Given : `C_(2)H_(6(g))rarr2C_((g))+6H_((g)), DeltaH=712 kcal`. The C - C bond energy is 112kcal, what is the C-H bond energy

Options

A. 88 kcal
B. 12 kcal
C. 50 kcal
D. 600 kcal

Explanation

To solve the problem, we need to determine the C-H bond energy given the reaction and the bond energy of the C-C bond.

### Step-by-Step Solution:

1. **Identify the Reaction and Given Data**:
The reaction provided is:
\[ C_2H_6(g) \rightarrow 2C(g) + 6H(g) \]
The enthalpy change (\(\Delta H\)) for this reaction is given as 712 kcal. The bond energy of the C-C bond is given as 112 kcal.

2. **Count the Bonds in Ethane (C2H6)**:
In ethane (C2H6), there is:
- 1 C-C bond
- 6 C-H bonds

3. **Set Up the Bond Energy Equation**:
The total bond energy change can be expressed as:
\[ \text{Total bond energy} = \text{Bond energy of C-C} + 6 \times \text{Bond energy of C-H} \]
This can be written as:
\[ 112 \text{ kcal} + 6 \times \text{Bond energy of C-H} = 712 \text{ kcal} \]

4. **Rearrange the Equation**:
To find the bond energy of C-H, we rearrange the equation:
\[ 6 \times \text{Bond energy of C-H} = 712 \text{ kcal} - 112 \text{ kcal} \]

5. **Calculate the Right Side**:
Calculate \(712 \text{ kcal} - 112 \text{ kcal}\):
\[ 712 - 112 = 600 \text{ kcal} \]

6. **Solve for the C-H Bond Energy**:
Now, divide by 6 to find the bond energy of one C-H bond:
\[ \text{Bond energy of C-H} = \frac{600 \text{ kcal}}{6} = 100 \text{ kcal} \]

### Final Answer:
The C-H bond energy is **100 kcal**.