Question

The dissociation energy of $C{H_4}$and ${C_2}{H_6}$are respectively $360$ and ${\text{620kcal/mol}}$. The bond energy of $C - C$ bond is:
A.$260{\text{kcal/mol}}$
B.${\text{180kcal/mol}}$
C.${\text{130kcal/mol}}$
D.${\text{80kcal/mol}}$

Answer 1

Hint:
We know that bond dissociation energy is the energy required to break a bond and form two atomic or molecular fragments. It is a type of endothermic process, as lots of energy is required for breaking bonds. As the electronegativity decreases among the functional groups the bond dissociation energy decreases.

Complete step by step answer:
Given:
Dissociation energy of $C{H_4}$= $320kJ/mol$
Dissociation energy of ${C_2}{H_6}$= $620kJ/mol$
Methane breaks into carbon and hydrogen. Here we have four carbon to hydrogen bonds. The expression is written as,
$C{H_4} \to C + 4H$
So, the bond dissociation energy of one C-H bond can be calculated as = $\dfrac{{360}}{4} = 90kJ/mol$
For ethane, we have one carbon to carbon bond and six carbon to hydrogen bonds.
Ethane will break down as,
${C_2}{H_6} \to 2C + 6H$
We know the heat required in the difference of bond dissociation energy of reactant and product.
$\Delta H = {(B.E)_R} - {(B.E)_P}$
Here, B.E = bond dissociation energy, R= reactant and P= product.
Since, the product contains elements as a whole, hence, B.E of product=0
$620 = {(B.E)_R}$
$620 = (6 \times B.{E_{C - H}}) + (1 \times B.{E_{C - C}})$
On substituting the known values we get,
$ \Rightarrow 620 = (6 \times 90) + B.{E_{C - C}}$
$ \Rightarrow B.{E_{C - C}} = 620 - 540$
On simplification we get,
$ \Rightarrow B.{E_{C - C}} = 80kJ/mol$
Hence, the bond dissociation energy of C-C bond is $80kJ/mol.$
The correct answer is option D.

Note: We need to know that the bond dissociation energy increases as the difference in the electronegativity of bonded atoms increases. For a highly stable bond the dissociation energy is higher. In alkyl groups, the dissociation energy of double bonded compounds which consist of one sigma and one pi bond is much higher than for single bonded compounds which contain only one sigma bond. Alkyl halides being more electronegative than other functional groups require high bond dissociation energy.