Hands-On Experiment To Verify Consistency from Bulk Density to

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

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Hands-On Experiment To Verify Consistency from Bulk Density to Atomic and Ionic Radii with Lumps of Metals and Ionic Compounds Seong Kyun Kim*,† and Seoung-Hey Paik*,‡ †

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School of Undergraduate Studies, College of Transdisciplinary Studies, Daegu Gyeongbuk Institute of Science and Technology, 333 Techno Jungang-daero, Hyeonpung-eup, Dalseong-gun, Daegu 42988, Republic of Korea ‡ Department of Chemistry Education, Korea National University of Education, 250 Taeseongtabyeon-ro, Gangnae-myeon, Heungdeok-gu, Chungju-si, Chungcheongbuk-do 28173, Republic of Korea S Supporting Information *

ABSTRACT: A hands-on experiment to obtain atomic and ionic radii with lumps of metal and ionic compounds is reported here. The experiment is performed with industrial-grade typical metals (iron, copper, aluminum, and lead) and single-crystal lumps of ionic compounds (sodium chloride, potassium chloride, and potassium bromide). Students measure the dimension of the given lumps with Vernier calipers and weigh them with a precision balance. After measuring the dimension and mass of the given lumps, students can calculate the atomic and ionic radius of each corresponding atom and ion with the obtained density values and information about the lattice structures. The obtained values of the metal atomic radii and the ionic radii of the ionic compounds are very close to the values in the literature. After this activity, the students came to appreciate that atomic radii, as typical submicroscopic and symbolic representations, are actually existing features and not an abstract concept. The experiment reported here is suitable for a first-year undergraduate general chemistry class as well as an introductory class at the high school level. KEYWORDS: First-Year Undergraduate/General, High School/Introductory Chemistry, Laboratory Instruction, Hands-On Learning/Manipulatives, Misconceptions/Discrepant Events, Atomic Properties/Structure, Ionic Bonding, Metals, Physical Properties, Solid State Chemistry, Solids

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INTRODUCTION There are many reports about the difficulty students have when attempting to learn chemistry.1−4 Mostly, the difficulty comes from misunderstandings of chemical concepts. Students who encounter basic-level chemistry first in high school or as an undergraduate face three levels of representation (symbolic, microscopic, and macroscopic).2 Because students cannot see microscopic representation, visualized submicroscopic representations, which are scientific models created by the overlap between the actual real microscopic world and symbolic representation, are introduced in chemistry education.3,5,6 Before students take chemistry as a subject, they have seen matter only at the macroscopic level, i.e., on the bulk scale, such as water, stone, and iron. They had few opportunities to understand submicroscopic and symbolic representations before entering chemistry class. They recognized matter with visually observable characteristics, such as the size, color, and phase. Although many chemical concepts are presented as symbolic representations to explain submicroscopic models, verifying macroscopic representations in connection with submicroscopic and symbolic levels is often omitted in chemistry classes (Figure 1). This is why students do not easily grasp that submicroscopic or symbolic representations are not abstract concepts, which would permit them a connection with related representations at the macroscopic level, i.e., in the real world. © XXXX American Chemical Society and Division of Chemical Education, Inc.

Figure 1. Three levels of chemical representations (links in the solid line are often omitted in chemistry classes).

The atomic radius is a typical example of this type of representation. It is a very important concept in chemistry, and it appears very frequently in chemistry textbooks not only in high school but also in undergraduate general chemistry classes.7−9 Although the concept of the atomic size is related to a number of other topics in textbooks, such as periodic trends and ionization energy levels,10 it is not easy for students to understand this concept properly, as they typically have not Received: November 22, 2018 Revised: June 3, 2019

A

DOI: 10.1021/acs.jchemed.8b00963 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

sufficient to be applied to this experiment. Cylindrical lump samples of iron, copper, aluminum, and lead are obtained by cutting 19−20 mm pieces of rods, widely used in industry and readily purchasable. Lump samples of ionic compounds (NaCl, KCl, KBr) are purchased from Ted Pella, Inc., as 10 × 10 × 10 mm3 cubic single crystals (Figure 2). Lumps of ionic

had the opportunity to encounter it before taking chemistry, and nobody can see an atom in the real world. Therefore, it can be an abstract concept to students who find it as submicroscopic and symbolic representation initially without connecting it to the real world.11 There are several reports about helping students to understand this concept.12−14 Theoretical calculations of atomic radii (symbolic)13 as well as the use of sports balls to compare atomic sizes (submicroscopic)14 can help students to understand the concept of “atomic radii”. However, these reports did not emphasize the relationship between the atomic radii (submicroscopic and symbolic) and the bulk properties (macroscopic). Here, a general chemistry experiment for first-year undergraduate students that focuses on understanding the relationship between macroscopic representation (the bulk density of materials) and submicroscopic and symbolic representation (atomic radii) is presented. In the experiment, students encounter familiar metal lumps consisting of iron, copper, aluminum, and lead. When measuring the volume and mass of each very familiar metal, students could determine the atomic radii from the unit cell information and compare the calculated radii with data from the literature. The calculation is likely familiar to chemists and chemistry instructors. It can be found in many textbooks, but these calculations are only theoretical activities. Such representations of atomic radii can remain abstract for students, even after solving these types of questions, because these calculations are connections only between symbolic representation and submicroscopic representation. In this regard, the experiment reported here focuses on a hands-on experience which helps students to associate submicroscopic and symbolic representations with macroscopic representations, as opposed to improving their calculation abilities per se. During this activity, students can associate the lattice structures and the atomic radii with visible lumps because the earlier density measuring activity endowed them with the recognition of the relationship between macroscopic representation and submicroscopic and symbolic representations. After the experiment, students come to understand that there is a direct relationship between macroscopic representation and symbolic and submicroscopic representation. This understanding is very important to students who are new to chemistry, and it can help to overcome the gaps between different levels of representations. As an advanced activity, students can calculate the ionic radii with lumps of ionic compounds. This experiment was developed for a first-year undergraduate/general chemistry laboratory course at Daegu Gyeongbuk Institute of Science and Technology (DGIST) over the past four years. A before and after survey study involving 69 freshmen in the most recent year was carried out to verify the educational effects of the experiment. The exercise is suitable for a 90 min lecture class as an activity and/or for a 2 h laboratory class with an adequate introduction and a clear understanding of the required concepts. The activity itself including the calculations requires about 40 min with metal lumps and 1 h with metals and ionic compounds.

Figure 2. Samples of lumps of metals and ionic compounds. Top: iron, copper, aluminum, and lead. Bottom: sodium chloride, potassium chloride, and potassium bromide, from left to right.

compounds also show high enough purity levels. The original use of these single-crystal ionic compounds is for growing epitaxial films. They are not expensive and are reusable, and they cost approximately $7−8 per crystal. The metal lumps should be stored in a moisture-free atmosphere for long-term storage to prevent surface oxidation. Samples of ionic compounds should be protected from moisture and water at all times. Handling with sufficient care is necessary for the ionic compound samples because they appear to be very similar to each other, making it nearly impossible to distinguish them on the basis of appearance. The other matter of concern is their fragile nature. Vernier calipers and precision balances are used to determine the density of the given lumps. The periodic table with atomic/ionic radii and pictures of the necessary crystal structures can be given to students.

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HAZARDS There is no need to use hazardous chemicals when conducting this experiment. The lumps of metals (iron, copper, aluminum, and lead) and ionic compounds (NaCl, KCl, KBr) are the only chemicals needed. Lead metal is a potential hazard when coming into contact with the skin directly, but this can be avoided with laboratory gloves. During the experiment, no chemical waste is produced.

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EXPERIMENTAL PROCEDURES

Stacking of Atoms and the Unit Cell

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Before starting the exercise, students should have enough knowledge about crystal lattice structures and unit cells. The stacking of atoms in a solid state and their lattice structures are essential preliminary knowledge students must have before studying atomic radii. There are various education models designed to impart this knowledge involving the use of

MATERIALS All metal lumps used for the experiment are industrial-grade products. Industrial grades of metal samples can be purchased easily, and their purity levels (typically 99.9−99.99%) are B




computer software,15,16 origami,17,18 paper and glue,19,20 plastic or magnet balls,21−25 and solid-state model kits.26 The instructor should discuss the following areas of knowledge with the students before the experiment class: types of possible crystal lattice structures (especially cubic structures, simple cubic, body-centered cubic, face-centered cubic), unit cells (the smallest repeating unit of a lattice structure), the n value (the number of atoms in a unit cell), and the CN (coordination number, number of neighboring atoms for any atom). At this time, 3D-model kits of the lattice structure can help students. After this discussion, students should be able to calculate the CN, and the Luc/R (Luc, length of a side of unit cell; R, atomic radii) ratio of each structure, as shown in Table 1 and Figure 3.

Figure 4. Measurement of the diameter of a cylindrical metal lump (iron).

Table 1. n Value, CN, and Luc/R Valuec of Crystal Lattice Structures na

CNb

Luc/Rc

Simple cubic (SC)

1

6

Body-centered cubic (BCC)

2

8

2 4 3 3

4

12

Crystal Lattice Structure

Face-centered cubic (FCC) a

2 2

b

Number of atoms in a unit cell. Number of neighboring atoms for any atom. cLuc: length of a side of a unit cell. R: atomic radii.

Volume, Mass, and Density Figure 5. Measurement of the mass of a metal lumps (copper and lead).

The volume of each lump sample can be obtained via measuring the diameter and height of a cylindrical lump with Vernier calipers (Figure 4). To minimize errors in these measurements, the measuring data are collected at least three times at different positions and the average values are used to calculate the volume. The mass of each lump is also determined with a precision balance (Figure 5). The density of the metal lump samples can easily be calculated with their volume and mass. Typical density data obtained in this manner is shown in Table 2. Students can compare their data with values reported in the literature. The calculated density values of the metal samples are very similar to those from the literature. The obtained density of iron is 7.847 g/cm3, not differing greatly from the literature value (7.870−7.876 g/cm3 at 20 °C).27 For copper, aluminum, and lead, values of 8.900, 2.710, and 11.12 g/cm3 are obtained, while the literature lists values of 8.96, 2.70, and 11.35 g/cm3 at 20 °C, respectively.28,29

Table 2. Calculation of Density of Metal Lumps

a

Metal Sample

Volume (mm3)

Mass (g)

Densitya (g/cm3)

Densityb (g/cm3)

Iron Copper Aluminum Lead

6195 6157 6221 5569

48.6165 54.7956 16.8560 61.9121

7.847 8.900 2.710 11.12

7.87 8.96 2.70 11.35

Experimentally obtained values. bValues in literature at 20 °C.

Atomic Radii

To calculate the atomic radii of the metals, information about the lattice structure of each metal and the atomic mass should be provided to the students. The lattice structure of iron is body-centered cubic (BCC), and copper, aluminum, and lead

Figure 3. Luc/R values of crystal lattice structures (simple cubic, body-centered cubic, and face-centered cubic, left to right). C




Table 3. Calculation of Atomic Radii of Metals Lattice Structure

nuca

Atomic Mass (g/mol)

Vucb (×10−29 m3)

Lucc (×10−10 m)

Luc/Rd

Rd (×10−10 m)

Iron

BCC

2

55.85

2.364

2.87

4 3 3

1.24

Copper

FCC

4

63.55

4.743

3.62

2 2

1.28

Aluminum

FCC

4

6.613

4.04

2 2

1.43

Lead

FCC

4

4.98

2 2

1.76

Metal

a

b

26.98 207.2

12.38

c

d

Number of atoms in a unit cell. Volume of unit cell. Length of a side of a unit cell. R: atomic radii.

Figure 6. Unit cell of the lattice of a rock-salt structure and the ratio of the side length of a unit cell to the ionic radii.

show a face-centered cubic structure (FCC) at room temperature.28,30 The volume of a unit cell (i.e., Vuc) is calculated using the following data and equations. When the atomic mass is multiplied by the number of atoms in a unit cell and divided by Avogadro’s number, the mass of a unit cell (i.e., wuc) is obtained. Students can calculate Vuc of each metal with their experimentally obtained density and the mass of a unit cell. • d: density of metal (experimentally obtained value) • nuc: number of atoms in a unit cell (calculated by students) • Vuc: the volume of a unit cell (calculated by students) • Luc: the length of the side of a unit cell (calculated by students) • wuc: the mass of a unit cell (calculated by students) • R: the atomic radius (calculated by students) • aw: atomic mass (given information) • fw: formula mass (given information) • NA: Avogadro’s number (given information, 6.022 × 1023) wuc =

n uc × aw NA

(1)

Vuc =

wuc n × aw = uc d NA × d

(2)

n uc × aw

3 3 V NA × d Luc uc R= = = (Luc /R ) (Luc /R ) (Luc /R )

For iron, which has a BCC structure at room temperature, an example of the calculation is as follows. The mass of a unit cell is calculated with the atomic mass of iron (55.847 g/mol), the number of atoms in a body-centered cubic unit cell (nuc = 2), and Avogadro’s number (NA = 6.022 × 1023). This gives a value of 1.855 × 10−22 g. After dividing this value by the density of iron, the obtained volume of the unit cell is 2.364 × 10−29 m3. The cube root of the volume of the unit cell gives the length of a side of a unit cell as 2.87 × 10−10 m, and the final calculated atomic radius of iron is 1.24 × 10−10 m. This value is nearly identical to the value from the literature (1.26 × 10−10 m).28,31 The atomic radii of other metals are also obtained with a similar calculation, as shown in Table 3. For copper and aluminum, the obtained values of the atomic radii are identical to the data from the literature (1.28 × 10−10 and 1.43 × 10−10 m, respectively),28,31 and the value of lead (1.76 × 10−10 m) is very similar to the literature value (1.75 × 10−10 m).32 Advance Activity with Ionic Compounds

As an advance activity, students can calculate ionic radii with several ionic compounds, such as sodium chloride, potassium chloride, and potassium bromide. These compounds are selected because they all have a rock-salt structure. In a rocksalt structure, the length of a side of a unit cell is double the sum of the ionic radii of the cation and anion, as shown in Figure 6.

The length of a side of a unit cell (i.e., Luc) is the cube root of the volume of the unit cell. The atomic radius of each metal (R) can be calculated using the Luc value and the Luc/R ratio of each lattice structure. Luc =

3

Vuc

(4)

Luc = 2(R+ + R−)

(5)

Unfortunately, a single crystal of sodium bromide was not available. Therefore, the instructor provided the density value

(3) D




2(R Na+ + R Cl−) = 5.64 × 10−10 m

of sodium bromide. When the compound is available, this activity will be more interesting and meaningful. The volume of each ionic compound lump sample is collected by measuring the length of each side of the cuboid. The data are also collected three times at different positions, and the average values are used. When measuring, students should wear laboratory gloves because ionic compounds are sensitive to moisture. The hardness of the crystal is low, and it can be broken if it comes into contact severely with the metal jaws of Vernier calipers. Thus, the crystals should be handled with care during the measurement process. The calculated density values (d) of the compounds are very similar to those from the literature. The obtained density values for NaCl, KCl, and KBr are 2.169, 1.997, and 2.717 g/ cm3, respectively. Reported literature values are 2.17,33 1.98,34 and 2.7435 g/cm3. The literature density value of NaBr, 3.21 g/ cm3, is provided to the students.36 (Table 4)

2(R K+ + R Cl−) = 6.28 × 10−10 m 2(R K+ + R Br−) = 6.63 × 10−10 m 2(R Na+ + R Br−) = 5.97 × 10−10 m

Students can obtain the radii of the other ions with simple calculations. The obtained values of the ionic radii are very similar to those from the literature, as shown in Table 6.37 Table 6. Experimentally Obtained Ionic Radii Ion

Volume (mm3)

Mass (g)

Densitya (g/cm3)

Densityb (g/cm3)

NaCl KCl KBr NaBr

1107 1190 1258

2.4013 2.3766 3.4177

2.169 1.997 2.717

2.17 1.98 2.74 3.21

a

The lattice structure of all four compounds is a rock-salt structure, and there are four cation−anion pairs (nuc = 4) in a unit cell. The volume of a unit cell (Vuc) and the length of the side of a unit cell (Luc) for each compound can be calculated similarly to the metal cases using the following equation. Vuc =

3

n uc × fw NA × d

1.02 1.38 1.81 1.96

1.98

Literature value is used for calculation.

EVALUATION OF THE EXPERIMENT Prelab and postlab questionnaires and assessments of the comprehension of related concepts for the 2019 freshman class at Daegu Gyeongbuk Institute of Science and Technology were used to verify the educational effects of this experiment. Of the students, 26% graduated from science high schools (or high schools for the gifted), while the others graduated from regular high schools. The Supporting Information includes the full questionnaire sets, the assessment questions about the comprehension of the concepts, and tables of the resulting data. The prelab questionnaire shows that there is a significant difference in the levels of preliminary knowledge between the two groups. Most of the students who graduated from science high schools gained theoretical knowledge of concepts related to those here, and 50% of them reported that they could remember how to calculate the atomic radius of a given metal from the density value and the lattice structure. However, only 5.9% of the students who graduated from regular high schools reported that they knew the calculation method. There are also statistically significant differences, at 33.3% and 2.0%, between the ratios of students having experiences similar to the experiments here between two groups. This significant difference between the two groups was clearly eliminated after the experiment was performed. More than 90% of the students in both groups reported that they could remember how to calculate the atomic radius from the density value and the lattice structure. Before and after assessments of the comprehension of related concepts also showed similar results. All students answered a 10 question assessment quiz before and after the experiment. The average score of each student group is shown in Figure 7. This result

Experimentally obtained values. bValues in literature at 20 °C.

3

1.01 1.33

■

a

Luc =

Literature Value (10−10m)

Na K+ Cl−a Br−

Table 4. Calculation of Density of Ionic Compound Lumps Ionic Compound Sample

Calculated Value (10−10m)

+

(6)

For sodium chloride, an example of the calculation is given below. The mass of a unit cell is calculated as 3.882 × 10−22 g with the formula mass (58.44 g/mol), nuc, and Avogadro’s number. After dividing this value by the experimentally obtained density (d), the calculated volume of the unit cell is found to be 1.790 × 10−28 m3. The cube root of the volume of the unit cell provides the length of the side of a unit cell (Luc), which is 5.64 × 10−10 m. In the same manner, the Luc values of the other compounds are calculated. These values are 6.28 × 10−10, 6.63 × 10−10, and 5.97 × 10−10 m for KCl, KBr, and NaBr, respectively (Table 5). After the calculation, the equations shown below were obtained. However, the ionic radii of four ions cannot be obtained with these equations. Hence, the instructor should provide the value of one ion, such as RCl− = 1.81 × 10−10 m.37 Table 5. Calculation of the Length of One Side of a Unit Cell Compound

nuca

Formula Mass (g/mol)

wucb (10−22 g)

Density (g/cm3)

Vucc (10−28 m3)

Lucd (10−10 m)

NaCl KCl KBr NaBr

4 4 4 4

58.44 74.55 119.0 102.9

3.882 4.952 7.904 6.835

2.169 1.997 2.717 3.21e

1.790 2.480 2.909 2.13

5.64 6.28 6.63 5.97

a

Number of ion pair in a unit cell. bMass of a unit cell. cVolume of unit cell. dLength of a side of a unit cell. eLiterature value. E




Figure 8. Change in the ratio of students who did not appreciate the relationship between the microscopic world and the real world by student groups.

Figure 7. Comparison of the average scores on the prelab and postlab assessments by student groups.

reflected students’ comprehension of related concepts. The average scores of two groups on the prelab assessment were 6.50 and 4.98 (out of 10), but the scores rose to 8.06 and 7.98 on the postlab assessment, and the difference vanished. Narrowing gaps among students, which arise due to the differences in the amounts of prerequisite learning, is important in first-year general chemistry classes, and this result shows that hands-on experience can help to achieve this goal. Before the experiment, about 40% of the students answered that they expected that the experimentally obtained atomic radii value would not be similar to the value in the literature because the microscopic world is not the real world. After the experiment, the ratio of students who thought so decreased to 2.9%, and most students appreciated the direct relationship between macroscopic density and microscopic atomic radii with confirmation that their obtained values are very similar to the values in the literature. There is no statistical difference among student groups. This definite change in their comprehension of the relationship between the macroscopic (bulk density) and microscopic (atomic radii) representations is the important pedagogical effect of this hands-on experiment (Figure 8). Figure 9 shows the ratio of students who realized the actual existence of the atomic radius and the lattice structure before and after the experiment. Approximately 50% of the students reported that the atomic radius and the lattice structure are simply theoretical explanations, and the ratio of students who thought that they do exist in practice was less than 40% according to the prelab questionnaire, irrespective of the high school from which they graduated. After the experiment, the ratio of students on the side of practical existence showed a significant increase, with this change being more significant in the group of students from regular high schools. This remarkable change strongly supports the contention that this experiment is an effective method for students, who have taken basic-level chemistry, to understand the representations of the atomic radius and the lattice structure properly. Interestingly, only 55.5% of students who graduated from science high schools agreed that the atomic radius and the lattice structure do exist in practice, even after the experiment.

Figure 9. Change in the ratio of students who realized that the atomic radius and the lattice structure actually exist in practice by student groups.

This tendency likely stems from obstinacy caused by intensive prerequisite education weighted toward theory without practical experiences from their science high schools (and high schools for gifted). This will be investigated in an upcoming study.

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CONCLUSION A protocol for performing a hands-on experiment to verify the consistency from macroscopic density to atomic and ionic radii with lumps of metals and ionic compounds has been described here. Through this experiment, students can gain significant realization of the existence of atomic radii and lattice structures and grasp the importance of understanding the relationship between macroscopic representation and submicroscopic and symbolic representations. After the experiment, students appeared to be able to understand that the representation of the atomic radii is an actually existing feature of elements and not an abstract F




(7) Zumdahl, S. S.; Zumdahl, S. A. Chemistry, 8th ed.; Brooks/Cole, Cengage Learning: Belmont, CA, 2010; pp 322−323, 325, 445−454, 909−910, 937. (8) McMurry, J. E.; Fay, R. C. General Chemistry, 2nd ed.; Pearson: Upper Saddle River, NJ, 2014; pp 88−90, 377−383. (9) Oxtoby, D. W.; Gillis, H. P.; Campion, A. Principle of Modern Chemistry, 7th ed.; Cengage Learning: Mason, OH, 2011; pp 224− 225. (10) Eymur, G.; Ç etin, P.; Geban, Ö . Analysis of the Alternative Conceptions of Preservice Teachers and High School Students Concerning Atomic Size. J. Chem. Educ. 2013, 90 (8), 976−980. (11) Osborne, R. J.; Cosgrove, M. M. Children’s conceptions of the changes of state of water. J. Res. Sci. Teach. 1983, 20 (9), 825−838. (12) Campbell, J. A. Atomic Size and the Periodic Table. J. Chem. Educ. 1946, 23 (11), 525−529. (13) Ping, M.; Xiubin, L.; Yuankai, W. A Formula for Calculating Atomic Radii of Metals. J. Chem. Educ. 1990, 67 (3), 218−219. (14) Pinto, G. Using Balls from Different Sports To Model the Variation of Atomic Sizes. J. Chem. Educ. 1998, 75 (6), 725−726. (15) Robinson, W. R. A Window on the Solid-State. J. Chem. Educ. 1994, 71 (4), 300. (16) Robinson, W. R.; Tejchma, J. F. A Window on the Solid State: Part I: Structures of Metals; Part II: Unit Cells of Metals; Part III: Structures of Ionic Solids; Part IV: Unit Cells of Ionic Solids. J. Chem. Educ. 1997, 74 (9), 1143−1144. (17) Yamana, S. An easily constructed model of a coordination polyhedron that represents the hexagonal closest packed structure. J. Chem. Educ. 1987, 64 (12), 1033−1034. (18) Yamana, S. An easily constructed model of a coordination polyhedron that represents the cubic closest packed structure. J. Chem. Educ. 1987, 64 (12), 1040. (19) Birk, J. P.; Yezierski, E. J. Paper-and-Glue Unit Cell Models. J. Chem. Educ. 2003, 80 (2), 157−159. (20) Sein, L. T., Jr.; Sein, S. E. Lattice Entertain You: Paper Modeling of the 14 Bravais Lattices on YouTube. J. Chem. Educ. 2015, 92 (8), 1419−1421. (21) Birk, J. P.; Coffman, P. R. Finding the face-centered cube in the cubic closest packed structure. J. Chem. Educ. 1992, 69 (12), 953− 954. (22) Mattson, B. Cubic Unit Cell Construction Kit. J. Chem. Educ. 2000, 77 (5), 622−623. (23) Ohashi, A. Using Latex Balls and Acrylic Resin Plates To Investigate the Stacking Arrangement and Packing Efficiency of Metal Crystals. J. Chem. Educ. 2015, 92 (3), 512−516. (24) Elsworth, C.; Li, B. T. Y.; Ten, A. Constructing Cost-Effective Crystal Structures with Table Tennis Balls and Tape That Allows Students To Assemble and Model Multiple Unit Cells. J. Chem. Educ. 2017, 94 (7), 827−828. (25) Collins, D. C. A Unit Cell Laboratory Experiment: Marbles, Magnets, and Stacking Arrangements. J. Chem. Educ. 2011, 88 (9), 1318−1322. (26) Sunderland, D. P. Studying Crystal Structures through the Use of Solid-State Model Kits. J. Chem. Educ. 2014, 91 (3), 432−436. (27) Cleaves, H. E.; Hiegel, J. M. Properties of High-Purity Iron. J. Res. Natl. Bur. Stand. 1942, 28 (5), 643−667. (28) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd ed.; Butterworth-Heinemann: Oxford, 1997; pp 1074, 1176, 222. (29) Densities of the Elements (data page). Wikipedia; https://en. wikipedia.org/wiki/Densities_of_the_elements_(data_page) (accessed June 2019). (30) Periodic Table; http://periodictable.com/ (accessed June 2019). (31) Atomic Radii of the Elements (data page). Wikipedia;https:// en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page) (accessed June 2019). (32) Lead. Wikipedia; https://en.wikipedia.org/wiki/Lead (accessed June 2019).

concept. The experimental data when very close to the literature values took students by surprise. They could determine the atomic and ionic radii by themselves and could see the direct connection with the bulk density. Through this hands-on process, students appreciate what microscopic representations are in chemistry and gain a viewpoint from which to see chemical concepts properly when they encounter them for the first time. Also, a significant improvement in the understanding of related concepts was observed after the experiment. This distinct improvement in the realization of related concepts is the major educational result of the handson experience of investigating the direct relationship between submicroscopic and symbolic representations (atomic radii and lattice structures) and macroscopic representation (bulk density), as proposed here.

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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.8b00963.

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Notes for instructors, editable experiment note for students, representative results from student groups, prelab and postlab questionnaires, prelab and postlab assessment sets, tables of the resulting data on the questionnaires (PDF, DOCX)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Seong Kyun Kim: 0000-0001-7233-9204 Seoung-Hey Paik: 0000-0002-0393-4533 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the DGIST Education Innovation Grant. The author would like to express gratitude to the instructors and students who participated in the experiment in the four years prior to this publication.

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Hands-On Experiment To Verify Consistency from Bulk Density to

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