The reaction `3O_(2)(g) rarr 2O_(3)(g), Delta_(r )H > 0`. What can be concluded about average energy per bond in `O_(2)` and `O_(3)`?

Options

A. The average energy per bond in`O_2` is greater than the average bond energy per bond in `O_3`
B. The average energy per bond in `O_2` is less than the average energy per bond in `O_3`
C. The average energy per bond in `O_2` is same as average energy per bond in `O_3`
D. No conclusion can be drawn about the average bond energies from this information alone

Explanation

To solve the problem regarding the reaction \(3O_2(g) \rightarrow 2O_3(g)\) with \(\Delta_r H > 0\), we need to analyze the average bond energies of \(O_2\) and \(O_3\).

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
The given reaction is endothermic, indicated by the positive \(\Delta_r H\). This means that energy is absorbed during the reaction.

2. **Write the Expression for Enthalpy Change**:
The enthalpy change for the reaction can be expressed in terms of bond energies:
\[ \Delta_r H = \text{Total bond energy of reactants} - \text{Total bond energy of products} \]
For this reaction:
\[ \Delta_r H = 3 \times \text{(Bond energy of } O_2) - 2 \times \text{(Bond energy of } O_3) \]

3. **Define Bond Energies**:
- The bond energy of \(O_2\) (which has a double bond) can be denoted as \(E_{O_2}\).
- The bond energy of \(O_3\) (which has one double bond and one single bond) can be denoted as \(E_{O_3}\).

4. **Express the Bond Energies**:
Since \(O_2\) has 2 bonds per molecule, the total bond energy for 3 moles of \(O_2\) is:
\[ 3 \times 2 \times E_{O_2} = 6E_{O_2} \]
For \(O_3\), which has 3 bonds in total (2 bonds in 2 moles):
\[ 2 \times 3 \times E_{O_3} = 6E_{O_3} \]

5. **Set Up the Equation**:
Now substituting these into the enthalpy change equation:
\[ \Delta_r H = 6E_{O_2} - 6E_{O_3} \]

6. **Analyze the Sign of \(\Delta_r H\)**:
Since \(\Delta_r H > 0\), we can write:
\[ 6E_{O_2} - 6E_{O_3} > 0 \]
Dividing through by 6 gives:
\[ E_{O_2} > E_{O_3} \]

7. **Conclusion**:
This indicates that the average energy per bond in \(O_2\) is greater than that in \(O_3\):
\[ \text{Average energy per bond in } O_2 > \text{Average energy per bond in } O_3 \]

### Final Answer:
The average energy per bond in \(O_2\) is greater than the average energy per bond in \(O_3\).