Problem 23 - Chemistry The Science in Context

Question

Diamond and the fullerenes are two allotropes of carbon. On the basis of their different structures and properties, predict which has the higher standard molar entropy.

Step-by-Step Solution

Answer

Answer: Fullerene is expected to have a higher standard molar entropy than diamond due to its less ordered and more flexible structure, allowing for more accessible conformations and molecular motions, which contribute to its entropy.

Step 1: Understand standard molar entropy

Standard molar entropy is a measure of the entropy (disorder or randomness) of one mole of a substance under standard conditions (1 atm pressure and a specified temperature, usually 298K). It is an extensive property, which means it depends on the amount of substance. A higher standard molar entropy implies a higher level of disorder or randomness in the substance.

Step 2: Examine the structures of diamond and fullerenes

Diamond has a highly ordered, crystalline structure where each carbon atom is covalently bonded to four other carbon atoms in a tetrahedral arrangement. This results in a rigid, strong, and stable lattice structure with little disorder. On the other hand, fullerenes are composed of carbon atoms bonded in a combination of pentagonal and hexagonal rings, forming cage-like, closed-shell molecules (e.g., C60). These molecules are relatively less ordered and have weaker forces between adjacent molecules compared to diamond.

Step 3: Consider the contribution of structure, properties, and motion to standard molar entropy

Entropy is a measure of disorder, and it depends on factors such as the structure of a substance, the presence of multiple conformations, vibrational and rotational motions, and translational motion. In general, a more disordered or less rigid structure (e.g., fullerene) will exhibit a higher entropy compared to a more ordered or rigid structure (e.g., diamond).

Step 4: Compare the entropy of diamond and fullerenes

Diamond has a highly ordered, rigid structure, while fullerenes have a less ordered and more flexible structure. Therefore, fullerenes are expected to have a higher standard molar entropy as there is more disorder in their structure, and they possess a greater number of accessible conformations and molecular motions, which contribute to their entropy.

Step 5: Conclusion:

Based on the differences in structures and properties, fullerene is predicted to have a higher standard molar entropy than diamond.

Key Concepts

Standard Molar Entropy

Standard molar entropy is a fundamental concept in chemistry that helps us understand the disorder present in a substance. It measures the randomness associated with one mole of a substance at standard conditions, typically 1 atm pressure and 298K temperature.
Under these conditions, the level of disorder or randomness is noted as being the standard molar entropy, which is an extensive property, meaning it scales with the amount of substance.
This value is influenced by several factors, including molecular structure, the presence of multiple molecular conformations, and how molecules vibrate, rotate, or move in space.
In general, substances with more complex structures and more ways to arrange themselves tend to have higher standard molar entropy.

Crystalline Structure

A crystalline structure refers to a systematic, orderly pattern of atoms or molecules. This is in contrast to non-crystalline (amorphous) substances without a defined arrangement.
Diamond serves as an excellent example of a crystalline structure. Each carbon atom in a diamond is covalently bonded to four other carbon atoms in a robust tetrahedral lattice.
This results in a very stable and ordered arrangement, giving diamond its remarkable hardness and rigidity. However, such order means a low level of disorder, leading to a lower standard molar entropy compared to more disordered structures.
On the other hand, structures that are less orderly, like that of fullerenes, have higher standard molar entropy.

Fullerenes

Fullerenes are fascinating molecules and one of novel allotropes of carbon besides diamond and graphite. What makes them unique is their closed-cage structures composed of carbon atoms arranged in pentagonal and hexagonal rings.
These structures resemble a soccer ball shape, like the famous C60, also known as a "buckyball".
Due to these cage-like formations, fullerenes exhibit considerable flexibility and a myriad of possible configurations. This flexibility and the weaker intermolecular forces compared to those in diamonds allow fullerene molecules to be more dynamic.
Hence, fullerenes can move and adjust shapes more freely, contributing to higher standard molar entropy compared to diamonds. Their structural versatility is why they typically have higher entropy, as the diverse molecular motions and accessible conformations increase the disorder.