Salt `P+ H_(2)SO_4rarrRoverset(BaCl_2)rarr` white ppt `(P)` is paramagnetic in nature and contains about 55% K .So (P) is

Options

A. `KO_2`
B. `K_2O`
C. `K_(2) SO_(4)`
D. `K_(2)O_2`

Answer

To solve the problem, we need to identify the salt \( P \) based on the given clues: it is paramagnetic and contains about 55% potassium. Let's analyze the options step by step.

### Step 1: Understanding Paramagnetism
Paramagnetic substances have unpaired electrons. Therefore, we need to find a compound that has unpaired electrons in its molecular structure.

### Step 2: Analyzing the Options
We will evaluate each option to see if it meets the criteria of being paramagnetic and containing about 55% potassium.

#### Option A: \( KO_2 \) (Potassium Superoxide)
1. **Dissociation**: \( KO_2 \) dissociates into \( K^+ \) and \( O_2^- \).
2. **Electrons in \( O_2^- \)**: The \( O_2 \) molecule has 16 electrons, and the extra negative charge adds one more electron, giving a total of 17 electrons.
3. **Molecular Orbital Configuration**: Filling the molecular orbitals:
- \( \sigma 1s^2 \)
- \( \sigma^* 1s^2 \)
- \( \sigma 2s^2 \)
- \( \sigma^* 2s^2 \)
- \( \sigma 2p_z^2 \)
- \( \pi 2p_x^2 \), \( \pi 2p_y^2 \)
- \( \pi^* 2p_x^1 \) (one unpaired electron)
4. **Conclusion**: \( KO_2 \) has one unpaired electron, making it paramagnetic.

#### Option B: \( K_2O \) (Potassium Oxide)
1. **Dissociation**: \( K_2O \) dissociates into \( 2K^+ \) and \( O^{2-} \).
2. **Electrons in \( O^{2-} \)**: Oxygen has 8 electrons, and with 2 extra electrons, it has a total of 10 electrons.
3. **Molecular Orbital Configuration**: All electrons are paired.
4. **Conclusion**: \( K_2O \) is diamagnetic.

#### Option C: \( K_2SO_4 \) (Potassium Sulfate)
1. **Dissociation**: \( K_2SO_4 \) dissociates into \( 2K^+ \) and \( SO_4^{2-} \).
2. **Electrons in \( SO_4^{2-} \)**: Sulfate has a total of 32 electrons (S has 16 and O has 16).
3. **Molecular Orbital Configuration**: All electrons are paired.
4. **Conclusion**: \( K_2SO_4 \) is diamagnetic.

#### Option D: \( K_2O_2 \) (Potassium Peroxide)
1. **Dissociation**: \( K_2O_2 \) dissociates into \( 2K^+ \) and \( O_2^{2-} \).
2. **Electrons in \( O_2^{2-} \)**: The \( O_2 \) molecule has 16 electrons, and with 2 extra electrons, it has a total of 18 electrons.
3. **Molecular Orbital Configuration**: All electrons are paired.
4. **Conclusion**: \( K_2O_2 \) is diamagnetic.

### Step 3: Calculating the Percentage of Potassium in \( KO_2 \)
1. **Molar Mass of \( KO_2 \)**:
- Potassium (K): 39 g/mol
- Oxygen (O): 16 g/mol (2 O = 32 g/mol)
- Total = 39 + 32 = 71 g/mol
2. **Percentage of Potassium**:
\[ \text{Percentage of K} = \left( \frac{39}{71} \right) \times 100 \approx 54.93\% \]
This is approximately 55%.

### Conclusion
Based on the analysis, the only compound that is paramagnetic and contains about 55% potassium is \( KO_2 \).

Thus, the salt \( P \) is \( KO_2 \).

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