Solubility from the Femtoscale to the Macroscale - ACS Publications

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Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

Solubility from the Femtoscale to the Macroscale David W. Pollock,*,† Giovanna T. Truong,† Jessica L. Bonjour,‡ and John A. Frost§ †

Cedarburg High School, Cedarburg, Wisconsin 53012, United States Department of Chemistry, University of WisconsinWhitewater, Whitewater, Wisconsin 53523, United States § Thermo Fisher Scientific, Madison, Wisconsin 53711, United States ‡

S Supporting Information *

ABSTRACT: Solubility is frequently introduced at the high school and introductory college levels through the symbolic domain using net ionic equations and solubility product constants. Students may become proficient with spectator ion cancellation and skilled with algorithmic mathematical applications of solubility without obtaining a deeper understanding of the underlying concept of solubility. We present a convenient chemical system that allows for rapid data collection through benchtop nuclear magnetic resonance (NMR) spectroscopy and simple evaporation experiments. NMR spectroscopy can measure the particulatelevel properties of hydrogen nuclei, objects on the order of a femtometer in size. Solvent evaporation to macroscopic solute residue ties solubility back to a visual frame of reference for students. Data collected from these dissimilar methods of measurement lend themselves to relating the particulate, macroscopic, and symbolic domains of understanding in a hands-on laboratory setting. KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Second-Year Undergraduate, Analytical Chemistry, Hands-On Learning/Manipulatives, Instrumental Methods, NMR Spectroscopy, Solutions/Solvents

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INTRODUCTION Fluency with the particulate, symbolic, and macroscopic domains is key to a deeper understanding of chemical phenomena.1−7 The use of particulate-level drawings has increased for introductory students, notably after the 2013 AP Chemistry redesign by the College Board in response to the National Research Council report Improving Advanced Study of Mathematics and Science in U.S. High Schools.8 The national AP Chemistry Exam was nearly devoid of particulaterelated questions prior to the 2013 revisions.2 Particulate diagrams of gaseous systems, ionic solutions, and stoichiometric relationships have since become commonplace on the AP Chemistry National Exam. The AP Chemistry Course and Exam Description9 provides a detailed accounting of the AP Chemistry curriculum and places an emphasis on the three domains through language such as the following (ref 8, p 82): The ability to use models and “pictures” to explain/represent what is happening at the particulate level is fundamental to understanding chemistry. The student must be able to draw representations of these particles (atoms, ions, molecules) whose behaviors we observe macroscopically in the laboratory. Students should be able to draw pictures that represent the particles we cannot observe but that match the accepted models for various phenomena... The three domains are additionally referenced heavily as part of an eight-page summary of Learning Objectives in the AP Chemistry Course Description as shown in Table 1. © XXXX American Chemical Society and Division of Chemical Education, Inc.

Table 1. Keyword Search for the Conceptual Domains in the Learning Objectives Summary of the AP Chemistry Course Description

a

Keyword

Number of References

Macroscopic Symbolic Particulate

10 3 7a

With additional references to “particle view” and “at the atomic level”.

It is interesting to note that the symbolic domain was explicitly referenced the fewest times, though it is likely the most comfortable, information dense, and common means of communication for chemical educators. The symbol NaCl(aq) may conjure specific chemical composition and dynamic interactions to the experienced practitioner. Unfortunately, the symbolic level may also provide the least meaning for new chemistry learners.10−13 At the high school and introductory college levels, solubility of salts is often taught in terms of following “solubility rules” and writing net ionic equations for simple precipitation or redox reactions. Students who are capable of writing net ionic symbolic equations often display a wide range of conceptual Received: December 15, 2017 Revised: March 12, 2018

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DOI: 10.1021/acs.jchemed.7b00965 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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errors when prompted to illustrate their work at the particulate level.7,14,15 Typical chemistry curricula also present solubility as a mathematical application of equilibrium. Students may become familiar with calculations involving solubility products but have poor visualization of what their calculations represent at the particulate level.16,17 Animations and simulations have been shown to aid in a deeper understanding of solubility and particulate knowledge.18−22 PhET and Molecular Workbench are two current examples of interactive simulations of molecular and ionic substances in aqueous solution involving both macroscopic and particulate representations.23−26 Additionally, research has described the use of lab time to develop a particulate conceptual understanding of solubility using handson particulate models which are beneficial for student learning.27 This paper describes a hands-on system that provides investigations at all three domains of understanding: macroscopic, symbolic, and particulate. Maleic acid is quite soluble in acetone, providing a convenient chemical system that allows for rapid experimental solubility data collection on both the macroscopic and the particulate scale which are then related through symbolic calculations. Low-field nuclear magnetic resonance (NMR) data interpreted at the particulate level can be used to perform solubility calculations at the symbolic level. Simple evaporative experiments provide a quick macroscale solubility determination of the same phenomena but at a scale that is more intuitive for students. The temperature dependence of solubility of this system can also be tracked across the three domains of understanding.

Figure 1. Qualitative temperature dependence of solubility (asterisk indicates thick slurry formed).

college campus to use an NMR instrument or to bring an instrument directly to the students’ classroom.28−32 The supernatant solutions obtained at different temperatures were analyzed in a Thermo Scientific picoSpin 45 NMR spectrometer. The maleic acid and acetone system provides a convenient set of chemical shifts for analysis. Even with a lowfield NMR spectrometer, the chemical shifts of the protons involved are fully resolved. A notable advantage of benchtop NMR spectroscopy is the capability to run samples rapidly in nondeuterated solvents.29 In addition, for this system, referencing compounds are not needed as the exact chemical shifts themselves are not important to students’ understanding. Spectra presented here are referenced using the acetone signal (2.05 ppm). Both the acidic and vinyl hydrogens are clearly resolved at expected chemical shift locations. Water was investigated as an alternative solvent, but the acidic protons are not observed due to proton transfer with the solvent during the time scale of the experiment. This creates a merged water/acid signal that may be confusing to students. Proton exchange is not an issue with acetone. The integrated values for the maleic acid signals were compared to the integrated value of the acetone signal to calculate solubility (Figure 2). The peak integration was analyzed to provide basic quantitative information. Since observation of the solubility trend, not accuracy, was the focus, quantitative NMR experimental design and data processing techniques were ignored in favor of speed and simplicity. As a result, data processed by novice high school students gave only slightly different results from those presented. Although general NMR analysis may go beyond the scope of typical high school or introductory college courses, the flow of the mathematical problem solving is straightforward (Figure 3). The described maleic acid/acetone system does not require an understanding of splitting patterns as all signals are singlets. Students must only relate the signal integration to the relative number of hydrogen atoms. These calculations utilize the link between intra- and intermolecular ratios in NMR spectroscopy to determine the particulate-level ratios between solute and solvent. Because NMR spectroscopic data is inherently related to the particulate level of matter, students may gain a greater

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QUALITATIVE MACROSCOPIC VISUALIZATION OF SOLUBILITY The saturated solutions used for investigation were produced by adding roughly 2 g of maleic acid to 6 mL of acetone inside a 2 dram reaction vial. This results in a visibly convincing quantity of insoluble maleic acid and also provides enough supernatant solution to run numerous experiments. Prior to each experiment, the contents were allowed to fully dissolve at 65 °C. In our experience, starting at 65 °C produced a higher precipitate height upon cooling in the various ice baths than the same sample did after cooling from room temperature, likely due to the rate of crystal growth. Macroscopic, qualitative observations of the temperature dependence of solubility establish that solute is present in solution and can increase or decrease in concentration as shown in Figure 1. The photographs are of the same sealed vial. When students are asked to make a prediction about solubility in these vials, they must switch to a particulate mode of thinking since the absence of a macroscopic solid implies the presence of dissolved particulates. As a side note, since the volumetric coefficient of expansion for acetone is over 6 times that of water (a typical student reference point), the total volume of solution noticeably changes over the temperature range found in Figure 1.

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PARTICULATE MEASUREMENTS USING NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY The introduction of less expensive benchtop NMR spectrometers makes it more likely for undergraduate students to have earlier access to this type of instrumentation. While access to an NMR spectrometer remains out of reach for most high school settings, outreach programs exist either to bring students onto a B



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Figure 2. 45 MHz 1H NMR spectrum of room temperature supernatant of a saturated maleic acid/acetone mixture normalized to the vinyl signal.

Figure 3. Particulate-scale NMR student problem-solving pathway along with data from Figure 2.

understanding of the relationship between particulate and mathematical/symbolic domains through executions of these calculations. The particulate-level solubility is found to be 6.63 molecules of acetone per 1 molecule of maleic acid at room temperature for the data presented in Figure 2. For purposes of comparison to typical solubility units and/or the results from the macroscopic evaporative technique, calculations can extend to relative gram values as presented in Figure 3. Extensions of the analysis to a lower temperature result in noticeable changes in integrated values (Figure 4). To a more advanced student, the strongly downfield chemical shift of the carboxylic acid proton signal should indicate a highly deshielded environment, indicative of hydrogen bonding interactions with other maleic acid molecules. The changing chemical shift of the carboxylic acid signal is evidence of a change in the proton chemical environment. As temperature is lowered, the observed chemical shift changes due to a decrease in dimer and oligomer formation at lower concentrations.

It may not be apparent to students why the supernatant from below ambient temperatures can be analyzed even when brought back to room temperatures while the supernatant from elevated temperatures cannot be used to perform the same analysis. It is recommended that instructors take care to clarify this important conceptual distinction.

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MACROSCOPIC MEASUREMENTS THROUGH EVAPORATION

Acetone is an advantageous solvent for the macroscopic domain due to its rapid evaporation rate. Data can quickly be generated by transferring a 0.2 mL sample of saturated solution to a watch glass on an analytical balance. Dryness is achieved in about 5 min using this volume, leaving a large amount of visible residue to be observed visually or, as an extension, by microscope. The crystals under minimal magnification show several regular 0.2−0.3 mm length crystals (Figure 5). C



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Figure 4. Comparison of maleic acid/acetone solutions at various temperatures normalized to the acetone signal.

from both the NMR data and evaporative techniques give comparable results and reinforce qualitative changes in solubility, as indicated in Table 2. In addition, the maleic acid/acetone ratios lend themselves to particulate modeling and provide a manageable visualization of solubility for students. The results from both techniques are summarized in Table 2. The results give good qualitative comparison of solubility of this system at various temperatures. One literature value has been reported as 35.77 g/100 g acetone at 29.7 °C,33 which fits well with our values since our data show a clear trend of increased solubility at higher temperatures. Another value has been reported at 38.6 g/100 g acetone at 20 °C,34 which is higher than our results at room temperature and does not agree with the first literature value or with our observed temperature−solubility trend.

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PARTICULATE MODELING While it is novel to have two techniques employing measurement on vastly different scales, this system is also especially convenient for its application to particulate-scale models. Research has shown that when students work with particulate-level diagrams to understand phenomena, their performance in all three domains increases.35 Solubility is a difficult topic for students to understand because using a particulate viewpoint is less intuitive than their most likely previously held “continuous matter” worldview. In investigations of children’s views of dissolution, younger children (ages 9−12) frequently hold the view that dissolution involves the disappearance of matter and that mass is therefore not conserved.36,37 As such, dissolving is not viewed as a reversible process. Evidence that sugar water tastes sweet is viewed as some sort of residual effect of sugar, not its continuing presence. Additional research found that these preconceptions were gradually corrected in the years between fourth and ninth grade, although conservation of mass and the reversibility of physical change remained difficult for roughly 20% of the ninth grade students investigated.38

Figure 5. Photo of maleic acid crystals at ×4 magnification under a digital microscope.

The calculations of solubility using this technique are intuitive and highlight basic definitions of solute, solvent, and solution. The mathematical problem solving (Figure 6) is a simple series of mass by difference calculations. The solubility is found to be 32.3 g maleic acid/100 g acetone for the data presented in Figure 6. Mathematical results

Figure 6. Macroscale evaporation student problem-solving pathway. D



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Table 2. Sample Calculated Solubilities of Maleic Acid in Acetone Technique

Solubilitya (g/100 g Acetone)

Approximate Maleic Acid/Acetone Molecule Ratio in Solution

Room temperature

NMR Evaporation

31.3 ± 1.3 32.5 ± 0.7

1/6

Ice bath

NMR Evaporation

23.3 ± 1.4 25.2 ± 0.5

1/8

Acetone/dry ice bath

NMR Evaporation

12.3 ± 1.5 12.4 ± 0.3

1/16

Temperature

a

n = 5.

Research has detailed common preconceptions for 11th grade students involving solubility.39,40 Many of the students in these studies believe that dissolving is merely a state change for the solute and is the same process as melting. Others in this age group frequently believe that a “chemical joining” occurs to produce a solute−solvent pair. Some students believe that dissolving is possible because the solute is able to occupy “air pockets” present in the solvent. They describe solutes as not dissolving due to the lack of available space for the solute to occupy. Furthermore, research has shown that even the students with a previous chemistry course struggle to indicate both the conservation of particles and the appropriate location of particles during other types of simple physical change.41 One study has shown that general particulate knowledge of common solution systems such as strong and weak acids can pose lingering conceptual problems well beyond the undergraduate level.42 The saturated maleic acid/acetone system has a large enough solute/solvent ratio to make it easy to represent on a particulate scale using a modest number of drawn molecules. Students can reinforce correct understanding of solubility by relating the molecular and macroscopic levels together through the use of particulate diagrams like those in Figure 7. Saturated Solution

While the presence of macroscopic solid should provide evidence of saturation, research has shown that students with correct definitions of the terms involved often mistakenly view this material as evidence of supersaturation.43 Other work has shown that students often believe that dissolving is a temporary process caused by the mechanical action of stirring.44 Sometimes students also believe that the solution contains undissolved solute.43 Since this system can be prepared in a matter of minutes, students can gain hands-on knowledge of saturated solution preparation and behavior. Dynamic simulations such as the PhET “Salts and Solubility” provide complementary views of saturation by allowing students to add an increasing amount of solute to a saturated solution while not seeing an increase in solution concentration. Each of the side-by-side graphics in Figure 8 indicates an equal number of sodium ions dissolved in solution despite noticeable differences in undissolved material.23 Although different interparticle interactions are present in the ionic system presented by PhET, the behavior at saturation is comparable to the molecular maleic acid/acetone system. This simulation allows for the user to change additional parameters besides the addition of further solute. The amount of solvent can be added or subtracted using the “faucets.” For clarity, the particulate view of water is not indicated.

Figure 7. Particulate model of saturated solutions involving 48 acetone molecules. The supernatant is transferred to a receiving vial for NMR and evaporative analysis.

The PhET simulation addresses one reason for observed amounts of undissolved material; however, this should not be confused with the explanation for the amount of solid maleic acid in the saturated column of Figure 7, which is based on temperature. The saturated column of Figure 7 serves as an aid in understanding the macroscopic height of insoluble maleic acid in Figure 1. Since the same vial is used at both E



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Figure 8. PhET simulation of saturated NaCl solutions in water with different quantities of undissolved material (readout of ion count not shown). Reproduced/adapted with permission. Copyright 2018 PhET Interactive Simulations.

inadequacies of models have been shown to be difficult for students to recognize.27,46 Known simplifications in particulate diagrams of this nature can be addressed as follows: • Static nature of particulate drawings. The dynamic nature of solubility can be emphasized with computer simulations and multimedia.23−26,47 Students have been shown to discount the role of particulate motion in their understanding of dissolution even though they view it as an important factor in their understanding of the states of matter.44,48 • Liquid level lines. Rather than drawing a line to show the solution’s surface, students should note that the particles drawn already provide this information.41 • White space. For readability, a fair amount of white space is introduced to most particulate diagrams. The molecules involved would in reality be in closer contact since these diagrams represent a condensed state of matter. The lack of appropriate intermolecular distances in particulate diagrams has been noted, especially for situations involving gases.49 Simulations using more appropriate distances can complement particulate diagrams.24 Additionally, the composition of the white space should be noted. Students may mistake white space in this diagram as “air” or “water” when, in this case, it truly is the absence of matter.2 For this specific case, some instructors may want to indicate the maleic acid dimers and oligomers as a refinement to the particulate representations presented.

temperatures, students should recognize that the same amount of total solute is present in each situation. The particulate diagrams help them recognize that only the proportion of dissolved solute to insoluble material has changed and that this is reflected macroscopically as precipitate height. Supernatant

The supernatant column of Figure 7 is the starting point for both NMR and evaporative analyses. It represents a visual depiction of concentration without relying on more abstract symbolic/mathematical concentration units such as molarity, mole fraction, or mass percent. When students use mathematical computations, their results can easily be related back to these diagrams since the change in solubility in this case roughly doubles from low temperature to high temperature. The shift from a heterogeneous mixture (the original saturated solution) to the homogeneous supernatant is an excellent opportunity for contrasting particulate depictions. Research has shown that students receiving particulate training for mixtures outperform peers who only learn about these concepts at the macroscopic level (example: homogeneous is the same throughout).45 Evaporation to Dryness

The removal of solvent from the supernatant by evaporation can be depicted by a model seen in the last column of Figure 7. Students watching the rapid change in mass on an analytical balance will note that something dramatic is happening. Appropriate questions for students to consider should be • “Where did the triangles go?” • “Why didn’t the squares go away, too?” • “What forces are at work?” The recovery of solid maleic acid serves to reinforce the reversible nature of dissolving and the fact that students have witnessed a physical change.38 For students who have never observed recrystallization firsthand, it may be surprising that the small repeating patterns of the solid depicted in particulate diagrams (Figure 7) can extend to create the crystalline structures such as those viewed under a microscope (Figure 5).

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FURTHER DISCUSSION While the focus of this paper involves using acetone as a solvent, maleic acid is even more soluble in water. On the other hand, maleic acid has low solubility in chloroform. A student fluent in converting between macroscopic and particulate representations should be able to construct models illustrating the attractive forces between molecules in these other systems to explain the differences in solubility. While maleic acid is highly soluble in both acetone and water, its geometric isomer fumaric acid has far lower solubility in each of these solvents. Saturated fumaric acid/acetone solutions at room temperature did not have enough fumaric acid to be

Limitations of Particulate Diagrams

Despite their utility, particulate models such as these can present difficulties in understanding. Simplifications and F



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while at the same time providing an introduction to basic NMR spectroscopy.

detectable using our NMR technique. The evaporative method produced a visible residue of fumaric acid from the solution that could be measured by mass subtractions. The lower solubility was more difficult for our mostly quick and qualitative approach to manage without a large increase in relative error. We found the solubility of fumaric acid to be 1.4 g/100 g ± 0.3 at room temperature (23 °C) over five trials which is still comparable to literature values of 1.17 g/100 g at 23.9 °C50 and 1.72 g/100 g at 30 °C.51 These values represent ratios of approximately 58 molecules acetone/1 molecule fumaric acid. When compared to the particulate diagram in Figure 7, this decrease in solubility represents “less than a single molecule” of fumaric acid present. The differences between solubility of maleic and fumaric acids in acetone provide a good opportunity for discussion of intermolecular attractions between solute and solvent. The use of Lewis structures to illustrate how these attractions differ provides another example of how we can use a particulate representation to make useful predictions about macroscopic properties. Since students are more often asked to consider ionic solutions at the particulate and symbolic level with dissociated salts, this example with a molecular solute may be unexpected. Common preconceptions or alternate conceptions documented about molecular dissolution include the following:15

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00965. Detailed calculations (PDF) Graphics presented in Figure 7 (ZIP) NMR spectrum for fumaric acid in acetone (PDF) NMR spectrum for maleic acid in water (PDF) NMR spectrum for maleic acid in chloroform (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

David W. Pollock: 0000-0001-7137-5908 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The 45 MHz picoSpin spectrometer used for data collection in this article was provided through a generous grant by Thermo Fisher Scientific. Initial training with the picoSpin was made possible by a Strategic Initiatives grant through the University of Wisconsin−Whitewater, Thermo Fisher Scientific, and the American Chemical Society Science Coaches Program. We also thank Kathleen Pollock for her contribution in obtaining digital microscopes through her grants from the Cedarburg Education Foundation and the ACS-Hach High School Chemistry Classroom Grant. We thank Kyle Langreck, Elliott Fairchild, and Will Langholz for lab testing and data collection. We also thank Nathaniel DeLano for technical support. Salt and Solubility screenshots were adapted with permission from PhET Interactive Simulations, University of Colorado Boulder, https://phet.colorado.edu.

• Molecules dissociate to individual neutral atoms • Molecules dissociate to ions • Molecules dissolve to form smaller subunits (example: disaccharides to monosaccharides) This work also showed that students more easily revised their working models of salt dissolution compared to sugar dissolution given appropriate experimental evidence. This discrepancy in understanding could be addressed using our system and its corresponding particulate model diagrams. The use of squares to represent maleic acid makes it less likely for students to exhibit some of these alternate conceptions even though they may still be held. It is suggested that instructors also emphasize molecular dissolution using more detailed models such as Lewis structures. Represented here is an attempt to connect chemical concepts from the lecture with laboratory work in order to build scientifically accepted conceptualizations of solubility. Additional work is required to determine if efforts to combine particulate and macroscopic techniques, such as those presented in this paper, result in better student understanding.

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REFERENCES

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CONCLUSION The work presented integrates symbolic, macroscopic, and particulate domains to foster a greater understanding of solutions and solubility. It especially focuses on temperature dependence of solubility, giving visual differences in precipitate “height” that can help students connect particulate processes with macroscopic observations. Traditional lab-type measurements using an analytical balance can present students with a familiar process on which to base their understanding of solubility while using more advanced technology, such as NMR spectroscopy. Students utilizing low-field NMR spectrometers can in this way catch a glimpse into modern lab techniques and begin to find their footing with more advanced instrumentation. This quickly run and easy-to-prepare system can be viewed as a means to relate the three domains of chemistry to solubility G



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Solubility from the Femtoscale to the Macroscale - ACS Publications

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