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 from the given dissociation energies of methane (CH₄) and ethane (C₂H₆), we can follow these steps:

### Step 1: Calculate the dissociation energy of one C-H bond in CH₄
- The dissociation energy of CH₄ is given as 360 kcal/mol.
- Since there are 4 C-H bonds in CH₄, the energy for one C-H bond is:

\[ \text{Energy per C-H bond} = \frac{360 \text{ kcal/mol}}{4} = 90 \text{ kcal/mol} \]

### Step 2: Write the dissociation energy equation for C₂H₆
- The dissociation energy of C₂H₆ is given as 620 kcal/mol.
- In C₂H₆, there are 6 C-H bonds and 1 C-C bond. Thus, we can express the total dissociation energy as:

\[ \text{Dissociation energy of C₂H₆} = (\text{Energy per C-H bond} \times 6) + (\text{Energy of C-C bond}) \]

### Step 3: Substitute the known values into the equation
- We already calculated the energy per C-H bond as 90 kcal/mol. Substituting this into the equation gives:

\[ 620 \text{ kcal/mol} = (90 \text{ kcal/mol} \times 6) + (\text{Energy of C-C bond}) \]

### Step 4: Calculate the total energy of the C-H bonds
- Calculate the total energy contributed by the 6 C-H bonds:

\[ 90 \text{ kcal/mol} \times 6 = 540 \text{ kcal/mol} \]

### Step 5: Solve for the C-C bond energy
- Now, we can rearrange the equation to solve for the C-C bond energy:

\[ \text{Energy of C-C bond} = 620 \text{ kcal/mol} - 540 \text{ kcal/mol} = 80 \text{ kcal/mol} \]

### Final Answer
The C-C bond energy is **80 kcal/mol**.

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