The dissociation energy of `CH_(4)(g)` is 360 kcal `mol^(-1)` and that of `C_(2)H_(6)(g) is 620 kcal mol^(-1)`. The C-C bond energy

Options

A. `260 kcal mol^(-1)`
B. `180 kcal mol^(-1)`
C. `130 kcal mol^(-1)`
D. `80 kcal mol^(-1)`

Answer

To find the C-C bond energy using the given dissociation energies of methane (CH₄) and ethane (C₂H₆), we can follow these steps:

### Step 1: Understand the Bond Dissociation Energies
- The dissociation energy of methane (CH₄) is given as 360 kcal/mol.
- The dissociation energy of ethane (C₂H₆) is given as 620 kcal/mol.

### Step 2: Determine the Number of Bonds in Each Molecule
- Methane (CH₄) has 4 C-H bonds.
- Ethane (C₂H₆) has 6 C-H bonds and 1 C-C bond.

### Step 3: Calculate the Energy per C-H Bond in Methane
- The total energy for breaking all 4 C-H bonds in methane is 360 kcal/mol.
- Therefore, the energy per C-H bond can be calculated as:
\[ \text{Energy per C-H bond} = \frac{360 \text{ kcal/mol}}{4} = 90 \text{ kcal/mol} \]

### Step 4: Set Up the Equation for Ethane
- The total dissociation energy for ethane is 620 kcal/mol.
- This energy includes the energy required to break 6 C-H bonds and 1 C-C bond.
- Let \( E_{C-C} \) be the bond energy of the C-C bond.
- The equation can be set up as:
\[ 620 \text{ kcal/mol} = 6 \times (\text{Energy per C-H bond}) + E_{C-C} \]
- Substituting the value of the C-H bond energy:
\[ 620 = 6 \times 90 + E_{C-C} \]

### Step 5: Solve for the C-C Bond Energy
- Calculate \( 6 \times 90 \):
\[ 6 \times 90 = 540 \text{ kcal/mol} \]
- Substitute this value back into the equation:
\[ 620 = 540 + E_{C-C} \]
- Rearranging gives:
\[ E_{C-C} = 620 - 540 = 80 \text{ kcal/mol} \]

### Final Answer
- The bond energy of the C-C bond in ethane (C₂H₆) is **80 kcal/mol**.

---