Question

Calculate from appropriate bond and stabilization energies the heats of reaction of chlorine with benzene to give (a) chlorobenzene and (b) 1,2 -dichloro-3,5-cyclohexadiene. Your answer should indicate that substitution is energetically more favorable than addition. Assume the bond dissociation energy for a \(\mathrm{C}=\mathrm{C} \pi\) bond to be \(65 \mathrm{kcal}\); the resonance stabilization energy of benzene to be \(36 \mathrm{kcal}\), and that of dichloro-3, 5 -cyclohexadiene to be \(3 \mathrm{kcal}\).

Short answer

The heat of reaction for chlorine substitution in benzene to form chlorobenzene is \(\Delta H_{substitution} = -23 \, \mathrm{kcal/mol}\), whereas the heat of reaction for addition to form 1,2-dichloro-3,5-cyclohexadiene is \(\Delta H_{addition} = -110 \, \mathrm{kcal/mol}\). As the substitution reaction has a higher (less negative) heat of reaction, it is energetically more favorable than the addition reaction, supporting the statement that chlorine substitution in benzene is preferred over addition.

Step-by-step solution

Calculate Cl-Cl dissociation energy and Cl-C bond energy

First, let's find the Cl–Cl dissociation energy and the Cl–C bond energy. The reactions that take place are: \[Cl_2 \rightarrow 2Cl \Rightarrow \text{Dissociation energy} = \mathrm{D(Cl-Cl)}\] \[Cl + C_6H_6 \rightarrow C_6H_5Cl\] From a table of bond dissociation energies, we can find: \[\mathrm{D(Cl-Cl)} = 59 \, \mathrm{kcal/mol}\] The energy required to form a Cl–C bond in chlorobenzene can also be found from a bond energy table: \[\mathrm{BE(C-Cl)} = 80 \, \mathrm{kcal/mol}\]

Calculate heat of reaction for Substitution (formation of chlorobenzene)

The overall substitution reaction can be written as: \[C_6H_6 + Cl_2 \rightarrow C_6H_5Cl + HCl\] To calculate the heat of reaction, we must sum up the dissociation energy of starting materials (Cl-Cl and C=C) and the stabilization energy of benzene, then subtract the energy released upon formation of the products (C-Cl and H-Cl bonds). \[\Delta H_{substitution} = \mathrm{D(Cl-Cl)} + \mathrm{D(C=C)} - \mathrm{BE(C-Cl)} - \mathrm{BE(H-Cl)} + \mathrm{Res. \, energy \,of\, benzene}\] \[\Delta H_{substitution} = 59 + 65 - 80 - 103 + 36 = -23 \, \mathrm{kcal/mol}\]

Calculate heat of reaction for Addition (formation of 1,2-dichloro-3,5-cyclohexadiene)

The overall addition reaction can be written as: \[C_6H_6 + 2 Cl_2 \rightarrow C_6H_4Cl_2 + 2 HCl\] To calculate the heat of reaction, we must sum up the dissociation energies of starting materials (2 Cl-Cl bonds and 2 C=C bonds) and the stabilization energy of benzene, then subtract the energy released upon formation of the products (2 C-Cl bonds and 2 H-Cl bonds) and the stabilization energy of 1,2-dichloro-3,5-cyclohexadiene. \[\Delta H_{addition} = 2 (\mathrm{D(Cl-Cl)} + \mathrm{D(C=C)}) - 2 (\mathrm{BE(C-Cl)} + \mathrm{BE(H-Cl)}) + \mathrm{Res. \, energy \,of\, benzene} - \mathrm{Res. \, energy \,of\, 1,2-dichloro-3,5-cyclohexadiene}\] \[\Delta H_{addition} = 2 (59 + 65) - 2 (80 + 103) + 36 - 3 = -110 \, \mathrm{kcal/mol}\]

Determine the energetically more favorable reaction

Now we can compare the heats of reaction for both substitution and addition: \[\Delta H_{substitution} = -23 \, \mathrm{kcal/mol}\] \[\Delta H_{addition} = -110 \, \mathrm{kcal/mol}\] Since the heat of reaction for the substitution (-23 kcal/mol) is higher (less negative) than the heat of reaction for the addition (-110 kcal/mol), the substitution is energetically more favorable than addition. This result supports the statement that chlorine substitution in benzene is energetically more favorable than addition.

Key concepts

Bond Dissociation Energy

Bond dissociation energy (BDE) is a crucial concept in thermochemistry and organic chemistry. It refers to the energy required to break a particular bond in a molecule to produce two radical fragments, each with one unpaired electron. In simple terms, BDE is the measure of the bond strength between two atoms.

When it comes to chlorobenzene synthesis, understanding the bond dissociation energy of the Cl-Cl bond is vital. The energy needed to break the Cl-Cl bond (found in tables as 59 kcal/mol) is one of the starting points for thermochemistry calculations, which are used to determine the overall energy changes during the reaction of benzene with chlorine. BDE is an intrinsic property determined experimentally and is influenced by the types of atoms and the molecular environment they're in.

To make learning about BDE more comprehensible, learners can visualize BDE as the 'energy price' to 'buy' individual atoms from their molecular 'partners.' Hence, for chlorine, we spend 59 kcal/mol to obtain two reactive chlorine atoms ready to bond with other atoms, such as carbon in benzene.

Stabilization Energy

Stabilization energy, especially in the context of organic compounds like benzene, is a concept that refers to the extra stability a molecule gains due to resonance or delocalization of electrons. Benzene, a ring with alternating double bonds, has a notable resonance stabilization energy, quantified as 36 kcal/mol.

The stabilization energy is significant because it impacts the molecule's reactivity. For instance, in the formation of chlorobenzene, benzene's stabilization energy must be considered to determine the actual energy cost of the reaction when one of its aromatic bonds is broken to accommodate a chlorine atom. In practice, this means that benzene is less reactive than what would be expected just by looking at the bond dissociation energies of its double bonds, due to this added 'stability cushion.'

A good educational analogy is to think of stabilization energy as a safety net that absorbs some of the 'falls' (or energy changes) a molecule takes during a reaction, making the molecule more stable and less reactive than its individual bonds might suggest.

Chlorobenzene Synthesis

Understanding the synthesis of chlorobenzene shines a light on the practical application of heats of reaction in organic chemistry. The process typically involves a substitution reaction, where chlorine replaces a hydrogen atom in benzene. As shown in the solution, calculating the energetics of chlorobenzene formation requires knowing the bond energies and stabilization energies involved.

During the synthesis, the relatively high stabilization energy of benzene makes the substitution reaction energetically more favorable compared to an addition reaction. This outcome is demonstrated through energy calculations, where the less negative heat of reaction indicates a more thermodynamically preferable process. Simplified, envision the synthesis like a dance, where chlorobenzene is formed by benzene 'dancing' with chlorine; they pair up after benzene releases a 'partner' hydrogen atom, which then couples with another chlorine atom to form HCl, all choreographed by the hands of thermodynamics.

Thermochemistry Calculations

Thermochemistry calculations are pivotal for understanding energetic aspects of chemical reactions such as formation of chlorobenzene. They involve quantifying the energy changes by balancing the input and the release of energies during bond making and breaking. The step-by-step solution models this by summing energy costs (dissociations and stabilization) and energy gains (formation of new bonds).

The calculations help predict whether a reaction is likely to occur spontaneously and can guide chemists in designing more effective synthetic routes. Just like a financial budget, where you weigh expenses against income, thermochemistry calculations require careful accounting of every energy 'transaction' in a reaction to predict the overall heat change (Delta H), with the 'bottom line' indicating if the process is energetically favorable or not.