Question

When benzene is treated with chlorine under the influence of ultraviolet light, a solid material of \(\mathrm{m}\). wt. 291 is formed. Quantitative analysis gives an empirical formula of \(\mathrm{CHC} 1 .\) (a) What is the molecular formula of the product? (b) What is a possible structural formula? (c) What kind of reaction has taken place? (d) Is the product aromatic? (e) Actually, the product can be isolated into six isomeric compounds, one of which is used as an insecticide (Gammexane or Lindane). How do these isomers differ from each other? (f) Are more than six isomers possible?

Short answer

The molecular formula of the product is \(\mathrm{C_6H_6Cl_6}\). A possible structural formula is hexachlorobenzene. The reaction is an electrophilic aromatic substitution. The product is aromatic, and the six isomers differ in the arrangement of chlorine atoms on the benzene ring. Only six isomers are possible.

Step-by-step solution

(a) Molecular formula

Given the information about the mass and empirical formula (\(\mathrm{CHCl}\)), we need to find the molecular formula. To determine the molecular formula, we first need to calculate the molar mass of the empirical formula: \[Molar\ mass\ of\ CHCl = \text{mass of C} + \text{mass of H} + \text{mass of Cl}\] \[=12.01 \,g/mol + 1.01\, g/mol + 35.45 \,g/mol = 48.47\, g/mol\] Now, we'll divide the molecular weight (291 g/mol) by the empirical formula molar mass (48.47 g/mol) and round it to the closest whole number. \[Ratio = \frac{291\, g/mol}{48.47 \,g/mol} \approx 6\] Now multiply the empirical formula by this ratio to obtain the molecular formula: Molecular Formula = \(\mathrm{C_6H_6Cl_6}\)

(b) Possible structural formula

Since the molecular formula is \(\mathrm{C_6H_6Cl_6}\) and benzene (C6H6) is involved in the reaction, we can propose a structural formula where all six hydrogen atoms in benzene are replaced by chlorine atoms under UV light. This forms hexachlorobenzene: 

(c) Type of reaction

The reaction that takes place is a substitution reaction because the hydrogen atoms in benzene are replaced by chlorine atoms in the presence of UV light. This type of reaction is called electrophilic aromatic substitution.

(d) Aromaticity

Yes, the product is aromatic because it retains the original planar ring structure of benzene with each carbon atom having a p-orbital that participates in the conjugated pi-system. Thus, hexachlorobenzene retains the characteristics of aromatic compounds.

(e) Differences between isomers

The six isomers differ from each other in the arrangement of chlorine atoms on the benzene ring. They are positional isomers, meaning the connectivity of the atoms remains the same, but the location of the chlorine atoms around the ring varies. The insecticide Gammexane or Lindane is one such isomer, with a specific arrangement of chlorine atoms on the benzene ring: 

(f) Number of possible isomers

There can be six isomers, as each chlorine atom has the possibility of being in different positions on the benzene ring. The possible six isomers are 1,2,3,4,5,6-hexachlorobenzene, 1,2,3,4,5,6-hexachlorobenzene (Gammexane or Lindane), 1,2,3,5,6-pentachlorobenzene, 1,2,4,5,6-pentachlorobenzene, 1,2,3,4,6-pentachlorobenzene, and 1,2,3,4,5,6-hexachlorobenzene. No more isomers are possible because the positions for chlorine substitution have been exhausted and other arrangements would result in redundant isomers.

Key concepts

Molecular Formula Calculation

To calculate the molecular formula, one must know both the empirical formula and the molar mass of a compound. The empirical formula represents the simplest whole-number ratio of the elements within a molecule, while the molecular formula shows the exact number of atoms of each element in a molecule.

Here's how to calculate the molecular formula: Find the molar mass of the empirical formula and divide the given molecular weight by this molar mass. The result is a ratio that is used to multiply each element in the empirical formula, yielding the molecular formula. For example, with a compound having an empirical formula of \(CHCl\) and a molecular weight of 291 g/mol, determination involves the following steps:
1. Calculate the molar mass of \(CHCl\): Carbon (C) is 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and chlorine (Cl) is 35.45 g/mol, summing up to 48.47 g/mol.
2. Divide the molecular weight of 291 g/mol by the molar mass of the empirical formula, getting an approximate ratio of 6.
3. Multiply the empirical formula by this ratio to obtain the molecular formula \(C_6H_6Cl_6\), which signifies a molecule with 6 carbons, 6 hydrogens, and 6 chlorines.

Empirical Formula

The empirical formula of a chemical compound is a symbolic representation that shows the simplest integer ratio of the different atoms present in the substance. It doesn't provide the exact number of atoms as the molecular formula does, but it offers essential clues about the composition of the substance.

An empirical formula is determined through quantitative analysis, usually expressed after measuring the masses of each element in a sample and converting these masses to moles. With the empirical formula, \(CHCl\), it shows there is one atom each of carbon and hydrogen, and one atom of chlorine for every atom of carbon, in the simplest ratio. When exploring empirical formulas, it is common to encounter compositions that do not reflect common molecular structures; it's simply a basic ratio that necessitates further examination and information to determine the true molecular formula.

Aromatic Compounds

Aromatic compounds are a class of molecules characterized by stable ring structures with electrons that are delocalized over the entire ring. This unique electronic configuration imparts certain chemical properties such as enhanced stability and unique reactivity patterns.

Benzene, the parent compound of the aromatic family, illustrates the concept of aromaticity with its six carbon atoms forming a planar hexagonal ring. Each carbon in the ring has a 'p' orbital, which overlaps with those of its neighbors, creating a conjugated system with electrons that are shared across the ring. Because of this characteristic, benzene and its derivatives exhibit special types of reactions, most notably electrophilic aromatic substitution, where the aromatic structure is preserved even after the reaction.

Substitution Reactions

Substitution reactions involve replacing one atom or functional group in a molecule with another atom or group. In the context of aromatic compounds, this type of reaction is known as electrophilic aromatic substitution (EAS).

In EAS, the aromatic ring acts as a rich source of electrons and attracts electrophiles - species deficient in electrons. These electrophiles replace a hydrogen atom on the aromatic ring. The reaction typically follows several stages, starting with the formation of a high-energy intermediate state, before returning to a stabilized aromatic structure. The outcome preserves the aromaticity of the original compound, which is a hallmark of EAS.

Isomers

Isomers are compounds with the same molecular formula but different structural arrangements. There are several types of isomerism, among them positional isomerism, which occurs when functional groups are located in different positions on the same skeleton structure.

In the case of hexachlorobenzene with a molecular formula of \(C_6H_6Cl_6\), isomerism arises because the chlorine atoms can attach to different positions on the benzene ring, leading to distinct compounds. Positional isomers, like the six forms of hexachlorobenzene, each with unique 3D arrangements and physical properties, demonstrate the great diversity that can arise from the same set of atoms. Identifying and studying these isomers is fundamental in chemistry to understand the variety of ways molecules can assemble and behave.