Given that `C(g)+4H(g)to CH_(4)(g) , Delta H =-166 kJ`. The bond energy of the C - H bond will be

Options

A. 208 kJ/mole
B. `-41.5` kJ/mole
C. 832 kJ/mole
D. 566 kJ/mole

Answer

To find the bond energy of the C-H bond in the reaction given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction and Given Data:**
The reaction provided is:
\[ C(g) + 4H(g) \rightarrow CH_4(g) \]
The enthalpy change (\(\Delta H\)) for this reaction is given as \(-166 \, \text{kJ}\).

2. **Understand the Meaning of \(\Delta H\):**
The negative sign indicates that the reaction is exothermic, meaning energy is released when one mole of methane (\(CH_4\)) is formed from carbon and hydrogen gases.

3. **Determine the Number of C-H Bonds:**
In the methane molecule (\(CH_4\)), there are 4 C-H bonds.

4. **Relate \(\Delta H\) to Bond Energies:**
The total energy released (\(-166 \, \text{kJ}\)) corresponds to the formation of 4 C-H bonds. Therefore, the bond energy for one C-H bond can be calculated by dividing the total energy change by the number of bonds formed.

5. **Calculate the Bond Energy of C-H:**
\[ \text{Bond Energy of C-H} = \frac{\Delta H}{\text{Number of C-H bonds}} = \frac{-166 \, \text{kJ}}{4} \]
\[ \text{Bond Energy of C-H} = -41.5 \, \text{kJ/mol} \]

### Final Answer:
The bond energy of the C-H bond is \(-41.5 \, \text{kJ/mol}\).

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