If `alpha` is the degree of dissociation of `K_(2)SO_(4)`, the Vant Hoff''s factor (i) used for calculating the molecular mass is :

Options

A. `1 + alpha`
B. `1 - alpha`
C. `1 + 2alpha`
D. `1 - 2alpha`

Explanation

To find the Van't Hoff factor (i) for potassium sulfate (K₂SO₄) given the degree of dissociation (α), we can follow these steps:

### Step 1: Understand the Dissociation of K₂SO₄
When potassium sulfate (K₂SO₄) dissolves in water, it dissociates into its constituent ions:
\[ K_2SO_4 \rightarrow 2K^+ + SO_4^{2-} \]

### Step 2: Initial Moles
Initially, we start with 1 mole of K₂SO₄ in the solution. At this point, there are no ions formed yet.

### Step 3: Degree of Dissociation
Let α be the degree of dissociation of K₂SO₄. This means that α moles of K₂SO₄ will dissociate into ions.

### Step 4: Change in Moles Due to Dissociation
- The change in moles of K₂SO₄ due to dissociation is -α (since α moles are dissociating).
- For every mole of K₂SO₄ that dissociates, 2 moles of K⁺ and 1 mole of SO₄²⁻ are produced.

### Step 5: Final Moles After Dissociation
After dissociation, the moles of each component will be:
- Moles of K₂SO₄ remaining = \( 1 - \alpha \)
- Moles of K⁺ produced = \( 2\alpha \)
- Moles of SO₄²⁻ produced = \( \alpha \)

### Step 6: Total Number of Particles After Dissociation
The total number of particles in the solution after dissociation can be calculated as:
\[ \text{Total particles} = \text{Moles of K₂SO₄ remaining} + \text{Moles of K⁺} + \text{Moles of SO₄²⁻} \]
\[ = (1 - \alpha) + (2\alpha) + (\alpha) \]
\[ = 1 - \alpha + 2\alpha + \alpha \]
\[ = 1 + 2\alpha \]

### Step 7: Van't Hoff Factor (i)
The Van't Hoff factor (i) is defined as the ratio of the actual number of particles in solution after dissociation to the number of formula units initially dissolved:
\[ i = \frac{\text{Total particles after dissociation}}{\text{Initial moles of K₂SO₄}} \]
\[ = \frac{1 + 2\alpha}{1} \]
\[ = 1 + 2\alpha \]

### Conclusion
Thus, the Van't Hoff factor (i) for K₂SO₄ is:
\[ i = 1 + 2\alpha \]