Question

There are two isomers of \(\mathrm{C}_{4} \mathrm{H}_{10}\). Suppose that each isomer is treated with \(\mathrm{Cl}_{2}\) and the products that have the composition \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{Cl}_{2}\) are isolated. Find the number of different products that form from each of the original \(\mathrm{C}_{4} \mathrm{H}_{10}\) compounds. Do not consider optical isomerism.

Short answer

n-Butane can form 2 different products and isobutane can also form 2 different products with the formula \texorpdfstring{\(C_4H_8Cl_2\texorpdfstring{\) when treated with \texorpdfstring{\(Cl_2\texorpdfstring{\) without considering optical isomerism.

Step-by-step solution

Identifying the Isomers of \texorpdfstring{\(C_4H_{10}\texorpdfstring{\) - Butane and Isobutane}

The two isomers of \texorpdfstring{\(C_4H_{10}\texorpdfstring{\) are n-butane and isobutane. n-Butane has a straight chain of four carbon atoms while isobutane has a branched chain with three carbon atoms in the main chain and a methyl group attached to the second carbon.

Determining Products for n-Butane

For n-butane, chlorination can result in substitution at one of the two equivalent terminal carbon atoms, giving one product, or at one of the two equivalent middle carbon atoms, giving a second product. Therefore, n-butane can yield two different di-substituted products with the formula \texorpdfstring{\(C_4H_8Cl_2\texorpdfstring{\) when treated with \texorpdfstring{\(Cl_2\texorpdfstring{\) - a 1,1-dichlorobutane and a 1,2-dichlorobutane.

Determining Products for Isobutane

For isobutane, chlorination can occur at the single terminal carbon atom, yielding one product, or at any of the three equivalent tertiary carbon atoms, yielding a second product. Thus, isobutane can form two different di-substituted products with the same formula - a 1,1-dichloro-2-methylpropane and a 1,3-dichloro-2-methylpropane.

Key concepts

Isobutane

Isobutane, also known as methylpropane, is one of the two isomers of the hydrocarbon with the molecular formula \( C_4H_{10} \). Unlike its straight-chain counterpart n-butane, isobutane has a more compact structure due to a branched chain. This means that three carbon atoms form the main chain while the fourth carbon (a methyl group) is attached to the second carbon atom in the chain.

Chemically, the structure of isobutane provides it with unique properties, such as a lower boiling point compared to n-butane, making it ideal for use in refrigerants and as a propellant in aerosols. The branching in isobutane also influences its reactivity, particularly in reactions like halogenation, as it offers different types of carbon atoms (tertiary and primary) for substitution.

n-Butane

n-Butane is the straight-chain isomer of the molecular formula \( C_4H_{10} \). Its structure consists of a continuous chain of four carbon atoms with hydrogen atoms filling the remaining valences of carbon to satisfy the tetravalency rule. This linear configuration leads to a higher boiling point relative to its isomeric form, isobutane.

In practical terms, n-butane's straight-chain structure also dictates its chemical reactivity, particularly in halogenation reactions. When n-butane undergoes such reactions, the different positions on the carbon chain offer diverse sites for halogens to attach, resulting in various substituted products. This feature is critical to understand as it directly affects the potential outcome of halogenation reactions when using n-butane as the starting material.

Halogenation Reactions

Halogenation reactions involve the addition of halogen atoms, such as chlorine or bromine, to organic molecules. In the context of hydrocarbons like \( C_4H_{10} \), these reactions usually proceed via a free radical mechanism, which occurs in multiple stages: initiation, propagation, and termination.

During the process, a halogen molecule (like \( Cl_2 \)) is split into radicals, which then react with the hydrocarbon to replace hydrogen atoms with halogen atoms. These reactions are not only specific to the type of halogen but also to the nature of the hydrocarbon and its structural isomers. For example, n-butane and isobutane will react with chlorine to produce different dihalogenated products because their structures influence the placement of the chlorine atoms. This specific character of halogenation is fundamental in synthetic organic chemistry for the generation of more complex molecules.

Organic Chemistry

Organic chemistry is a branch of chemistry that deals with carbon-containing compounds and their reactions. Central to organic chemistry is understanding how different structures, such as straight-chain and branched isomers like n-butane and isobutane, react under various conditions.

The structural versatility of carbon allows for a vast array of organic molecules, each with its own unique properties and reactivity. Through organic chemistry, scientists can design and synthesize new compounds for a wide range of applications, including pharmaceuticals, materials, and energy sources. The study of reactions such as halogenation is crucial within this field as it illustrates the principles of chemical reactivity and molecular transformation, which are at the heart of organic synthesis.