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 analyze the reaction \(3O_2(g) \rightarrow 2O_3(g)\) with \(\Delta_r H > 0\), we need to draw conclusions about the average energy per bond in \(O_2\) and \(O_3\).

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
The given reaction is endothermic because \(\Delta_r H > 0\). This means that energy is absorbed during the reaction.

2. **Understand Bond Energies**:
The bond energy is the amount of energy required to break a bond. In an endothermic reaction, the total bond energy of the reactants is less than that of the products.

3. **Write the Bond Energy Equation**:
For the reaction, we can express the change in enthalpy (\(\Delta_r H\)) in terms of bond energies:
\[ \Delta_r H = \text{Total bond energy of reactants} - \text{Total bond energy of products} \]
For our reaction:
\[ \Delta_r H = 3 \times (\text{Bond energy of } O_2) - 2 \times (\text{Bond energy of } O_3) \]

4. **Substitute Known Values**:
Let \(E_{O_2}\) be the average bond energy per bond in \(O_2\) and \(E_{O_3}\) be the average bond energy per bond in \(O_3\).
- \(O_2\) has a double bond, so each \(O_2\) contributes 2 bonds.
- \(O_3\) has a resonance structure with an average of 1.5 bonds per \(O_3\) molecule (due to the presence of a double bond and a single bond).
Thus, we can rewrite the equation as:
\[ \Delta_r H = 3 \times 2E_{O_2} - 2 \times 1.5E_{O_3} \]

5. **Set Up the Inequality**:
Since \(\Delta_r H > 0\), we have:
\[ 6E_{O_2} - 3E_{O_3} > 0 \]
Rearranging gives:
\[ 6E_{O_2} > 3E_{O_3} \]
Dividing both sides by 3:
\[ 2E_{O_2} > E_{O_3} \]

6. **Conclusion**:
This implies:
\[ E_{O_2} > \frac{1}{2}E_{O_3} \]
Since \(E_{O_3}\) is based on the average bond energy of three bonds, we can conclude that the average energy per bond in \(O_2\) is greater than the average energy per bond in \(O_3\).

Thus, the correct conclusion is that the average energy per bond in \(O_2\) is greater than the 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 \(O_3\).**