The enthalpy change for the reaction, `C_(2)H_(6)(g)rarr2C(g)+6H(g)` is X kJ. The bond energy of C-H bond is :

Options

A. `(X)/(2)`
B. `(X)/(3)`
C. `(X)/(6)`
D. data insufficient

Explanation

To solve the problem regarding the enthalpy change for the reaction \( C_2H_6(g) \rightarrow 2C(g) + 6H(g) \) and to find the bond energy of the C-H bond, we can follow these steps:

### Step 1: Identify the bonds in the reactant
In ethane (\( C_2H_6 \)), there are:
- 1 C-C bond
- 6 C-H bonds

### Step 2: Write the expression for the total energy required to break these bonds
To break the bonds in \( C_2H_6 \) into individual atoms (2 carbon atoms and 6 hydrogen atoms), we need to account for the energy required to break both the C-C bond and the C-H bonds.

Let:
- \( z \) = bond energy of one C-H bond
- \( y \) = bond energy of the C-C bond

The total energy required to break all the bonds in \( C_2H_6 \) can be expressed as:
\[ \text{Total energy} = 6z + y \]

### Step 3: Relate the total energy to the enthalpy change
According to the problem, the enthalpy change for the reaction is given as \( X \) kJ. Therefore, we can set up the equation:
\[ 6z + y = X \]

### Step 4: Analyze the information given
The problem does not provide the value of \( y \) (the bond energy of the C-C bond). Without this information, we cannot isolate \( z \) (the bond energy of the C-H bond) because we have two unknowns in our equation.

### Conclusion
Since we do not have enough information to determine the bond energy of the C-H bond, we conclude that the data is insufficient to solve for \( z \).

### Final Answer
The bond energy of the C-H bond cannot be determined from the given information. Therefore, the answer is that the data is insufficient.

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