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 \( C(g) + 4H(g) \rightarrow CH_4(g) \) with \( \Delta H = -166 \, \text{kJ} \), we can follow these steps:

### Step 1: Understand the Reaction
The reaction involves the formation of methane (\( CH_4 \)) from one carbon atom and four hydrogen atoms, both in the gaseous state. The negative value of \( \Delta H \) indicates that the reaction is exothermic, meaning energy is released when the bonds are formed.

### Step 2: Write the Bond Energy Equation
The change in enthalpy (\( \Delta H \)) for a reaction can be expressed in terms of bond energies. The equation can be written as:
\[ \Delta H = \text{Bond Energy of Reactants} - \text{Bond Energy of Products} \]
In this case, since we are starting with individual atoms (not molecules), the bond energy of the reactants is zero because there are no bonds to break.

### Step 3: Identify the Bond Energies
- For the reactants: \( C(g) + 4H(g) \) has no bonds, so the bond energy is \( 0 \).
- For the product: \( CH_4(g) \) has 4 C-H bonds. Let the bond energy of one C-H bond be \( BE_{C-H} \).

Thus, the bond energy of the products can be expressed as:
\[ \text{Bond Energy of Products} = 4 \times BE_{C-H} \]

### Step 4: Substitute into the Equation
Substituting the values into the bond energy equation we get:
\[ -166 \, \text{kJ} = 0 - (4 \times BE_{C-H}) \]
This simplifies to:
\[ -166 \, \text{kJ} = -4 \times BE_{C-H} \]

### Step 5: Solve for \( BE_{C-H} \)
Now, we can solve for the bond energy of the C-H bond:
\[ 4 \times BE_{C-H} = 166 \, \text{kJ} \]
\[ BE_{C-H} = \frac{166 \, \text{kJ}}{4} \]
\[ BE_{C-H} = 41.5 \, \text{kJ/mol} \]

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

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