van't Hoffer factor for acetic acid in aqueos medium at infinite dilution is

Options

A. 2
B. 1
C. `1//2`
D. 3

Answer

To find the van't Hoff factor (i) for acetic acid (CH₃COOH) in aqueous medium at infinite dilution, we can follow these steps:

### Step 1: Understand the Van't Hoff Factor
The van't Hoff factor (i) is defined as the number of particles into which a solute dissociates in solution. It can be calculated using the formula:
\[ i = \alpha \cdot (n + 1 - \alpha) \]
where:
- \( \alpha \) = degree of dissociation (the fraction of the solute that dissociates)
- \( n \) = number of ions formed from one formula unit of the solute

### Step 2: Identify the Substance and its Dissociation
The substance in question is acetic acid (CH₃COOH). As a weak acid, it does not dissociate completely under normal conditions. However, at infinite dilution, it can be assumed to dissociate completely:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]

### Step 3: Determine the Values of \( \alpha \) and \( n \)
- At infinite dilution, acetic acid dissociates completely, so the degree of dissociation \( \alpha = 1 \).
- The number of ions \( n \) formed from one formula unit of acetic acid is 2 (one acetate ion and one hydrogen ion).

### Step 4: Substitute the Values into the Formula
Now, we can substitute the values of \( \alpha \) and \( n \) into the van't Hoff factor formula:
\[ i = \alpha \cdot (n + 1 - \alpha) \]
Substituting \( \alpha = 1 \) and \( n = 2 \):
\[ i = 1 \cdot (2 + 1 - 1) \]
\[ i = 1 \cdot (2) \]
\[ i = 2 \]

### Step 5: Conclusion
Thus, the van't Hoff factor for acetic acid in aqueous medium at infinite dilution is:
\[ i = 2 \]

The correct option is option 1.

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