Calculate the bond energy of `Cl-Cl` bond from the following data:
`CH_(4)(g)+Cl_(2)(g)rarrCH_(3)Cl(g)+HCl(g), Delta H= -100.3 kJ`. Also the bond enthalpies of `C-H, C-Cl,H-Cl` bonds are `413,326` and `431 kJ mol^(-1)` respectively.

Explanation

To calculate the bond energy of the Cl-Cl bond from the given reaction data, we will follow these steps:

### Step 1: Write the reaction and the given data
The reaction provided is:
\[ \text{CH}_4(g) + \text{Cl}_2(g) \rightarrow \text{CH}_3\text{Cl}(g) + \text{HCl}(g) \]
The enthalpy change (\(\Delta H\)) for this reaction is given as:
\[ \Delta H = -100.3 \, \text{kJ} \]

### Step 2: Identify the bonds in reactants and products
In the reactants:
- CH₄ has 4 C-H bonds.
- Cl₂ has 1 Cl-Cl bond.

In the products:
- CH₃Cl has 3 C-H bonds and 1 C-Cl bond.
- HCl has 1 H-Cl bond.

### Step 3: Write the bond energy equation
Using the formula for bond dissociation enthalpy:
\[ \Delta H = \text{(Bonds broken)} - \text{(Bonds formed)} \]
We can express this as:
\[ \Delta H = [4 \times \text{(C-H)} + 1 \times \text{(Cl-Cl)}] - [3 \times \text{(C-H)} + 1 \times \text{(C-Cl)} + 1 \times \text{(H-Cl)}] \]

### Step 4: Substitute the known bond energies
The bond energies are given as:
- C-H bond = 413 kJ/mol
- C-Cl bond = 326 kJ/mol
- H-Cl bond = 431 kJ/mol

Substituting these values into the equation:
\[ -100.3 = [4 \times 413 + 1 \times X] - [3 \times 413 + 1 \times 326 + 1 \times 431] \]

### Step 5: Calculate the left side of the equation
Calculating the left side:
- Bonds broken:
\[ 4 \times 413 = 1652 \, \text{kJ} \]
- Bonds formed:
\[ 3 \times 413 = 1239 \, \text{kJ} \]
\[ 1239 + 326 + 431 = 1996 \, \text{kJ} \]

### Step 6: Substitute and simplify the equation
Now substituting these values back into the equation:
\[ -100.3 = [1652 + X] - 1996 \]
This simplifies to:
\[ -100.3 = 1652 + X - 1996 \]
\[ -100.3 = X - 344 \]

### Step 7: Solve for X (the bond energy of Cl-Cl)
Rearranging gives:
\[ X = -100.3 + 344 \]
Calculating this:
\[ X = 243.7 \, \text{kJ/mol} \]

### Final Answer
The bond energy of the Cl-Cl bond is:
\[ \boxed{243.7 \, \text{kJ/mol}} \]