Given that, `C(g)+4H(g)rarrCH_(4)(g),DeltaH=-166kJ`. The bond energy C-H will be

Options

A. `-416` kJ/mol
B. `-41.5` kJ/mol
C. 832 kJ/mol
D. None

Answer

To find the bond energy of the C-H bond in the reaction \( C(g) + 4H(g) \rightarrow CH_4(g) \) with \(\Delta H = -166 \, \text{kJ}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction given is:
\[ C(g) + 4H(g) \rightarrow CH_4(g) \]
This indicates that one carbon atom combines with four hydrogen atoms to form methane (\(CH_4\)).

2. **Understand the Enthalpy Change**:
The enthalpy change (\(\Delta H\)) for this reaction is given as \(-166 \, \text{kJ}\). This negative value indicates that the reaction is exothermic, meaning energy is released when the bonds are formed.

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

4. **Calculate the Bond Energy**:
The bond energy for one C-H bond can be calculated by dividing the total enthalpy change by the number of bonds formed:
\[ \text{Bond Energy (C-H)} = \frac{\Delta H}{\text{Number of C-H bonds}} = \frac{-166 \, \text{kJ}}{4} \]

5. **Perform the Calculation**:
\[ \text{Bond Energy (C-H)} = \frac{-166}{4} = -41.5 \, \text{kJ/mol} \]

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