Question

Propose a structural formula for the compound } \mathrm{C}_{10} \mathrm{H}_{16} \text { and account for its formation.

Short answer

Question: Determine the degree of unsaturation in the molecule C10H16 and propose a structural formula for the compound. Answer: The degree of unsaturation in C10H16 is 3, indicating the presence of 3 pi bonds and/or rings in the molecule. There can be several possible structural isomers, but without further information such as NMR, IR, or MS analysis, we cannot specify a single isomer. A few possible isomers include a molecule with one cyclohexane ring and four pi bonds on a butene chain, a molecule with two cyclopentane rings, or a molecule with one cyclohexane ring and a propene chain with pi bonds.

Step-by-step solution

Determine the Degree of Unsaturation

The degree of unsaturation in a molecule gives us the number of pi bonds and/or rings present in the molecule. It can be calculated using the following formula: Degree of Unsaturation \(= \frac{2n + 2 - x}{2}\) Here, n is the number of carbon atoms in the formula and x is the number of hydrogen atoms (or equivalent). For \(\mathrm{C}_{10}\mathrm{H}_{16}\), n = 10 and x = 16. Degree of Unsaturation \(= \frac{2(10) + 2 - 16}{2} = \frac{22 - 16}{2} = \frac{6}{2} = 3\) So, there are 3 pi bonds and/or rings present in the molecule.

Create Structural Isomers

Keeping in mind the degree of unsaturation, we can propose several structural isomers of \(\mathrm{C}_{10}\mathrm{H}_{16}\). Some possible isomers include: 1. A molecule with one cyclohexane ring and four pi bonds (double bonds) on a butene chain. 2. A molecule with two cyclopentane rings and no pi bonds. 3. A molecule with one cyclohexane ring and three pi bonds (double bonds) on a propene chain and one pi bond within the ring. 4. A molecule with one cyclohexane ring, two pi bonds (double bonds) in a butene chain, and one pi bond within the ring. These are just a few of the possible isomers. Keep in mind that there can be more possibilities.

Account for the Formation

As we have multiple possibilities for the structural isomers of the molecule, the information given to us is not enough to fully specify a single isomer. To pinpoint an exact structure, we would need more information about the molecule, such as NMR, IR, or MS analysis. Each of the isomers we proposed above could be formed through different organic reactions. For example: 1. The formation of a butene chain with four double bonds (1,3-butadiene) can be achieved by dehydrohalogenation reactions or condensation of alkynes. 2. The formation of two cyclopentane rings can be achieved through intramolecular reactions, such as Diels-Alder reactions involving dienes and dienophiles. 3. Molecules will one cyclohexane ring and pi bonds on a propene chain could be formed through a Diels-Alder reaction or other cyclization reactions. Again, without knowing the exact structural formula, it's difficult to give a specific reaction that would form the molecule.

Key concepts

Degree of Unsaturation

When exploring the complex world of organic molecules, one concept that stands out is the 'degree of unsaturation'. This term refers to the total number of rings and pi (π) bonds within a molecule.

In a more technical sense, the degree of unsaturation determines the number of hydrogen atoms less than the maximum possible for a saturated hydrocarbon with the same number of carbon atoms. For saturated hydrocarbons, (alkanes), the general formula is \( C_nH_{2n+2} \). Consequently, the degree of unsaturation indicates the presence of double bonds, triple bonds, or rings—each contributing one degree of unsaturation.

The calculation is a straightforward formula: \( \text{Degree of Unsaturation} = \frac{{2n + 2 - x}}{{2}} \), where \(n\) is the number of carbon atoms and \(x\) is the number of hydrogens. In the example of \(C_{10}H_{16}\), the exercise reveals three degrees of unsaturation, suggesting that there could be combinations of three double bonds, rings, or triple bonds—each contributing to the molecule's unique structure.

This tool is invaluable for chemists as they can deduce important structural features of a molecule even without seeing its actual structure, guiding them in determining possible structural isomers.

Organic Chemistry

Organic chemistry is a sub-discipline within chemistry that involves the scientific study of the structure, properties, composition, reactions, and synthesis of organic compounds—molecules that contain carbon. It's a vast field that covers various substances, many of which we encounter in daily life, including plastics, pharmaceuticals, petrochemicals, and food additives.

The essence of organic chemistry revolves around carbon atoms and how they can bond with various other atoms, particularly hydrogen, oxygen, nitrogen, and sometimes sulfur or phosphorus. This ability to form stable bonds with many elements including itself results in a vast array of possible molecules, each with unique chemical and physical properties. Organic chemists explore the synthesis of new compounds, unravel the structures of existing ones, and develop an understanding of their reactivity and behavior.

Role of Structural Isomers in Organic Chemistry

In organic chemistry, structural isomers play a significant role. These are molecules with the same molecular formula but different structural formulas. This means they have the same number of atoms of each element, but these atoms are connected in different ways. Understanding and identifying these isomers is essential for organic chemists as they explain the diverse behaviors and properties of organic compounds with the same molecular compositions.

Structural Formula

The beauty of organic molecules lies not just in their composition but also in how their atoms are connected—their structural formula. A structural formula represents the arrangement of atoms within a molecule, unlike the molecular formula which only provides the count of each atom type. This graphical representation lays out the specific connections between atoms, clearly illustrating the molecule's geometry.

The structural formula is a critical tool in organic chemistry. It communicates much more information than a molecular formula. It depicts how atoms bond and the type of bonds - single, double, or triple, and how these connections affect the molecule's geometry and physical and chemical properties. For instance, butane (\(C_4H_{10}\)) and isobutene (\(C_4H_{10}\)) share the same molecular formula but have different structural formulas, leading to vastly different properties.

In creating structural isomers for \(C_{10}H_{16}\), the various combinations of bonds and rings that can reach up to the degree of unsaturation provide a richness of possible structures. Each isomer would have different chemical and physical properties and would be suited for different reactions or purposes in the chemical world.