Question

A compound of formula \(\mathrm{C}_{5} \mathrm{H}_{12}\) gives only a single monobromo substitution product of formula \(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{Br}\). What is the structure of this \(\mathrm{C}_{5} \mathrm{H}_{12}\) isomer? (Notice that carbon can form both continuous chains and branched chains. Also notice that structures such as the following represent the same isomer because the bonds to carbon are tetrahedral and are free to rotate.)

Short answer

The isomer is neopentane (2,2-dimethylpropane).

Step-by-step solution

Analyze the Molecular Formula

The compound \(\mathrm{C}_{5} \mathrm{H}_{12}\) indicates a hydrocarbon called pentane, which has five carbon atoms and twelve hydrogen atoms.

Consider Isomeric Possibilities

For a \(\mathrm{C}_{5} \mathrm{H}_{12}\) compound, the possible structural isomers are pentane, isopentane (2-methylbutane), and neopentane (2,2-dimethylpropane).

Determine Monobromination Products

The problem states only a single monobromo substitution product \(\mathrm{C}_{5} \mathrm{H}_{11}\mathrm{Br}\) is formed. This means the hydrocarbon must have identical hydrogen atoms that can be replaced to form only one kind of monobromo product.

Eliminate Inappropriate Isomers

- For linear pentane, replacing a hydrogen with a bromine atom can happen at different positions leading to multiple products. - In isopentane, different monobromo isomers can still be formed. - Neopentane, however, has highly symmetric carbon and hydrogen arrangements, leading to only one type of monobromo compound.

Conclusion

The structure that supplies only one monobromo product is neopentane. It has a central carbon forming a cross-like structure with identical \(\mathrm{CH}_{3}\) groups.

Key concepts

Isomer Identification

Isomer identification is an essential concept in organic chemistry that revolves around understanding different compounds that share the same chemical formula but exhibit diverse structures. Compounds like those with the formula \(\mathrm{C}_{5}\mathrm{H}_{12}\) can have various shapes, such as linear or branched chains. There are three major isomers for this formula: pentane, isopentane (also known as 2-methylbutane), and neopentane (2,2-dimethylpropane).

The key to identifying an isomer involves understanding its structural attributes. By examining the number of carbon atoms and the layout of hydrogen atoms, you can determine which isomer matches a given description. For example, all three mentioned isomers have five carbon atoms, but their arrangement differs, affecting their chemical properties.

Monobromo Substitution

Monobromo substitution is a chemical reaction where one hydrogen atom in a hydrocarbon is replaced with a bromine atom. The formula \(\mathrm{C}_{5}\mathrm{H}_{11}\mathrm{Br}\) indicates that such a process has occurred on a \(\mathrm{C}_{5}\mathrm{H}_{12}\) compound. The reaction typically happens when the hydrocarbon is exposed to bromine in the presence of light or heat.

The significance of having just one monobromo substitution product is crucial. It suggests that all hydrogens are equivalent, meaning the replacement of any hydrogen results in the same brominated compound. The implication is a high level of symmetry in the molecule, which narrows down the possible isomers significantly.

Molecular Symmetry

Molecular symmetry involves the spatial arrangement of atoms in a molecule that allows it to remain unchanged under specific operations like rotation or reflection. Among the \(\mathrm{C}_{5}\mathrm{H}_{12}\) isomers, neopentane exhibits remarkable symmetry. It is arranged in a way that any hydrogen atom can be replaced by bromine, yielding the same monobromo product.

Neopentane's central carbon atom forms a sort of cross with \(\mathrm{CH}_{3}\) groups, leading to its symmetrical nature. Because of this structure, it is the only isomer capable of forming a single monobromo substitution product, demonstrating how molecular symmetry influences chemical behavior.

Structural Isomers

Structural isomers are compounds with the same molecular formula but different connectivity between atoms. These variations give rise to unique physical and chemical properties. For the molecular formula \(\mathrm{C}_{5}\mathrm{H}_{12}\), the primary structural isomers include pentane, isopentane, and neopentane.

Pentane is a straight-chain compound, whereas isopentane and neopentane have branched structures. The identification of structural isomers involves analyzing how atoms, particularly carbon and hydrogen, are lined up. Recognizing how these changes affect properties is fundamental in organic chemistry. In our analysis, the structural features of neopentane—specifically its symmetry—play a vital role in forming only one monobromo product, exemplifying how structural isomerism affects chemical reactions.