The oxidation number of oxygen in `K_(2)O, K_(2)O_(2)` and `KO_(2)` are respecitvely

Options

A. `-2, -2, -2`
B. `-2, -1, -2`
C. `-1, -2, -(1)/(2)`
D. `-2, -1, -(1)/(2)`

Explanation

To find the oxidation number of oxygen in the compounds \( K_2O \), \( K_2O_2 \), and \( KO_2 \), we will analyze each compound step by step.

### Step 1: Determine the oxidation number of oxygen in \( K_2O \)

1. **Identify the oxidation state of potassium (K)**: Potassium is an alkali metal and typically has an oxidation state of +1.
2. **Set up the equation**: Let the oxidation state of oxygen be \( x \).
\[ 2(+1) + x = 0 \]
(The overall charge of the compound is zero since it is neutral.)
3. **Solve for \( x \)**:
\[ 2 + x = 0 \implies x = -2 \]
4. **Conclusion**: The oxidation number of oxygen in \( K_2O \) is **-2**.

### Step 2: Determine the oxidation number of oxygen in \( K_2O_2 \)

1. **Identify the oxidation state of potassium (K)**: Again, potassium has an oxidation state of +1.
2. **Set up the equation**: Let the oxidation state of oxygen be \( x \).
\[ 2(+1) + 2x = 0 \]
(There are 2 oxygen atoms in this compound.)
3. **Solve for \( x \)**:
\[ 2 + 2x = 0 \implies 2x = -2 \implies x = -1 \]
4. **Conclusion**: The oxidation number of oxygen in \( K_2O_2 \) is **-1**.

### Step 3: Determine the oxidation number of oxygen in \( KO_2 \)

1. **Identify the oxidation state of potassium (K)**: Potassium has an oxidation state of +1.
2. **Set up the equation**: Let the oxidation state of oxygen be \( x \).
\[ 1 + 2x = 0 \]
(There are 2 oxygen atoms in this compound, and it is a superoxide.)
3. **Solve for \( x \)**:
\[ 1 + 2x = 0 \implies 2x = -1 \implies x = -\frac{1}{2} \]
4. **Conclusion**: The oxidation number of oxygen in \( KO_2 \) is **-1/2**.

### Final Summary of Oxidation States
- In \( K_2O \): -2
- In \( K_2O_2 \): -1
- In \( KO_2 \): -1/2

### Final Answer
The oxidation numbers of oxygen in \( K_2O \), \( K_2O_2 \), and \( KO_2 \) are respectively **-2, -1, and -1/2**.

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