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

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$i_{A} > i_{B} > i_{C}$

$l_{A} = l_{B} = l_{C}$

$i_{A} < i_{B} > i_{C}$

$i_{A} < i_{B} < i_{C}$

answer is A.

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Detailed Solution

We are given three aqueous solutions of NaCl labeled A, B, and C, with concentrations 0.1 M, 0.01 M, and 0.001 M respectively. We need to determine the order of the van't Hoff factor (i) for these solutions. Here is a step-by-step analysis:

Step 1: Understanding the van't Hoff Factor (i)

The van't Hoff factor (i) represents the number of particles into which a solute dissociates when it dissolves in a solution. For NaCl, which dissociates into Na⁺ and Cl^- ions, the theoretical value of i is 2, because one formula unit of NaCl dissociates into two ions: Na⁺ and Cl^-.

Step 2: Consider the Effect of Concentration on Dissociation

The degree of dissociation (α) of an electrolyte like NaCl increases as the concentration of the solution decreases. In other words, as the concentration decreases, more NaCl dissociates into its constituent ions.

Step 3: Analyze the Concentrations of the Solutions

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 Solution C, the concentration of NaCl decreases.

Step 4: Relate Concentration to Degree of Dissociation

Since the degree of dissociation (α) increases with dilution, we can predict the dissociation for each solution:

Solution C (0.001 M): This will have the highest degree of dissociation, as it is the most diluted solution.
Solution B (0.01 M): This will have a moderate degree of dissociation.
Solution A (0.1 M): This will have the lowest degree of dissociation, as it is the most concentrated solution.

Step 5: Determine the Order of Van't Hoff Factor (i)

Since the van't Hoff factor (i) is directly related to the degree of dissociation (i = 1 + α), the order of i for the solutions will be based on the degree of dissociation:

Solution C: The highest degree of dissociation, thus the highest i value.
Solution B: A moderate degree of dissociation, so its i value will be higher than A but lower than C.
Solution A: The lowest degree of dissociation, thus the lowest i value.

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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