Oxidation number of potassium in ` K _ 2 O`, ` K_2 O _ 2 and K O _ 2 ` , respectively, is :

Options

A. ` + 1 ,+2 and + 4 `
B. ` + 1, + 1 and +1 `
C. `+1,+4 and +2`
D. ` + 2, + 1 and + ( 1 ) /(2) `

Answer

To determine the oxidation number of potassium (K) 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 in \( K_2O \)

1. **Identify the oxidation state of oxygen**: In oxides, oxygen typically has an oxidation state of -2.
2. **Set up the equation**: For \( K_2O \), let the oxidation number of potassium be \( x \). The compound has 2 potassium atoms and 1 oxygen atom.
\[ 2x + (-2) = 0 \]
3. **Solve for \( x \)**:
\[ 2x - 2 = 0 \\ 2x = 2 \\ x = +1 \]
4. **Conclusion**: The oxidation number of potassium in \( K_2O \) is +1.

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

1. **Identify the oxidation state of oxygen in peroxides**: In peroxides, oxygen has an oxidation state of -1.
2. **Set up the equation**: For \( K_2O_2 \), let the oxidation number of potassium be \( x \). The compound has 2 potassium atoms and 2 oxygen atoms.
\[ 2x + 2(-1) = 0 \]
3. **Solve for \( x \)**:
\[ 2x - 2 = 0 \\ 2x = 2 \\ x = +1 \]
4. **Conclusion**: The oxidation number of potassium in \( K_2O_2 \) is +1.

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

1. **Identify the oxidation state of oxygen in superoxides**: In superoxides, oxygen has an oxidation state of -1/2.
2. **Set up the equation**: For \( KO_2 \), let the oxidation number of potassium be \( x \). The compound has 1 potassium atom and 2 oxygen atoms.
\[ x + 2(-\frac{1}{2}) = 0 \]
3. **Solve for \( x \)**:
\[ x - 1 = 0 \\ x = +1 \]
4. **Conclusion**: The oxidation number of potassium in \( KO_2 \) is +1.

### Final Answer
The oxidation numbers of potassium in \( K_2O \), \( K_2O_2 \), and \( KO_2 \) are all +1.