Bond energies of few bonds are given below :
`Cl-Cl="242.8 kJ mol"^(-1), H-Cl="431.8 kJ mol"^(-1)`.
`O-H="464 kJ mol"^(-1), O=O=""442 kJ mol"^(-1)`
Using the B.E., calculate `DeltaH` for the following reaction, `2Cl_(2) +2H_(2)Orarr4HCl+O_(2)`

Options

A. `"906 kJ mol"^(-1)`
B. `"172.4 kJ mol"^(-1)`
C. `"198.8 kJ mol"^(-1)`
D. `"442 kJ mol"^(-1)`

Explanation

To calculate the change in enthalpy (ΔH) for the reaction \(2Cl_2 + 2H_2O \rightarrow 4HCl + O_2\) using bond energies, we can follow these steps:

### Step 1: Identify the bonds broken and formed
In the given reaction:
- **Reactants**:
- \(Cl_2\) (2 moles) contains 1 Cl-Cl bond per molecule, so 2 Cl-Cl bonds are broken.
- \(H_2O\) (2 moles) contains 2 O-H bonds per molecule, so 4 O-H bonds are broken in total.

- **Products**:
- \(HCl\) (4 moles) contains 1 H-Cl bond per molecule, so 4 H-Cl bonds are formed.
- \(O_2\) contains 1 O=O bond.

### Step 2: Write the bond energy equation
Using the bond energies provided:
- Cl-Cl bond energy = \(242.8 \, kJ/mol\)
- H-Cl bond energy = \(431.8 \, kJ/mol\)
- O-H bond energy = \(464 \, kJ/mol\)
- O=O bond energy = \(442 \, kJ/mol\)

The formula for ΔH is:
\[ \Delta H = \text{(Bond energies of bonds broken)} - \text{(Bond energies of bonds formed)} \]

### Step 3: Calculate the bond energies of the reactants
- For \(Cl_2\):
\[ 2 \text{ Cl-Cl bonds} = 2 \times 242.8 \, kJ/mol = 485.6 \, kJ \]
- For \(H_2O\):
\[ 2 \text{ H2O} \rightarrow 4 \text{ O-H bonds} = 4 \times 464 \, kJ/mol = 1856 \, kJ \]
- Total bond energy of reactants:
\[ \text{Total (Reactants)} = 485.6 \, kJ + 1856 \, kJ = 2341.6 \, kJ \]

### Step 4: Calculate the bond energies of the products
- For \(HCl\):
\[ 4 \text{ HCl bonds} = 4 \times 431.8 \, kJ/mol = 1727.2 \, kJ \]
- For \(O_2\):
\[ 1 \text{ O=O bond} = 442 \, kJ \]
- Total bond energy of products:
\[ \text{Total (Products)} = 1727.2 \, kJ + 442 \, kJ = 2169.2 \, kJ \]

### Step 5: Calculate ΔH
Now substituting the values into the ΔH equation:
\[ \Delta H = 2341.6 \, kJ - 2169.2 \, kJ = 172.4 \, kJ \]

### Final Answer
\[ \Delta H = 172.4 \, kJ/mol \]