We have three aqueous solutions of NaCl labelled as A, B and C with concentration `0.1 M , 0.01 "and" 0.001` M , respectively . The value of van't Hoff factor for these solutions will be in the order :

Options

A. `i_(A)lti_(B)lti_(C)`
B. `i_(A)gti_(B)gti_(C)`
C. `i_(A)=i_(B)=i_(C)`
D. `i_(A)lti_(B)gti_(C)`

Explanation

To find the order of the van't Hoff factor (I) for the given NaCl solutions A, B, and C with concentrations of 0.1 M, 0.01 M, and 0.001 M respectively, we can follow these steps:

### Step 1: Understand the Van't Hoff Factor
The van't Hoff factor (I) is defined as the ratio of the number of particles in solution after dissociation to the number of formula units initially dissolved. For NaCl, which dissociates into Na⁺ and Cl⁻ ions, the van't Hoff factor can be expressed as:
\[ I = \frac{\text{Number of particles after dissociation}}{\text{Total initial moles}} \]

### Step 2: Analyze the Dissociation of NaCl
When NaCl dissolves in water, it dissociates into two ions:
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
This means that for every mole of NaCl that dissolves, it produces 2 moles of ions. Therefore, in an ideal case, the van't Hoff factor for NaCl would be 2.

### Step 3: Consider the Effect of Concentration on Dissociation
The degree of dissociation (α) of an electrolyte like NaCl is influenced by its concentration. As the concentration decreases (i.e., as we dilute the solution), the degree of dissociation increases due to the increased separation of ions in a more dilute solution. This means:
- At higher concentrations (like 0.1 M), the dissociation is less complete, resulting in a lower value of I.
- At lower concentrations (like 0.001 M), the dissociation is more complete, resulting in a higher value of I.

### Step 4: Compare the Solutions
Given the concentrations:
- Solution A: 0.1 M
- Solution B: 0.01 M
- Solution C: 0.001 M

Since the degree of dissociation increases as the concentration decreases, we can conclude:
- \( I_A < I_B < I_C \)

### Step 5: Write the Final Order
Thus, the order of the van't Hoff factor for the solutions A, B, and C is:
\[ I_A < I_B < I_C \]

### Conclusion:
The correct answer is that the value of the van't Hoff factor for these solutions will be in the order:
\[ I_A < I_B < I_C \]