For a given value of degree of dissociation, which of the following have correct Van't Hoff factor?

Options

A. `NaCl`,`i=2+alpha`
B. `Ca(NO_(3))_(2)`,`i=1+2alpha`
C. `K_(4)[Fe_(3)(CN_6)]`,`i=1+4alpha`
D. `(NH_(3))_(3)PO_(4)`,`i=3+alpha`

Answer

To solve the problem regarding the Van't Hoff factor (i) for a given degree of dissociation (α), we need to understand how to calculate the Van't Hoff factor based on the dissociation of ionic compounds in solution.

### Step-by-Step Solution:

1. **Understanding Degree of Dissociation (α)**:
- The degree of dissociation (α) is the fraction of the total number of moles of a solute that dissociates into ions. For example, if α = 0.5, then 50% of the solute has dissociated.

2. **Identifying the Dissociation of Ionic Compounds**:
- For ionic compounds like NaCl, they dissociate into their constituent ions. For NaCl, it dissociates into Na⁺ and Cl⁻.

3. **Calculating the Van't Hoff Factor (i)**:
- The general formula for calculating the Van't Hoff factor (i) for a solute that dissociates into n ions is:
\[ i = 1 + (n - 1)α \]
- Here, n is the total number of ions produced from one formula unit of the solute.

4. **Example Calculation for NaCl**:
- For NaCl, n = 2 (Na⁺ and Cl⁻).
- Therefore, the Van't Hoff factor (i) for NaCl is:
\[ i = 1 + (2 - 1)α = 1 + α \]

5. **Example Calculation for Other Compounds**:
- If we consider a compound that dissociates into 3 ions (like CaCl₂), then n = 3.
\[ i = 1 + (3 - 1)α = 1 + 2α \]
- For a compound that dissociates into 5 ions (like AlCl₃), then n = 5.
\[ i = 1 + (5 - 1)α = 1 + 4α \]

6. **Evaluating the Options**:
- Based on the calculations above, we can evaluate the given options to determine which have the correct Van't Hoff factor based on their degree of dissociation.

### Conclusion:
- The correct Van't Hoff factors for the given compounds will be:
- For NaCl: \( i = 1 + α \)
- For CaCl₂: \( i = 1 + 2α \)
- For AlCl₃: \( i = 1 + 4α \)
- The incorrect one would be the one that does not follow the formula \( i = 1 + (n - 1)α \).