Four solutions of `K_(2)SO_(4)` with the following concentration 0.1 m, 0.01 m, 0.001 m and 0.0001 m are available. The maximum value of Van’t Hoff factor (i) will be of:

Options

A. 0.0001 m solution
B. 0.001 m solution
C. 0.01 m solution
D. 0.1 m solution

Answer

To determine the maximum value of the Van’t Hoff factor (i) for the given solutions of K2SO4, we can follow these steps:

### Step 1: Understand the Van’t Hoff Factor
The Van’t Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For K2SO4, it dissociates into 3 ions:
- 2 K⁺ ions
- 1 SO4²⁻ ion

Thus, for complete dissociation, the theoretical maximum value of i for K2SO4 is:
\[ i = 2 + 1 = 3 \]

### Step 2: Consider the Degree of Dissociation
The degree of dissociation (α) refers to the fraction of the solute that dissociates into its constituent ions. The Van’t Hoff factor can also be expressed in terms of α:
\[ i = 1 + (n - 1) \cdot \alpha \]
where n is the number of particles formed from one formula unit of the solute.

### Step 3: Analyze the Effect of Concentration on Degree of Dissociation
As the concentration of the solution decreases (dilution), the degree of dissociation (α) increases. This is due to the reduced ion-ion interactions in more dilute solutions, allowing more solute to dissociate.

### Step 4: Compare the Given Concentrations
The concentrations provided are:
- 0.1 m
- 0.01 m
- 0.001 m
- 0.0001 m

As we move from 0.1 m to 0.0001 m, we are diluting the solution. Therefore, the degree of dissociation will be highest in the most dilute solution (0.0001 m).

### Step 5: Determine the Maximum Van’t Hoff Factor
Since the degree of dissociation increases with dilution, the maximum value of the Van’t Hoff factor will occur in the 0.0001 m solution. Thus, we can conclude that:
- The maximum value of the Van’t Hoff factor (i) will be closest to 3 in the 0.0001 m solution.

### Final Answer
The maximum value of the Van’t Hoff factor (i) will be in the 0.0001 m solution.

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