ź13.8) kJ/mol

16.7 kJ/mol

Consider an alternate “set-up” using a DRF (Figure 16). The top hemisphere is always set up as a phosphate donation (similar to an acid half reaction) and the numerical value is taken directly from a table of phosphate transfers and placed to the right of the upper half reaction. The lower hemisphere is always a phosphate acceptance (similar to a base half reaction). One starts with the phosphate, finds the reaction in the table that contains the two other components, and completes the lower hemisphere in a manner that effects the transfer. Since the lower half is the reverse reaction (to the transfer box) of the upper half, the sign of that process is negative with respect to the upper half. Three additional quantitative applications are presented in the online supplement.

Figure 17. Mechanistic layer on top of a dynamic reaction figure.

H H

H C

H

Cl

Cl C

H

CH3 H

H H H

CH2Cl

H C

C H

Mechanistic Dimension of Dynamic Reaction Figures The mechanistic dimension of chemistry is for the most part missing from general chemistry and is first encountered as a significant endeavor in organic. Consider the DRF for the ionization of HCl that has an additional dimension added (Figure 17); the manner in which this process occurs, that is, its mechanism, is highlighted. An electron pair from the weak base, water, “attacks” HCl producing the hydronium ion and releasing the chloride ion. Consider now the electrophilic addition of HCl to an alkene (not typically connected to the ionization of a strong acid). The “mechanistic” DRF for this reaction (Figure 18) shows the pi electron pair in the double bond of ethylene (acting as a base) attacking the hydrogen in HCl with the formation of the carbocation and the chloride ion. The chloride, now acting 390

Figure 18. Mechanistic dynamic reaction figure for the reaction of HCl with an alkene.

as a base, attacks the unstable carbocation to give chloroethane as the final product. This connection between a fundamental idea in general chemistry and an important mechanism in organic chemistry is seldom made explicitly. The use of DRFs in this comparative fashion illustrates a chemistry conservation principle that is often a hard sell for students: Do not memorize x different reactions, learn one idea that has x different applications. That common idea is explicit in the conserved portion of DRFs having the same type of chemistry.


In the Classroom

A Closer Look at Redox Reactions It is instructive to look at typical treatments of redox reactions in general chemistry in contrast to treatments of redox reactions in organic and biochemistry. In the first case, attention is paid to the formal charge of each species and a set of very specific rules is implemented. In the case of organic chemistry, there is seldom an attempt to “balance” the redox process; instead the usual inorganic oxidizing or reducing agents are “lost” on the reaction arrow. In biochemistry, there is generally some attempt at balancing in terms of electron transfers effected by redox couples (such as NAD+–NADH), but quite often there is little connection made to the underlying oxidation–reduction reactions. DRFs can be used to clarify exactly how electron transfer occurs in redox reactions. Consider the biochemical oxidation of a generalized secondary alcohol to a ketone coupled to the reduction of NAD+ to NADH (Figure 19). The actual redox reaction involves a change in the formal oxidation number of carbon in the upper hemisphere from +1 to +2 with a change in the formal oxidation number of carbon in the lower hemisphere from ‒1 to ‒2. There is also a concomitant acid–base reaction that is often ignored. DRFs allow for nice inventory control of protons (or hydronium ions) and more importantly clearly demonstrate the fact that oxidation states and acid–base status are often connected, a critical consideration for a living cell that requires pH control. The online supplement contains two additional examples in which DRFs are used to clarify redox processes. Discussion DRFs have great potential in two general ways: (i) as useful tools to enhance student success in learning chemistry and (ii) as demonstration devices and integrative vehicles that can be used to dissect certain chemical processes, show underlying mechanisms, and make connections between different phenomena. In my opinion, we, the instructors, are innovative in the use of technology to present and deliver content but are not as creative in developing tools that aid in learning what we present. There are different problem-solving strategies for different types of chemistry concept areas. We all know what these are and we teach a variety of them—we give the students the tools that we know will work for each type of problem. But do we consider that perhaps we provide too many tools and students get confused about which tools to use. Wouldn’t it be prudent to consider using fewer tools that have greater versatility? Perhaps the most famous tool of this sort is the Swiss army knife. I view DRFs as a “Swiss army knife chemistry tool” that can be used to solve numerous problems that are currently solved using different chemistry tools. The challenge our general chemistry students face is similar to the one I faced when I took my first college calculus course. I was mechanically good in problem solving, followed the rules, and obtained the right answer most of the time but did not have the slightest idea of what this all meant. My enlightenment was due to an explanation from an older student coupled to what I now recognize was an unnoticed gradual transition from being a mechanical problem solver to a conceptual one. I believe that DRFs can be used to facilitate this transition from concrete to abstract thinking. The use of DRFs to obtain correct chemical equations is menu driven and mechanical. A few easily learned rules and a

OH R

C H

O R á

NAD

H2O

Hź

á

(H and ź 2e )

Há

R

C

NADH

R á

H3O

Figure 19. In-depth look at common biochemical redox reaction using a dynamic reaction figure.

simple matrix need to be memorized. The creation of the figures allows for checking charge balance and conservation principles; what is transferred has to be accepted; the charge of reactants has to equal the charge of products; atoms of reactants have to equal the atoms of products; and product species have to have a rational relationship to reactant species. The following “flow” occurs in the student’s cognitive development: simple mechanics and generalization → flexible use → ability to use more complex related tools. The learning that arises from the exercise of making correct DRFs, especially in areas where the chemistry is more complex should not be underestimated. This effort helps the student more clearly see the underlying chemistry and to see the bigger picture. In fact, a very deliberate effort has been made in this article to make connections between different subdisciplines of chemistry. The demonstration potential of DRFs involves being able to draw figures to visually display the underlying chemical transformations that are embedded (but not shown) in chemical equations. A remarkable quantity of the “reaction chemistry” that constitutes topical coverage in general chemistry is not only amenable to the use of DRFs, but the figures generated are both simple and consistent in form. Consider this development for the concept of acidity– basicity using DRFs. The definitions of Brønsted acids and bases as proton donor and acceptor, respectively, are shown in Figures 1 through 4. DRFs clearly show this in a manner that the linear approach cannot. The fact that the base has an electron pair that can be viewed as attacking the susceptible hydrogen atom on the acid species can be added to generalized or specific figures such as Figures 3 through 7 to give figures such as Figure 17. The next logical development is to add the notion that the extent to which this type of reaction can occur is dependent on how willing (strong) the acid is to lose a proton coupled to the ability (strength) of the base to remove that proton. Specific structures can then be added and the standard arguments invoking strengths of bonds and concentrations of electron density can be made. If desired, a quantitative value (Ka, Kb) reflecting these considerations can be added. This “layering” effect has the pedagogic consequence of adding an extra level of understanding on top of something that a student has already learned. The nature of redox reactions can be “layered” in a similar fashion. Students have a difficult time identifying redox pro-


391

In the Classroom

cesses, let alone picking out the species that are being oxidized and reduced. DRFs unambiguously demonstrate the transfer of electrons across a DRF. The structural and quantitative aspect, such as that described for acid base reactions, can then be added. In summary, DRFs allow for the introduction of a consistent framework into general chemistry (of course applied with care and attention to chemical reality). Properly developed, this approach could serve as a means of developing a formalism that could then be further refined in other subdisciplines without having to introduce the student to an entirely different way of doing things. The example of how the ionization of an acid can be “connected” to the electrophilic addition of hydrochloric acid to ethylene is a specific example of the possibilities that exist. Literature Cited 1. Gillespie, R. J.; Spencer, J. N.; Moog, R. S. J. Chem. Educ. 1996, 73, 617. 2. Gillespie, R. J.; Spencer, J. N.; Moog, R. S. J. Chem. Educ. 1996, 73, 622. 3. Spencer, J. N.; Moog, R. S.; Gillespie, R. J. J. Chem. Educ. 1996, 73, 627.

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4. Spencer, J. N.; Moog, R. S.; Gillespie, R. J. J. Chem. Educ. 1996, 73, 631. 5. de Vos, W.; van Berkel, B.; Verdonk, A.D. J. Chem. Educ. 1994, 71, 743. 6. Russell, J. W.; Kozma, R. B.; Jones, T.; Wykoff, J.; Marx, N.; Davis, J. J. Chem. Educ. 1997, 74, 330. 7. Schultz, E. J. Chem. Educ. 1997, 74, 868. 8. Parkin, G. J. Chem. Educ. 2006, 83, 791. 9. de Vos, W.; Verdonk, A. H. J. Chem. Educ. 1987, 64, 1010. 10. de Vos, W.; Verdonk, A. H. J. Chem. Educ. 1987, 64, 692. 11. de Vos, W.; Verdonk, A. H. J. Chem. Educ. 1986, 63, 972. 12. de Vos, W.; Verdonk, A. H. J. Chem. Educ. 1985, 62, 648. 13. de Vos, W.; Verdonk, A. H. J. Chem. Educ. 1985, 62, 238. 14. de Vos, W.; Pilot, A. J. Chem. Educ. 2001, 78, 494. 15. DeWit, D. G. J. Chem. Educ. 2006, 83, 1625.

Supporting JCE Online Material

http://www.jce.divched.org/Journal/Issues/2008/Mar/abs386.html Abstract and keywords Full text (PDF) with links to cited JCE articles Supplement Addtional DRF examples and resources for instructors


Dynamic Reaction Figures: An Integrative Vehicle for Understanding

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