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) lt i_(B) lt i_(C)`
B. `i_(A) gt i_(B) gt i_(C)`
C. `i_(A) = i_(B) = i_(C)`
D. `i_(A) lt i_(B) gt i_(C)`

Answer

To determine the order of the van't Hoff factor (i) for the three aqueous solutions of NaCl (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 (i)
The van't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For NaCl, which dissociates into Na⁺ and Cl⁻ ions, the theoretical value of i is 2, as one formula unit of NaCl produces two ions.

### Step 2: Consider the effect of concentration on dissociation
The degree of dissociation (α) of an electrolyte like NaCl increases with dilution. This means that as the concentration of the solution decreases, the extent to which NaCl dissociates into Na⁺ and Cl⁻ ions increases.

### Step 3: Analyze the concentrations
- Solution A: 0.1 M NaCl
- Solution B: 0.01 M NaCl
- Solution C: 0.001 M NaCl

As we move from solution A to C, the concentration decreases.

### Step 4: Relate concentration to degree of dissociation
Since the degree of dissociation (α) increases with dilution, we can conclude:
- Solution C (0.001 M) will have the highest degree of dissociation.
- Solution B (0.01 M) will have a moderate degree of dissociation.
- Solution A (0.1 M) will have the lowest degree of dissociation.

### Step 5: Determine the order of van't Hoff factor (i)
Since i is directly related to the degree of dissociation (i = 1 + α), we can summarize:
- Solution C will have the highest i value.
- Solution B will have a lower i value than C but higher than A.
- Solution A will have the lowest i value.

Thus, the order of the van't Hoff factor for the solutions is:
**i_C > i_B > i_A**

### Final Answer:
The value of the van't Hoff factor for these solutions will be in the order: **i_C > i_B > i_A**.

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