Fuming `H_2SO_4` (oleum) is a homogenous mixture of `H_2SO_4` and `SO_3`.Then which of the following statement(s) are correct :

Options

A. If `H_2SO_4` and `SO_3` are equimolar in an oleum sample, then strength of oleum is 110.11%
B. If `H_2SO_4 and SO_3` are having equal masses in an oleum sample, then strength of oleum is 111.25 %
C. Strength of an oleum sample may be less than 100%
D. If strength of oleum is (100+x) % , then x g of water to be added to 100 g oleum sample convert whole of `SO_3` to `H_2SO_4`

Explanation

To solve the question regarding fuming H₂SO₄ (oleum) and determine which statements are correct, we need to analyze the properties of oleum and the implications of the given statements.

### Step-by-Step Solution:

1. **Understanding Fuming H₂SO₄ (Oleum)**:
- Oleum is a solution of sulfur trioxide (SO₃) in sulfuric acid (H₂SO₄). It is a homogeneous mixture.

2. **Analyzing the First Statement**:
- **Statement**: If H₂SO₄ and SO₃ are equimolar in an oleum sample, then the strength of oleum is 110.11%.
- **Analysis**: The strength of oleum is defined as the mass percentage of H₂SO₄ in the mixture. When H₂SO₄ and SO₃ are equimolar, we can calculate the strength based on their molar masses. The molar mass of H₂SO₄ is approximately 98 g/mol and SO₃ is approximately 80 g/mol. The total mass of the solution would be the sum of the masses of H₂SO₄ and SO₃. The calculation shows that the strength is indeed around 110.11%.
- **Conclusion**: This statement is **correct**.

3. **Analyzing the Second Statement**:
- **Statement**: If H₂SO₄ and SO₃ are having equal masses in an oleum sample, then the strength of oleum is 111.25%.
- **Analysis**: If H₂SO₄ and SO₃ have equal masses, we can again calculate the strength. The total mass would be the sum of the two equal masses, and the mass percentage of H₂SO₄ can be calculated. This results in a strength of approximately 111.25%.
- **Conclusion**: This statement is **correct**.

4. **Analyzing the Third Statement**:
- **Statement**: The strength of oleum sample may be less than 100 percent.
- **Analysis**: The strength of oleum is always greater than 100% because it contains more H₂SO₄ than the standard concentration of pure H₂SO₄ (which is 100%). Therefore, the strength cannot be less than 100%.
- **Conclusion**: This statement is **incorrect**.

5. **Analyzing the Fourth Statement**:
- **Statement**: If the strength of oleum is 100x percent, then x grams of water need to be added to 100 grams of oleum to convert all SO₃ to H₂SO₄.
- **Analysis**: To convert SO₃ to H₂SO₄, we need to add water. The stoichiometry of the reaction shows that for every mole of SO₃, one mole of water is required to produce one mole of H₂SO₄. The amount of water needed can be calculated based on the strength and the amount of SO₃ present in the oleum.
- **Conclusion**: This statement is **correct**.

### Final Summary of Statements:
- **Correct Statements**: 1, 2, and 4.
- **Incorrect Statement**: 3.