Q16-19P - Organic Chemistry (Mcmurry)

Question

Refer to Table 6-3 on page 170 for a quantitative idea of the stability of a benzyl radical. How much more stable (in kJ/mol) is the benzyl radical than a primary alkyl radical? How does a benzyl radical compare in stability to an allyl radical?

Step-by-Step Solution

Answer

A benzyl radical is more stable than the primary alkyl radical by $\frac{\text{46 kJ}}{\text{mol}}$. The benzyl radical is stable as the allyl radical.

Step 1: Bond dissociation energy

Bond dissociation energy constitutes the energy needed to cleave a bond into radical fragments when the molecule is at gas phase at $\mathbf{25}\mathbf{°}\mathbf{C}$.It is measured in  $\frac{\mathrm{kJ}}{\mathrm{mol}}$ . A radical comprising lesser bond dissociation energy is more stable.

Step 2: Stability of different radicals

Bond dissociation energy estimates the energy needed to break a bond into two radical fragments. A radical will have higher energy and less stability than the initial compound that came from. The C-H bond dissociation energy for ethane is  $\frac{\text{421kJ}}{\text{mol}}$ and for the methyl group C-H bond for toulene is $\frac{\text{375 kJ}}{\text{mol}}$  .So less energy is required to form a benzyl radical than the ethyl radical. A benzyl radical is more stable than the primary alkyl radical by $\frac{\text{46 kJ}}{\text{mol}}$. The bond dissociation energy of allyl C-H bond is $\frac{\text{369 kJ}}{\text{mol}}$ .This indicates that the benzyl radical is stable as the allyl radical. 

Bond dissociation energy of molecules