Which compound corresponds vant Hoff factor (i) to be equal to 2 in dilute solution:

Options

A. `K_(2)SO_(4)`
B. `NaHSO_(4)`
C. Sugar
D. `MgSO_(4)`

Answer

To determine which compound corresponds to a van't Hoff factor (i) equal to 2 in a dilute solution, we need to analyze the dissociation of various compounds into their constituent ions. The van't Hoff factor (i) represents the number of particles (ions) produced when a solute dissolves in a solvent.

### Step-by-Step Solution:

1. **Understand the van't Hoff factor (i)**:
- The van't Hoff factor (i) is defined as the number of particles into which a solute dissociates in solution. For example, if a compound dissociates into 3 ions, its van't Hoff factor is 3.

2. **Identify the compounds given**:
- The compounds to consider are K2SO4, NaHSO4, sugar, and MgSO4.

3. **Analyze the dissociation of each compound**:
- **K2SO4**:
- Dissociates into 2 K⁺ ions and 1 SO₄²⁻ ion.
- Total ions = 2 + 1 = 3.
- Therefore, i = 3.

- **NaHSO4**:
- Dissociates into Na⁺ and HSO₄⁻.
- HSO₄⁻ can further dissociate into H⁺ and SO₄²⁻.
- Total ions = 1 (Na⁺) + 1 (HSO₄⁻) + 1 (H⁺) + 1 (SO₄²⁻) = 3.
- Therefore, i = 3.

- **Sugar**:
- Sugar is a non-electrolyte and does not dissociate into ions.
- Therefore, i = 1.

- **MgSO4**:
- Dissociates into 1 Mg²⁺ ion and 1 SO₄²⁻ ion.
- Total ions = 1 + 1 = 2.
- Therefore, i = 2.

4. **Conclusion**:
- The compound that corresponds to a van't Hoff factor (i) equal to 2 is **MgSO4**.

### Final Answer:
The compound that corresponds to a van't Hoff factor (i) equal to 2 in a dilute solution is **MgSO4**.