From Ashes to Diamonds: Carbon Allotropy

 

ACCM Concepts

• This Exemplar will teach the following concept(s) from the ACS Examinations Institute General Chemistry ACCM: 

II.A.2.a. Bonds formed between two nonmetals tend to be covalent, while bonds formed between a metal and a nonmetal tend to be ionic in character.

III.A.2.b. Some elements have allotropes–multiple stable forms.

IV.A.2.a. Graphical summaries of the phase behavior of one-component systems called phase diagrams, are useful tools for a compact understanding of the phase behavior of these systems.

IV.C.1.b. Forces are present between molecules, and the categories of these forces (dispersion, dipole-dipole, and hydrogen bonding in particular) are important organizational ideas for conceptualizing the physical properties of chemical systems.

Introduction

This page will discuss the various factors that play into allotropy in the context of a revolutionary process that turns ashes into diamonds. Using carbon as the primary example, this page will delve into the role that chemical bonds and intermolecular forces play in the physical properties of different allotropes. Finally, phase diagrams will allow us to visualize how heat and pressure can manipulate the formation and reconstruction of these allotropes.

Carbon Allotropy

In 2017, Shark Tank–a popular business reality show in which companies seek out investments–shocked viewers across the United States when a company, Eterneva, claimed they could transform the ashes of a loved one into real diamonds (3). The “sharks”–the ruthless, billionaire investors on the show–couldn’t believe what they were hearing, finding Eterneva’s claims to be something out of a fantasy novel. However, what sounds like science fiction can actually be explained through science–specifically, the chemistry of allotropy.

To begin, allotropy arises when a single element (a unique substance that cannot be further broken down) can exist in multiple stable, crystal forms (1). Specifically, carbon contains various different allotropes, the most notable of them, graphite and diamond. Interestingly, although graphite and carbon have vastly different physical properties, they are derived from the same element, and thus, their physical and chemical differences can be attributed to differences in their structure and bond identities (1). Carbon, the sixth element on the Periodic Table, has six protons and four valence (shell) electrons, leaving four “spots” open for chemical bonding with the goal of filling the octet of eight valence electrons. In diamond, carbon forms four nonpolar covalent bonds with other carbon atoms, meaning that four pairs of electrons are evenly shared between the central carbon and adjacent carbon atoms. This creates a tetrahedral configuration that develops into a three-dimensional crystal lattice structure when present in larger quantities (5). 

On the other hand, graphite has a layered structure, in which each carbon atom forms three nonpolar covalent bonds with adjacent carbon molecules, giving carbon a trigonal planar shape and a two-dimensional property; carbon’s fourth atom becomes delocalized and free to spread and move about the entire sheet of atoms (5). These two-dimensional layers of graphite interact with one another via London Dispersion forces, a type of intermolecular force that arises when electrons of adjacent atoms occupy positions that create temporary dipoles, or charges. When the positive region, or dipole, of one atom is attracted to the partially negative dipole of another atom, a London dispersion force is created (4). These different properties of the diamond and graphite allotropes of carbon cause them to have vastly different structures. What would these different structures look like? In figure one below, you can respectively see the molecular differences between the allotropes. 

Figure 1: An image showing the structural differences between two allotropes of carbon: diamond and graphite respectively. 

Exercise 1

Analyze figure one above. What are the chemical properties, forces, and structural differences?

Answer

The carbon allotropes structures are different by their dimensionality. Diamond has a three-dimensional tetrahedral network structure while graphite is two-dimensional trigonal planar and sheet-like. Furthermore, graphite has London Dispersion forces interactions between network molecules with delocalized electrons. Both carbon allotropes contain covalent bonding. These structural differences cause many differences in the properties such as its appearance and hardness.

Although covalent bonds and dispersion forces both attract substances together, the former is much stronger, because it involves a sharing of electrons, while the latter arises from weak, instantaneous dipoles. As a result, diamond is incredibly durable and is, in fact, the hardest material on earth while graphite is brittle and breaks apart easily, making it ideal for usage in pencils (5). Furthermore, the delocalized electrons in graphite allow for the carbon sheets to move around and slide across one another with relative ease, making it especially useful as a dry lubricant. While carbon’s tightly bound electrons make diamond a good insulator and give it a high melting point, graphite’s low melting point and electrical conductivity are a result of its electron delocalization (5).

Figure 2: A Phase diagram of carbon depicting the different allotropes at different temperatures and pressures

From Ashes to Diamond

These carbon allotropes are essential to the process in which Eterneva, and other similar companies, harvest human or animal ashes that are transformed into diamonds. Humans are all partially made up of carbon, most abundantly present as calcium carbonate. When a body is cremated, 0.5 to 4% of the body’s carbon (calcium carbonate) from the bones remain in the ashes, which are sent to the diamond growing lab where scientists purify and extract this compound. From there, calcium carbonate is decomposed via a chemical reaction that splits the compound into its component elements: calcium, oxygen, and carbon in a graphite powder form. Finally, by applying immense heat (2,500 degrees fahrenheit) and pressure (850,000 pounds per square inch), graphite is transformed into a raw diamond, which is then cut into the desired shape to maximize its luminosity (3). 

Eterneva capitalizes upon the ability for elements to change phases and structures by manipulating heat and pressure (3). As indicated by the phase diagram above (see figure 2), the structure and phase of carbon compounds can be altered by changing the environment in which it is present. When enough heat and pressure are applied to graphite, its bonds can be broken and rearranged. This process reconfigures the carbon atoms from trigonal planar graphite sheets that interact with one another via dispersion forces to a tetrahedral structure, forming the carbon allotrope, diamond (5).

Exercise 2

Suppose you have just harvested 1.23 g of calcium carbonate from the ashes of a loved one. How many grams of diamond will theoretically be formed? If you produce only 0.0520 g of diamond, what is your percent yield? Write out the equation for the reaction that produces graphite from calcium carbonate under the right conditions, as well as the equation for the reaction that produces diamond.

Answer

1. Write out the chemical reactions that occur.

CaCO_{3 (s)} → Ca_(s) + C_(s,graphite) + 3/2 O_{2 (s)}

2 CaCO_{3 (s)} → 2 Ca_(s) + 2 C_(s,graphite) + 3 O_{2 (s)}

C(s, graphite) → C_{(s, diamond)}

2. Divide your amount of calcium carbonate by its molar mass (molar mass CaCO₃ = 110.98 g/mol) to get the moles of calcium carbonate. 

1.23g / 110.98 g/mol CaCO₃ = 0.01108 mol CaCO₃

3. Use the respective molar ratios to calculate the amount of diamond in moles.

0.01108 mol CaCO₃ * 2 mol C_(s,graphite) / 2 mol CaCO₃ * 1 mol C_(s,diamond) / 1 mol mol C(s, graphite) = 0.01108 mol C_(s,diamond)

4. Use the molar mass of diamond (carbon) to find the grams of diamond produced in the reaction.

0.01108 mol C_(s,diamond) * 12.011 g/mol C_(s,diamond) = 0.1331 g C_(s,diamond)

5. Calculate the percent yield

0.0520g C_(s,diamond) / 0.1331g C_(s,diamond) * 100 = 39.1% yield

Definition: Term

Allotropy - The existence of two or more physical forms of a chemical element.

Element - A pure substance that cannot be broken down by any physical or chemical means into simpler substances.

Delocalized Electron - Electron that is not associated with a single atom or covalent bonds but instead moves around a solid. 

Dipole - A bond whose ends have opposite charges 

London Dispersion Force - A type of intermolecular force that arises when electrons of adjacent atoms occupy positions that create temporary dipoles

Phase Diagram - A graphical representation of the physical states of a substance under different conditions of temperature and pressure

Nonpolar Covalent Bond - An intramolecular bond in which a pair of electrons is evenly shared between two electrons. 

Valence Electron - An electron in the outer shell of an atom that can participate in the formation of chemical bonds. 

References 

1.  Allotropy. Allotropy - an overview | ScienceDirect Topics. https://www.sciencedirect.com/topics...ring/allotropy (Accessed 2022-12-07)

2. Carbon basic phase diagram.png - wikimedia commons. https://commons.wikimedia.org/wiki/F...se_diagram.png (Accessed 2022-12-07)

3. How it works. Eterneva. https://www.eterneva.com/how-it-works (Accessed 2022-12-07)

4. London Dispersion Forces. Chem Purdue. https://chem.libretexts.org/Bookshel...and_Properties (Accessed 2022-12-07)

5. Clark, J. (2021, February 3) Graphite and diamond - structure and properties. Chemistry LibreTexts. Libretexts. https://www.chem.purdue.edu/gchelp/l.../disperse.html (Accessed 2022-12-07)