Question

At the time Kekule presented his structure for \(\mathrm{C}_{6} \mathrm{H}_{6}\), the alternate structure called prismane was proposed by Landenburg. How many possible dibromo prismanes are possible?

Short answer

There are 15 possible dibromo prismanes that can be formed from a prismane molecule.

Step-by-step solution

Understand the structure of prismane

Prismane is an isomer of benzene, with the chemical formula \(\mathrm{C}_6\mathrm{H}_6\). Its structure consists of three interconnected cyclopropane rings, which form a triangular arrangement. Each carbon atom in prismane is connected to two other carbon atoms and one hydrogen atom.

Identify the carbon atoms where bromine can be added

Since there are six carbon atoms in a prismane molecule and each of them has one hydrogen atom attached, we can add a bromine atom to any of the six carbon atoms by replacing the hydrogen atom. In essence, any of six carbon atoms can be substituted by a bromine atom.

Calculate the number of dibromo prismanes

To find the number of possible dibromo prismanes, we need to determine how many ways we can pick two carbon atoms from the six available carbon atoms to attach the bromine atoms. This can be calculated using the combination formula: \[\binom{n}{k} = \frac{n!}{k!(n-k)!}\] where \(n\) is the total number of elements (carbon atoms in our case), \(k\) is the number of elements to be chosen, and the ! symbol denotes the factorial of a number. So, to choose two carbon atoms from the six available, we can apply the combination formula: \[\binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6!}{2!4!} = \frac{720}{2\cdot 24} = 15\]

Conclusion

There are 15 possible dibromo prismanes that can be formed from a prismane molecule.

Key concepts

Prismane Structure

Prismane presents a unique structure that differs significantly from the well-known benzene ring. In prismane, each of the six carbon atoms is part of a cyclopropane ring, forming a triangular shape. This geometry is quite intriguing, as it results in a structure where bonds are under considerable strain.
Each carbon atom in the prismane structure connects to two other carbon atoms and a single hydrogen atom. This distinctive shape and bonding give prismane remarkable chemical properties.
The structural distinction makes it a fascinating case study in the complex world of molecular geometry and provides a base for understanding why different isomers have different physical properties.

Combinatorial Chemistry

Combinatorial chemistry involves the rapid synthesis and screening of large libraries of molecules. It helps in identifying potential chemical compounds for further study or use in various applications. This approach is exceptionally powerful in the context of generating structural isomers, like those seen in prismane derivatives.
In the context of dibromo prismanes, combinatorial chemistry allows for exploring numerous ways two bromine atoms can be added to prismane's structure. By considering permutations and combinations, one can exhaustively identify all possible structural variations. The calculation of 15 possible dibromo prismanes highlights how combinatorial methods aid in comprehensively understanding potential isomers before synthesis.

Chemical Isomerism

Isomerism describes molecules with the same chemical formula but different structural arrangements, leading to diverse physical and chemical properties. Prismane offers a striking example of isomerism, serving as an isomer of benzene, sharing the formula \\(\mathrm{C}_6\mathrm{H}_6\).
The unique structure of prismane creates a variety of isomers when subjected to substitutions, such as adding bromine atoms. Dibromo prismane exemplifies this, where multiple bromine atoms can be arranged in different configurations around the prismane scaffold, each resulting in a distinct isomer.
Understanding chemical isomerism is crucial for predicting molecule behavior and properties, influencing everything from basic chemical research to the development of new pharmaceuticals.

Bromination in Organic Compounds

Bromination is a common technique in organic chemistry used to introduce bromine atoms into molecules. The process involves the substitution of a hydrogen atom by a bromine atom, often enhancing the molecular reactivity.
In the case of prismane, bromination can occur at each of the six carbon positions, allowing for the formation of different substituted compounds. Dibromo prismanes result from replacing two of the hydrogen atoms with bromine atoms, yielding a variety of structural forms.
Bromination significantly alters the chemical properties of the original compound, affecting factors such as solubility, boiling point, and reactivity. This makes dibromo prismanes especially interesting for further study in both academic research and industrial applications.