Question

The dissociation energy of $C{H_4}$ is $400Kcal/mol$ and that of ethane is $670kcal/mol$ ,the $C - C$ bond energy is:
A.$270kcal$
B.$70kcal$
C.$200kcal$
D.$240kcal$

Answer 1

Hint:Bond dissociation energy is the energy required to break the bond or we can say that bond dissociation energy is used to measure the strength of a bond. By determining the bond energy of a single $C - H$ bond we can easily find out the bond energy of the $C - C$ bond.

Complete step-by-step answer:Here we see that $C{H_4}$ will dissociate as:
$C{H_4}(g) \to C(g) + 4H(g)$
dissociation energy $(\Delta H)$$ = 400Kcal/mol$
So, the bond dissociation energy for a single $C - H$ bond will be $ = \dfrac{{400}}{4}$
 since there are $4$ $CH$ present in $C{H_4}$so we divide the bond energy by $4$
therefore, bond energy of $C - H$ bond $ = 100kcal/mol$
The dissociation reaction of ${C_2}{H_6}$ is:
${C_2}{H_6}(g) \to 2C(g) + 6H(g)$
 dissociation energy $(\Delta H)$ $ = 670kcal/mol$
To find bond energy of $C - C$ bond we will use the formula:
$\Delta H = $ ( $C - C$ bond energy) $ + 6 \times $ ( $C - H$ bond energy)
$\Rightarrow C - C$ bond energy $ = \Delta H - 6 \times $ ( $C - H$ bond energy)
$\Rightarrow C - C$ bond energy $= 670 - (6 \times 100) \\$
$\Rightarrow C - C$ bond energy $= 670 - 600 \\$
$\Rightarrow C - C$ bond energy $= 70kcal/mol \\$

Additional information: The bond dissociation energy is the energy required by an endothermic process to break a bond and form two atomic or molecular fragments. The more the bond dissociation energy will be, the more will be the stability of the bond.

Hence the correct answer is Option B.

Note:The bond between fluorine atom and silicon atom will have the strongest dissociation energy while the covalent bonds between atoms or molecules will have weak dissociation energies. In diatomic molecules the value of bond dissociation energy is the same as the bond energy of the molecule.