Arrange `O_(2),O_(2)^(-),O_(2)^(2-),O_(2)^(+)` in increasing order of bond energy.

Answer

To arrange \( O_2, O_2^-, O_2^{2-}, O_2^+ \) in increasing order of bond energy, we need to determine the bond order for each species. The bond energy is directly proportional to the bond order, so we will calculate the bond order for each molecule.

### Step-by-Step Solution:

1. **Determine the number of electrons in each species:**
- \( O_2 \): Each oxygen atom has 8 electrons, so for two oxygen atoms, the total is \( 16 \) electrons.
- \( O_2^- \): This species has one extra electron, giving a total of \( 17 \) electrons.
- \( O_2^{2-} \): This species has two extra electrons, resulting in \( 18 \) electrons.
- \( O_2^+ \): This species has one less electron, resulting in \( 15 \) electrons.

2. **Calculate the bond order for each species:**
- **Bond order** is calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \]
- For \( O_2 \) (16 electrons): The bond order is \( 2 \).
- For \( O_2^- \) (17 electrons): The bond order decreases by \( 0.5 \) to \( 1.5 \).
- For \( O_2^{2-} \) (18 electrons): The bond order decreases further to \( 1 \).
- For \( O_2^+ \) (15 electrons): The bond order increases to \( 2.5 \).

3. **Summarize the bond orders:**
- \( O_2 \): Bond order = \( 2 \)
- \( O_2^- \): Bond order = \( 1.5 \)
- \( O_2^{2-} \): Bond order = \( 1 \)
- \( O_2^+ \): Bond order = \( 2.5 \)

4. **Arrange the species in increasing order of bond energy:**
- Since bond energy is directly proportional to bond order, we can arrange them based on their bond orders:
- \( O_2^{2-} \) (Bond order = 1)
- \( O_2^- \) (Bond order = 1.5)
- \( O_2 \) (Bond order = 2)
- \( O_2^+ \) (Bond order = 2.5)

Thus, the increasing order of bond energy is:
\[ O_2^{2-} < O_2^- < O_2 < O_2^+ \]