Question

Thermodynamically the most stable form of carbon is (a) diamond (b) graphite (c) fullerenes (d) coal

Short answer

Graphite is the thermodynamically most stable form of carbon.

Step-by-step solution

Identify the Concept

Understanding what is meant by 'thermodynamically most stable form of carbon' involves knowing that it is the form with the lowest Gibbs free energy under standard conditions. For carbon, this is determined by its crystal structure and bonding.

Recall Forms of Carbon

The different forms of carbon include diamond, graphite, fullerenes, and coal. Each form has distinct properties, structures, and stability.

Assess Stability of Diamond and Graphite

Diamond has a 3D tetrahedral crystal lattice that makes it extremely hard. Graphite has a planar structure with layers held together by weak forces, making it more thermodynamically stable as lower energy is associated with the molecular arrangement.

Consider Fullerenes and Coal

Fullerenes (like C60) have a closed spherical structure and are not as stable as graphite due to lower molecular cohesion. Coal is a complex mixture and not a pure form, so its stability is varied and less than that of crystalline forms like graphite.

Conclusion

Graphite is the thermodynamically most stable form of carbon under standard conditions because it has the lowest Gibbs free energy compared to other forms.

Key concepts

Forms of Carbon

Carbon, as an element, can take on several different forms, also known as allotropes. Each form has distinct characteristics owing to the variation in atomic arrangement and bonding. The primary allotropes include:

• Diamond: Known for its hardness and brilliance, diamond consists of carbon atoms bonded in a 3D tetrahedral lattice. This makes it incredibly strong but less stable under ambient conditions.
• Graphite: Characterized by its planar layers, graphite is soft and slips easily, making it ideal for pencils. These layers are bonded with weak van der Waals forces, enhancing its thermodynamic stability.
• Fullerenes: These molecules, like C60, look like soccer balls and are made up of hexagonal and pentagonal rings. They are fascinating but not the most stable form of carbon.
• Coal: A natural, carbon-containing material with a mixture of carbon's crystalline forms. Its lack of purity and varying structure reduce its stability compared to more uniform allotropes.

Carbon's ability to form such diverse structures is a testament to its versatility and essential role in many fields, from industry to natural processes.
Understanding these forms is key to grasping why graphite stands out as the most stable allotrope.

Gibbs Free Energy

Gibbs free energy is a crucial concept in understanding thermodynamic stability. It determines the spontaneity of a process and the stability of a system. The formula for Gibbs free energy is:\[ G = H - TS \]where:

• \(G\) is the Gibbs free energy.
• \(H\) is the enthalpy, or total heat content.
• \(T\) is the temperature in Kelvin.
• \(S\) is the entropy, or disorder of the system.

For carbon, thermodynamic stability, or the most stable form, is the one with the lowest Gibbs free energy. Thus, thermodynamic principles predict that at normal temperature and pressure, graphite is more stable than diamond.
Lower Gibbs free energy for graphite arises due to its layered structure, which allows for more flexibility and lower energy configurations, compared to diamonds' rigid framework. This makes graphite the preferred form under standard environmental conditions.

Crystal Structures

In determining the stability of carbon's forms, crystal structure plays a pivotal role. The arrangement of atoms impacts properties like hardness, conductivity, and thermodynamic stability.
Diamond's Crystal Structure
Diamond boasts a cubic lattice where each carbon atom is tetrahedrally bonded to four others. This dense and interconnected 3D structure renders diamond extremely hard and optically brilliant.
Graphite's Crystal Structure
Graphite, on the other hand, has a hexagonal lattice. Its sheets of carbon atoms stack atop one another like pages in a book, held loosely by van der Waals forces. This architecture affords graphite its lubricating properties and higher thermodynamic stability.
Fullerenes' Crystal Structure
Fullerenes form cage-like structures, with carbon atoms arranged in a spherical shape. Though intriguing, they lack the cohesive strength of the lattice structures found in diamond and graphite. The differences in these structures directly influence their respective properties and stability. Thus, understanding crystal structures is crucial to comprehending why graphite is the most thermodynamically stable form of carbon under standard conditions.