Bond dissociation energy of `CH_(4)` si 360 kJ/mol and `C_(2)H_(6)` has 620 kJ mol. Then bond dissociation energy of C-C bond is :-

Options

A. 170 kJ/mol
B. 50 kJ/mol
C. 80 kJ/mol
D. 220 kJ/mol

Explanation

To find the bond dissociation energy of the C-C bond in C2H6, we can follow these steps:

### Step 1: Understand the Bond Dissociation Energy of CH4
The bond dissociation energy (BDE) of CH4 (methane) is given as 360 kJ/mol. This energy is required to break all four C-H bonds in CH4 to form gaseous carbon and hydrogen atoms.

### Step 2: Calculate the Energy per C-H Bond in CH4
Since CH4 has four C-H bonds, we can calculate the bond dissociation energy for one C-H bond:
\[ \text{BDE of one C-H bond} = \frac{\text{Total BDE of CH4}}{\text{Number of C-H bonds}} = \frac{360 \text{ kJ/mol}}{4} = 90 \text{ kJ/mol} \]

### Step 3: Understand the Bond Dissociation Energy of C2H6
The bond dissociation energy of C2H6 (ethane) is given as 620 kJ/mol. In C2H6, there are six C-H bonds and one C-C bond.

### Step 4: Write the Reaction for C2H6
The reaction for the dissociation of C2H6 into gaseous carbon and hydrogen can be represented as:
\[ \text{C2H6 (g)} \rightarrow 2 \text{C (g)} + 6 \text{H (g)} \]
The total energy change (ΔH) for this reaction is given as 620 kJ/mol.

### Step 5: Set Up the Equation for C2H6
The total bond dissociation energy for C2H6 can be expressed in terms of the bond energies:
\[ \Delta H = 6 \times \text{BDE of C-H} + \text{BDE of C-C} \]
Substituting the known values:
\[ 620 \text{ kJ/mol} = 6 \times 90 \text{ kJ/mol} + \text{BDE of C-C} \]

### Step 6: Solve for the C-C Bond Dissociation Energy
Calculating the left side:
\[ 620 \text{ kJ/mol} = 540 \text{ kJ/mol} + \text{BDE of C-C} \]
Now, isolate the BDE of the C-C bond:
\[ \text{BDE of C-C} = 620 \text{ kJ/mol} - 540 \text{ kJ/mol} = 80 \text{ kJ/mol} \]

### Conclusion
The bond dissociation energy of the C-C bond in C2H6 is **80 kJ/mol**.

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