# Improving the Understanding of Chemistry by Using the Right Words: Transforming Inorganic Formulas for Insight into Chemical Structure

Miguel Reina, Bruno Landeros-Rivera, Jesús Gracia Mora, Hervé This, Vo Kientza, Antonio Reina

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Miguel Reina, Bruno Landeros-Rivera, Jesús Gracia Mora, Hervé This, Vo Kientza, Antonio Reina. Improving the Understanding of Chemistry by Using the Right Words: Transforming Inorganic Formulas for Insight into Chemical Structure. Journal of Chemical Education, 2025, 10.1021/acs.jchemed.5c00074. [PDF] [ DOI ]

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# Improving the Understanding of Chemistry by Using the Right Words: Transforming Inorganic Formulas for Insight into Chemical Structure

Miguel Reina,* Bruno Landeros-Rivera,* Jesús Gracia Mora,* Hervé This,* and Antonio Reina*

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Cite This: https://doi.org/10.1021/acs.jchemed.5c00074

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Supporting Information

**ABSTRACT:** In this study, we present a novel method for writing chemical formulas to address common misconceptions in chemistry education. Building on our previous work, where we defined molecules and reticulums based on the number of chemical bonds, we introduce the term "layered structure" to describe chemical species with a conceptually infinite number of chemical bonds in a two-dimensional network. These definitions help distinguish among chemical species and the entities that compose them. We highlight chemical formulas do not convey structural information and that using them without providing such information can hinder student understanding. To resolve this, we propose a new notation system that differentiates the structure of chemical substances while retaining detailed compositional information: we suggest using slashes (//) to denote layered structures and curly brackets ({}; to represent reticulums, distinguishing them from molecular substances. This proposal was tested with professors and undergraduate students at Facultad de Química, UNAM. Our findings suggest that this new notation system clarifies the structural differences between various chemical entities and species and enhances the understanding of chemical composition and bonding in educational settings. By making these distinctions explicit, students and educators can more accurately interpret chemical formulas and their structures. This approach has the potential to improve chemistry education by addressing key conceptual misunderstandings. We are preparing a second part to further explore the scope and limitations of our proposal.

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**KEYWORDS:** General Public, Chemical Education Research, Inorganic Chemistry, Communication/Writing, Textbooks/Reference Books, Descriptive Chemistry, Periodicity/Periodic Table

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## INTRODUCTION

In our previous works we had revisited topics taken for granted and discussed them from a historical comparative perspective, but most importantly, proposed solutions to existing problems. We have stressed the importance of precision in naming what we truly intend to describe, a task that upon closer examination is anything but trivial.¹⁻⁴ Through this scrutiny, we have reexamined the meanings and concepts of elements and atoms. In our exploration, we have introduced two new definitions based on the structural aspects of chemical systems. We redefined the term "molecule" as a stable and electrically neutral chemical entity with a finite number of chemical bonds (0 to *n*, with *n* a finite integer number) and introduced the term "reticulum" as a stable and electrically neutral chemical species with a conceptually infinite number of chemical bonds connecting all the chemical entities within the structure while also attempting to disambiguate the concept of a compound (category of chemical species or entities).¹,⁴

From this discussion, an interest arises in distinguishing between three-dimensional lattices and two-dimensional layered structures. Some materials exist as two-dimensional structures that interact through van der Waals forces to bind the layers together. These layers may be one atom thick, as in graphite, or several atoms thick, as in birnessite (δ-MnO₂).⁵,⁶ The main difference between a layered structure and a reticulum lies in the

dimensional extent of the bonding interactions (Figure 1). While a layered structure exists in two dimensions (plane or quasi-plane extended structures) with weak interactions between the layers, a reticulum has no independent layered structure but rather a three-dimensional structure and all entities are connected within the structure by chemical bonds. We suggest, employing the term "layered structure", defined as a stable and electrically neutral chemical species with a conceptually infinite number of chemical bonds in a two-dimensional network. In a layered structure, each two-dimensional structure interacts with its neighbor(s) through weak intermolecular interactions, but no chemical bonds are formed between the sheets. For example, graphite has a layered structure, a two-dimensional plane structure with a conceptually infinite number of bonds, whereas NaCl has a three-dimensional structure with a conceptually infinite number of bonds. Graphite

Received: January 16, 2025

Revised: May 14, 2025

Accepted: May 27, 2025

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<figure><img src="image_12.png" /><figcaption>**Figure 1.** Difference between molecules such as CO₂, layered substances such as graphite, and reticulums like NaCl.</figcaption></figure>

is then a layered structured substance, whereas sodium chloride is a reticulum.

It is important to note that a layered structure, as the chemical object we defined, suggests the presence of multilayers, with several layers interacting by weak intermolecular forces; however, this definition also includes monolayers, where a single layer maintains the characteristic structural organization. In fact, known materials with a single layer are scarce. One example of these materials is graphene, which has a flat two-dimensional monolayered carbon atom structure.⁷ Graphene can serve as a building material for buckminsterfullerene (C₆₀), carbon nanotubes (CNTs), and carbon graphite. Moreover, materials with mono-, bi-, and oligo-layer (3–10 layers) 2D carbon atom structures are considered as types of graphene, while materials with multilayers are considered graphite.⁸ In our definition, both graphene and graphite can be considered “layered structures”.

This manuscript introduces a simple yet innovative method for writing the chemical formulas of inorganic compounds. This approach enables us, at a symbolic level, to clarify whether a given entity is a molecule, a layered structure, or a reticulum. The proposal has proven highly beneficial for the teachers and students who have engaged with it, as will be demonstrated in the subsequent discussion (see section *Activities with students and teachers*).

■ THE RELATIONSHIP BETWEEN CHEMICAL FORMULAS AND STRUCTURES FOR INORGANIC COMPOUNDS

Let us examine three systems that seem simple but are not at all, and that call into question the extent of chemical formulas. These three systems are boron trichloride, aluminum trichloride, and gallium trichloride, BCl₃, AlCl₃, and GaCl₃, respectively. It can be observed, that chemical formulas refer to macroscopic chemical species, but also to submicroscopic chemical entities. Written as they appear, one might be tempted to think that all three systems are molecular, that the atom of the group 13 is the central atom, and that for each valence electron of B, Al, and Ga,

there is a chlorine atom bonded. Indeed, we have observed that students tend to assume molecularity before considering reticular or layered structures. In Figure 2, what one would probably draw *a priori* as a Lewis structure is presented.

<figure><img src="image_13.png" /><figcaption>**Figure 2.** Lewis structures of BCl₃, AlCl₃, and GaCl₃.</figcaption></figure>

Although these Lewis structures are valid from a fundamental standpoint, a slightly deeper examination of the systems indicates that they do not match reality. At room temperature, boron trichloride, BCl₃, is a gas consisting of planar trigonal molecules in which the boron atom is bonded to three chlorine atoms.⁹,¹⁰ In this case, the Lewis structure that can be drawn from the chemical formula is correct. Aluminum trichloride, AlCl₃, is a white solid. In the solid state, aluminum trichloride has a layered structure. In this arrangement, the system has an octahedral geometry, meaning that each aluminum atom is surrounded by 6 chlorine atoms. In the unit cell, there are 12 chlorine atoms and 4 aluminum atoms (Figure 3), so the reduced atom ratio is effectively Al:Cl = 1:3, resulting in AlCl₃.¹¹,¹² It is clear that the structure of AlCl₃ cannot be deduced from the chemical formula alone, without computational or other tools. Lastly, gallium trichloride, GaCl₃, is a colorless deliquescent solid consisting of dimers, molecules with the chemical formula Ga₂Cl₆.¹³,¹⁴ In this case, each gallium atom is bonded to four chlorine atoms. Two chlorine atoms form a bridge between the two gallium atoms. Again, although the composition ratio remains Ga:Cl = 1:3, if only the chemical formula is known, it is impossible to deduce that it is a dimer. In two of the three cases studied, the chemical formula is an oversimplification of the actual structure. In terms of the balance between information and abstraction, we now clarify that the chemical formulas of AlCl₃ and GaCl₃ are incomplete. Figure 3 shows the correct structures of the three systems.

Let us now focus on aluminum trichloride, AlCl₃. The structure of aluminum trichloride varies with temperature and
<figure><img src="image_14.png" /><figcaption>**Figure 3.** Actual structures of BCl₃, AlCl₃, and Ga₂Cl₆ (see Figures S1–S3). We recommend that readers refer to ref 12, which contains an interactive crystal structure that clearly illustrates the layered structure of AlCl₃.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 4.** {NaCl}, {CaF₂}, {TiO₂} and {C} structures. The curly brackets clearly indicate that these chemical systems are reticulums. (See Figures S4–S8.)</figcaption></figure>

its aggregation state. In the solid state, aluminum trichloride has a layered structure, as explained above, but in gas phases at low temperatures, aluminum trichloride, AlCl₃, behaves as a dimer, where for every two aluminum atoms there are six chlorine atoms, just like gallium trichloride, and should be written Al₂Cl₆.¹⁵⁻¹⁸ Again, the atom ratio is respected and is in line with the chemical formula, without the chemical formula assertively communicating the structural nature of the system. Finally, in gas phase at high temperatures, aluminum trichloride, AlCl₃, dissociates into a monomeric structure analogous to BCl₃, with the same atom ratio as in the previous analysis. In all three cases, the atom ratio is the same and corresponds to the chemical formula; however, in no case could the structure of the system be predicted. If one relies solely on the chemical formula, it is not possible to predict the structure. How can we ensure that our students, colleagues, or general public audience understand what type of system we are talking about? There are two ways to solve the problem; the first is by searching the system's structure, and the second is by knowing *a priori* that aluminum trichloride could have all those possibilities. Next, we introduce our proposal to solve this issue.

■ A POSSIBLE SOLUTION TO THE PROBLEM OF THE RELATIONSHIP BETWEEN THE CHEMICAL FORMULA AND STRUCTURE

The proposed solution allows for the differentiation of molecules, layered structures, and reticulums. We propose writing layered structures in slashes (//), and reticulums in curly brackets ({{}) to clearly differentiate them from substances made of molecules. This notation was chosen to avoid confusion with the parentheses or square brackets used for polymers. For

example, in the case of boron, aluminum, and gallium trichlorides, the notation we propose would be BCl₃ for boron trichloride because it is a molecule, /AlCl₃/ for aluminum trichloride because it is a layered structure. For gallium trichloride, which is a dimeric molecule, we propose the following chemical formula: Ga₂Cl₆. In reality, there is no reason not to use the molecular formula rather than the empirical formula for a chemical entity. The use of slashes and curly brackets to denote layered structures and reticulums, respectively, is particularly simple and allows for quick differentiation between a discrete system, that is, an entity, and those that are constituted by the conceptually infinite repetition of entities. In our previous work, we have demonstrated that students can overcome documented misconceptions, such as the belief that sodium chloride is made of molecules, and can correctly distinguish between molecules and reticulums when the chemical structures of systems are shown.¹⁻⁴ Now, with this new chemical formula writing, showing the structures could no longer be necessary, though we still strongly recommend it. Thus, common sodium chloride, usually written as NaCl and therefore impossible to differentiate whether it is a molecule or a reticulum, would be written as {NaCl}, or the lattices of calcium fluoride and titanium oxide, which are normally written as CaF₂ and TiO₂, respectively, would be written with this system as {CaF₂} and {TiO₂}, respectively.¹⁹⁻²¹

Interesting examples are allotropes, which consist solely of atoms from the same element. For example, in carbon diamond, each carbon atom is bonded to four others, forming a tetrahedron in the reticulum. For this case, we propose the following notation: {C}, where the curly brackets indicate that it
is a reticulum.²² Graphite, on the other hand, is a layered structure composed only of carbon atoms. In this case, the proposed notation would be C/C (Figure 1).²³ In Figure 4, the previously discussed structures and new chemical formulas are presented.

In summary, we propose different notations to refer to different things:

* Molecules such as water are noted H₂O.

* Dimers like gallium trichloride are noted Ga₂Cl₆.

* Layered structures such as aluminum trichloride and carbon graphite are noted/AlCl₃/ and/C/, respectively.

* Reticulums such as diamond are noted {C}.

This notation proposal, as discussed with students and educators (see section below), has sparked interesting questions and discussions. Further information can be extracted from the formula if some precision is made. As a result, we are preparing a contribution focusing on the addition of coordination numbers to these formulas.²⁴ This will provide deeper structural insights into layered structures and reticulums. We will show how this notation has impacts in solid state chemistry for both metallic lattices and ionic solids. We will explore the historical approaches to classifying binary crystal structures and demonstrate how our proposal can be used to determine the crystalline structures of reticulums, both mono- and poly-elemental, from the new formula. Furthermore, we discuss the limitations of this model compared to existing models.

## ACTIVITIES WITH STUDENTS AND TEACHERS

The activities conducted with the students were identical to those performed with the professors. A preliminary questionnaire was administered (Figure 5), followed by a presentation of

1. How true is the following statement?
   "From a chemical formula, one can always determine the structure of the system."

Always
Never
Almost always
Almost never

2. Identify if the following systems are molecules (M), reticulums (R), or layered structures (L) based on the images.

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3. Identify if the following systems are molecules (M), dimers (D), reticulums (R), or layered structures (L) based on the chemical formulas.

<table><thead><tr><th>Pre-test</th><th>NaCl</th><th>GaCl<sub>3</sub></th><th>AlCl<sub>3</sub></th><th>SiI<sub>4</sub></th><th>TiO<sub>2</sub></th></tr></thead><tbody><tr><td></td><td>AuF<sub>5</sub></td><td>CdI<sub>2</sub></td><td>SiS<sub>2</sub></td><td>CuF<sub>2</sub></td><td></td></tr></tbody></table>

<table><thead><tr><th>Post-test</th><th>{NaCl}</th><th>Ga<sub>2</sub>Cl<sub>6</sub></th><th>/AlCl<sub>3</sub>/</th><th>SiI<sub>4</sub></th><th>{TiO<sub>2</sub>}</th></tr></thead><tbody><tr><td></td><td>Au<sub>2</sub>F<sub>10</sub></td><td>/CdI<sub>2</sub>/</td><td>/SiS<sub>2</sub>/</td><td>{CuF<sub>2</sub>}</td><td></td></tr></tbody></table>

Students, n = 276 Professors, n = 18

<caption>Figure 5. Pre- and post-test activities with students and teachers.</caption>

the main ideas. The forty-minute presentation emphasized the points discussed in this manuscript: the difficulty of understanding the structure from a chemical formula, and the introduction of our proposed formula notation, as illustrated in the examples here. Afterward, a 10-to-15 min discussion was held with both students and professors to gather their doubts and comments. A second questionnaire was administered to both groups (Figure 5). The questionnaires were identical,

except for the use of our proposed formula notation in the post-test. Below, we present both the questionnaires and the results obtained.

The 276 students participating in the activity were mainly first- and third-semester students (89%) from one of six majors (Chemistry, Chemical Engineering, Biological Pharmaceutical Chemistry, Food Chemistry, Metallurgical Chemical Engineering, and Chemistry and Materials Engineering) at the Facultad de Química, UNAM. Among them, 46% were female, and 93% were younger than 21 years old. The 18 professors were from the Inorganic and Nuclear Chemistry Department at the same institution and were currently teaching General Chemistry I, General Chemistry II, and/or Inorganic Chemistry I. All data related to these groups are available in the Supporting Information.

When we asked students and professors about the relationship between chemical formulas and structure, the most common response for both groups was, "Almost always" (Figure 6). This response indicates that both students and educators have a preconceived notion that chemical formulas should be related to the structure of chemical systems. From our perspective, this suggests that as chemists, we are familiar with certain structures and have already associated them with their corresponding chemical formulas. However, this knowledge is largely empirical and based on experience, as demonstrated by the results from question 3, where neither students nor professors could accurately determine the structure from the chemical formula. This contrasts sharply with the results of the second question, in which both groups correctly identified whether a system is a molecule, layered structure, or reticulum when analyzing its structure, which corroborates the importance of showing the structures.

The results of the questionnaire after introducing slashes and curly brackets in the chemical formulas were unequivocal. In the post-test, the most frequent answer to the question, "From a chemical formula, one can always determine the structure of the system.", was "Never". Both groups revised their preconceived notions about the utility of chemical formulas in predicting the structure of chemical systems. The distinction between molecules, layered structures, and reticulums based on structural analysis became even clearer, a topic that had already been explored in depth in previous studies.¹⁻⁴ The structural representation allows both teachers and students to easily determine whether a chemical system is molecular or a reticulum and to identify layered structures more effectively. The results are even more pronounced in the final question, in which the participants were asked to identify the nature of a chemical structure based on its chemical formula. The average score for students increased from 1.86 to 8.72 out of 9, while for teachers, it rose from 2.7 to 8.3. The significant increase in both groups indicates that this new formulation helps clearly distinguish between chemical systems with different structures and overcomes common misconceptions, such as the belief that sodium chloride is a molecule. These results suggest that this approach can be effectively employed by teachers at the undergraduate level. We believe these formulas can be introduced from the first exposure to chemistry (usually in middle school) to the early years of university-level education.

Data collection from all participants (students and teachers) followed an ethical consent procedure. All agreed to share personal academic information, while the authors of this article committed to using this data solely for its intended purpose—specifically, the evaluations and opinions presented here.
Students

<figure><img src="image_17.png" /><figcaption>Q2: Identify if the following systems are molecules (M), reticulums (R), or layered structures (L) based on the images.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Q3: Identify if the following systems are molecules (M), dimers (D), reticulums (R), or layered structures (L) based on the chemical formulas.</figcaption></figure>

<figure><img src="image_19.png" /></figure>

Professors

<figure><img src="image_20.png" /><figcaption>Q2: Identify if the following systems are molecules (M), reticulums (R), or layered structures (L) based on the images.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Q3: Identify if the following systems are molecules (M), dimers (D), reticulums (R), or layered structures (L) based on the chemical formulas.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 6.** Results of the pre- and post-test activities with students and teachers.</figcaption></figure>

## CONCLUSIONS

In summary, we have demonstrated that a new method for writing chemical formulas can address common misconceptions encountered in the chemistry classroom. Building on our previous work, where we defined the terms *molecule* and *reticulum* based on the number of chemical bonds, we introduced the term *layered structure* to describe chemical species with a conceptually infinite number of chemical bonds in a two-dimensional network. These definitions allow for a clear distinction between chemical entities and chemical species. However, we have consistently observed, and proved that students and educators find it challenging to distinguish between them solely by reading the substance's chemical formula. In fact, chemical formulas provide clear information about a substance's composition but not its chemical structure.

To address this issue, we propose a novel notation that clearly differentiates the structure of any chemical substance without losing information about its composition. Specifically, we suggest using slashes to denote layered structures and curly brackets to represent reticulums, thereby distinguishing them from substances composed of molecules.

The usefulness of this proposal was tested with 18 professors and 276 undergraduate students at Facultad de Química, UNAM, yielding outstanding results. From our standpoint, adopting these definitions, along with the novel formula notation, will help overcome misconceptions regarding the distinction between molecular, layered and reticular chemical species. Finally, a further study is being prepared to discuss the impact of adding more precision by including coordination numbers, as well as the scope and limitations of our proposal. By continuing to refine and expand upon this notation system, we hope to provide educators with a robust tool for teaching
complex chemical concepts more effectively, ultimately leading to a deeper and more accurate understanding of chemistry among students.

## ASSOCIATED CONTENT

**SI** Supporting Information

The Supporting Information is available at https://pubs.acs.org/doi/10.1021/acs.jchemed.5c00074.

Various questions and results from the students' and professors' quizzes, as well as three-dimensional structures of the different examples presented (PDF)

Various questions and results from the students' and professors' quizzes, as well as three-dimensional structures of the different examples presented (DOCX)

## AUTHOR INFORMATION

### Corresponding Authors

**Miguel Reina** - Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México; ● orcid.org/0000-0003-4959-4105; Email: mreina@quimica.unam.mx

**Bruno Landeros-Rivera** - Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México; Email: brunolanderos@quimica.unam.mx

**Jesús Gracia Mora** - Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México; Email: jgracia@quimica.unam.mx

**Hervé This** - Université Paris-Saclay, INRAE AgroParisTech, 75005 Paris, France; Group of Molecular Gastronomy, Inrae-AgroParisTech, International Centre for Molecular Gastronomy, F-75005 Paris, France; ● orcid.org/0000-0001-8067-1215; Email: herve>this@agroparistech.fr

**Antonio Reina** - Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México; ● orcid.org/0000-0001-7527-7176; Email: antonio.reina.0711@quimica.unam.mx

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.jchemed.5c00074

### Notes

Every participant granted permission for the collected data to be used for academic purposes. The authors used an ethical consent procedure approved according to procedures established by the Facultad de Quimica, UNAM.

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

The authors thank the meaningful discussions with all the faculty members and students, especially with Karla Salas-Martin (FQ, UNAM).

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