Consider the following molecules
`underset(I)(O_(2)),O_(2)underset(II)(("AsF"_(6))),underset(III)(KO_(2))`
Choose the correct answer.

Options

A. The correct decreasing bond order is `II gt I gt III`.
B. The correct decreasing order of bond length is `III gt II gt I`.
C. The bond strength of I is less than that of III.
D. Bond dissociation energy is highest in case of III.

Explanation

To solve the question regarding the bond order of the given molecules \(O_2\), \(AsF_6\), and \(KO_2\), we will analyze each molecule step by step.

### Step 1: Understanding Bond Order
Bond order is defined as the number of chemical bonds between a pair of atoms. It can be calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]
Higher bond order indicates stronger bonds.

### Step 2: Analyzing \(O_2\)
For molecular oxygen (\(O_2\)):
- It has a total of 16 electrons.
- The molecular orbital configuration is: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \pi_{2p_y}^*^1\).
- Bond order calculation:
\[ \text{Bond Order of } O_2 = \frac{(10 - 6)}{2} = 2 \]

### Step 3: Analyzing \(AsF_6\)
For \(AsF_6\):
- In this case, \(AsF_6\) can be viewed as a complex where the \(O_2\) is present as \(O_2^+\).
- The bond order for \(O_2^+\) is calculated similarly:
\[ \text{Bond Order of } O_2^+ = \frac{(10 - 5)}{2} = 2.5 \]

### Step 4: Analyzing \(KO_2\)
For potassium superoxide (\(KO_2\)):
- In \(KO_2\), the \(O_2\) exists as \(O_2^-\).
- The bond order for \(O_2^-\) is:
\[ \text{Bond Order of } O_2^- = \frac{(10 - 7)}{2} = 1.5 \]

### Step 5: Comparing Bond Orders
Now we can summarize the bond orders:
- \(O_2\) has a bond order of 2.
- \(AsF_6\) (as \(O_2^+\)) has a bond order of 2.5.
- \(KO_2\) (as \(O_2^-\)) has a bond order of 1.5.

### Step 6: Conclusion
The decreasing order of bond strength (and hence bond order) is:
\[ AsF_6 > O_2 > KO_2 \]
Thus, the correct answer is option A: \(AsF_6\) (II), \(O_2\) (I), \(KO_2\) (III).