Formation of ozone takes place as `O_(2)(g) + O(g) rarr O_(3)(g) , DeltaH^(@) =- 107 . 2kJ` . Assuming `O = O` bond energy as `498.8 kJ mol^(-1)`, the average bond energy of ozone is

Options

A. `391.6 kJmol^(-1)`
B. ` 606 . 0 kJmol^(-1)`
C. ` 107.2kJ mol^(-1)`
D. ` 302 .6 kJ mol^(-1)`

Explanation

To find the average bond energy of ozone (O₃), we can use the given reaction and the bond energies involved. Let's break it down step by step.

### Step 1: Write the reaction and identify the given values
The formation of ozone is represented by the reaction:
\[ O_2(g) + O(g) \rightarrow O_3(g) \]
Given:
- \(\Delta H^\circ = -107.2 \, \text{kJ}\)
- Bond energy of \(O=O\) (double bond) = \(498.8 \, \text{kJ/mol}\)

### Step 2: Understand the bond energies involved
In the reaction, we have:
- One \(O=O\) bond in \(O_2\)
- One \(O\) atom that will form bonds in ozone
- Ozone (O₃) has a resonance structure, which means it has equivalent bonds that can be considered when calculating average bond energy.

### Step 3: Write the expression for the change in enthalpy
The change in enthalpy for the reaction can be expressed in terms of bond energies:
\[ \Delta H^\circ = \text{Bond energies of reactants} - \text{Bond energies of products} \]
For this reaction:
- Bond energy of \(O_2\) (1 O=O bond) = \(498.8 \, \text{kJ/mol}\)
- Bond energy of \(O\) = \(0 \, \text{kJ/mol}\) (since it is a single atom)
- Bond energy of \(O_3\) can be represented as \(3 \times BE_{O}\) (since there are three bonds in ozone).

### Step 4: Set up the equation
Substituting the values into the equation:
\[ -107.2 \, \text{kJ} = (498.8 + 0) - 3 \times BE_{O} \]
This simplifies to:
\[ -107.2 = 498.8 - 3 \times BE_{O} \]

### Step 5: Rearranging the equation
Rearranging gives:
\[ 3 \times BE_{O} = 498.8 + 107.2 \]
\[ 3 \times BE_{O} = 606 \, \text{kJ} \]

### Step 6: Solve for the average bond energy of ozone
Now, divide by 3 to find the average bond energy:
\[ BE_{O} = \frac{606}{3} = 202 \, \text{kJ/mol} \]

### Conclusion
The average bond energy of ozone (O₃) is:
\[ \boxed{202 \, \text{kJ/mol}} \]