Question

Calculate the \(\Delta H^{\circ}\) for the following reaction step. What can you say regarding the possibility of bromination at a vinylic hydrogen? $$ \mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{Br} \cdot \longrightarrow \mathrm{CH}_{2}=\mathrm{CH} \cdot \quad+\quad \mathrm{HBr} $$

Short answer

Answer: Bromination at a vinylic hydrogen is less likely to occur spontaneously under standard conditions because the standard enthalpy change is positive, indicating that the reaction is endothermic and requires additional energy input to proceed.

Step-by-step solution

Identify the bonds involved in the reaction

In the given reaction, there are three types of bonds involved- C=C, Br•, and C-H. The reaction can be represented as breaking a C=C bond and a Br• bond, followed by the formation of a new C-H bond and a new C-Br bond.

Use bond dissociation energies

We will now use the bond dissociation energies (BDE) of the involved bonds to calculate the \(\Delta H^{\circ}\) for the reaction. The BDE values are as follows (all values in kJ/mol): C=C: 612 Br•: 193 C-H: 413 C-Br: 276 The equation for \(\Delta H^{\circ}\) calculation using BDE values is: $$ \Delta H^{\circ} = \sum \mathrm{BDE}(\text{bonds broken}) - \sum \mathrm{BDE}(\text{bonds formed}) $$

Calculate \(\Delta H^{\circ}\) for the reaction

According to the given reaction: Bonds broken: 1 C=C and 1 Br• Bonds formed: 1 C-H and 1 C-Br Using the BDE values, we can now calculate \(\Delta H^{\circ}\): $$ \Delta H^{\circ} = [(1\times 612) + (1 \times 193)] - [(1 \times 413) + (1 \times 276)] = (612 + 193) - (413 + 276) = 805 - 689 = 116 \, \text{kJ/mol} $$

Evaluate the possibility of bromination at a vinylic hydrogen

We found that the standard enthalpy change (\(\Delta H^{\circ}\)) for this reaction is positive, which means the reaction is endothermic. An endothermic reaction requires energy to be added to the system for the reaction to proceed. Thus, bromination at a vinylic hydrogen is less likely to occur spontaneously under standard conditions based on the positive \(\Delta H^{\circ}\). However, that does not mean the reaction is impossible; rather, it requires additional energy, such as external heat or a catalyst, to overcome the energy barrier and proceed. In conclusion, bromination at a vinylic hydrogen is less likely to occur spontaneously under standard conditions, but it can still be achieved under certain conditions by providing the required energy input or using a catalyst.

Key concepts

Bond Dissociation Energy

Bond dissociation energy (BDE) is a crucial concept in understanding how chemical reactions occur and how much energy is needed to break certain bonds. It represents the amount of energy required to break a bond in a molecule, producing atoms or radicals. This is measured in kilojoules per mole (kJ/mol).

In a chemical reaction, certain bonds are broken, and others are formed. To calculate the overall energy change of a reaction, we need to look at the bond dissociation energies of all the bonds that are involved. This involves:

• Calculating the total energy needed to break the original bonds in the reactants.
• Calculating the total energy released when new bonds are formed in the products.

The overall enthalpy change (\( \Delta H^{\circ} \)) for a reaction can then be calculated using the equation: \[\Delta H^{\circ} = \sum \text{BDE(bonds broken)} - \sum \text{BDE(bonds formed)}\]In this reaction, the relevant bond energies are:

• C=C bond: 612 kJ/mol
• Br• bond: 193 kJ/mol
• C-H bond: 413 kJ/mol
• C-Br bond: 276 kJ/mol

Calculating with these values gives an idea if the reaction is endothermic or exothermic, helping predict if the reaction will occur spontaneously.

Vinylic Hydrogen

Vinylic hydrogen refers to a hydrogen atom that is bonded to a carbon atom, which is part of a carbon-carbon double bond (C=C). These hydrogens are associated with molecules that have double-bonded carbon atoms, such as in alkenes like ethylene (CH₂=CH₂).

Vinylic hydrogens are typically less reactive than other types of hydrogens due to the stability of the double bond. The electron cloud in the double bond provides additional stability, making these hydrogens less likely to participate in reactions compared to hydrogens bonded to other carbon configurations.

In the case of bromination, attempting to substitute a vinylic hydrogen with a bromine (Br•) involves breaking a relatively strong C-H bond and forming a new C-Br bond. This can be energetically unfavorable due to:

• The high bond dissociation energy required to break the C-H bond.
• The strength and stability of the existing double bond configuration.

This results in a positive enthalpy change (\( \Delta H^{\circ} \)), indicative of an endothermic reaction where energy input is required for the reaction to proceed.

Endothermic Reaction

An endothermic reaction is one where energy is absorbed from the surroundings. This is recognized by a positive enthalpy change (\( \Delta H^{\circ} \)), meaning it requires an input of energy to proceed.

In the given reaction involving the bromination of ethylene, the enthalpy change is calculated to be +116 kJ/mol. This positive value indicates that the reaction is endothermic. Here's why this matters:

• Endothermic reactions are often not spontaneous, meaning they don't happen on their own without external energy input.
• Such reactions might need additional energy, like heat, to proceed.

Understanding whether a reaction is endothermic helps in determining the conditions needed for it to occur. In industrial or laboratory settings, strategies to overcome this energy barrier involve using catalysts or altering reaction conditions (such as increasing temperature) to make the reaction feasible.