Question

There are three constitutional isomers with the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{12}\). When treated with chlorine at \(300^{\circ} \mathrm{C}\), isomer A gives a mixture of four monochlorination products. Under the same conditions, isomer B gives a mixture of three monochlorination products and isomer \(C\) gives only one monochlorination product. From this information, assign structural formulas to isomers \(A, B\), and \(C\).

Short answer

Question: Identify the structural formulas of isomers A, B, and C, given that they have the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{12}\), and yield 4, 3, and 1 monochlorination products, respectively. Answer: Isomer A: n-Pentane; Isomer B: Isopentane (2-methylbutane); Isomer C: Neopentane (2,2-dimethylpropane)

Step-by-step solution

Draw possible structural formulas for the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{12}\).

Draw the possible constitutional isomers of pentane (\(\mathrm{C}_{5} \mathrm{H}_{12}\)): n-pentane, isopentane (also known as 2-methylbutane), and neopentane (also known as 2,2-dimethylpropane).

Determine the number of monochlorination products for each isomer.

For each isomer, identify the number of positions at which hydrogen can be replaced by chlorine. This will give us the number of possible monochlorination products. n-Pentane has four non-equivalent positions: three different hydrogens at the ends, and two sets of identical hydrogens on the middle carbons. Monochlorination would result in 4 products. Isopentane has three non-equivalent positions: one type of hydrogen on the central carbon, another type on the methyl group attached to the central carbon, and a third type on the terminal carbons of the main chain. Monochlorination would result in 3 products. Neopentane has only one type of hydrogen, present on the four methyl groups. Monochlorination would result in 1 product.

Assign structural formulas to isomers A, B, and C.

Isomer A gives four monochlorination products, which corresponds to n-Pentane. Isomer B gives three monochlorination products, which corresponds to isopentane (2-methylbutane). Isomer C gives only one monochlorination product, which corresponds to neopentane (2,2-dimethylpropane). Therefore, the structural formulas for the three isomers are: Isomer A: n-Pentane Isomer B: Isopentane (2-methylbutane) Isomer C: Neopentane (2,2-dimethylpropane)

Key concepts

Molecular Formula

The concept of a molecular formula is integral in understanding the composition of chemicals. It represents the exact number of atoms of each element present in a molecule. In our context, the molecular formula \(\mathrm{C}_{5}\mathrm{H}_{12}\) describes an alkane, which is a hydrocarbon with single bonds only, consisting of five carbon atoms and twelve hydrogen atoms.

However, this formula does not provide any information about the structure or arrangement of those atoms, which is why compounds with the same molecular formula can have different structural arrangements and, consequently, different physical and chemical properties. These compounds are known as isomers, and more specifically, constitutional isomers when they differ in the connectivity of their atoms.

Monochlorination of Alkanes

Monochlorination refers to a chemical reaction where one hydrogen atom in an alkane is substituted with a chlorine atom. In the presence of heat or light, a chlorine molecule can split into two chlorine atoms, each of which is highly reactive and can replace a hydrogen atom in the alkane.

The interesting aspect of monochlorination, particularly when applied to alkanes, is that the number of possible monochlorination products depends on the number of non-equivalent hydrogen atoms present in the molecule. A non-equivalent hydrogen atom is one that, upon replacement by chlorine, would result in a unique chloroalkane. Thus, alkanes with a more complex structure can yield a higher number of unique monochlorination products, offering insight into the structure of the original alkane.

Structural Formulas of Isomers

Structural formulas depict the arrangement of atoms in a molecule. When compounds have the same molecular formula but differ in the structural formula, they are known as structural isomers. Understanding the structure is crucial since it influences the chemical behavior of the molecule.

For example, n-pentane, isopentane, and neopentane all share the same molecular formula \(\mathrm{C}_{5}\mathrm{H}_{12}\) but have different structural formulas. n-Pentane has a linear chain structure, isopentane has a branched structure with a central carbon bonded to three other carbons and a methyl group, and neopentane has a more compact structure with all carbons connected to a central carbon atom.

These structural differences explain the varying number of monochlorination products obtained from each isomer when subjected to the same reaction conditions. As such, by analyzing the products of such chemical reactions, chemists can deduce the underlying structural formulas of the isomers.