The electrolyte solutions show abnormal colligative porperties.To account for this effect we define a quantity called the Van't Hoff factor given by
`i=("Actual number of particles in solution after dissociation")/("Number of formula units initially dissolved in solution")`
`i=1 ("for non-electrolytes")`
`igt1 ("for electrolytes, undergoing dissociation")`
`ilt1 ("for solutes, undergoing association")`
Answer the following questions:
certain substances trimerize when dissolved in a solvent `A`. The Van't Hoff factor `i` for the solutions is

Options

A. 2
B. `1/3`
C. `3`
D. `0`

Explanation

To determine the Van't Hoff factor \( i \) for a substance that trimerizes when dissolved in a solvent \( A \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Trimerization**: When a substance trimerizes, it means that three molecules of the solute combine to form one larger molecule. For example, if we have three molecules of \( A \) that combine to form \( A_3 \), we can represent this as:
\[ 3A \rightarrow A_3 \]

2. **Initial Concentration**: Let's assume the initial concentration of the solute \( A \) is \( C \) mol/L. Before any reaction occurs, we have \( C \) moles of \( A \) per liter.

3. **Change in Concentration**: After trimerization, the concentration of \( A_3 \) formed will be \( \frac{C \alpha}{3} \), where \( \alpha \) is the degree of trimerization (the fraction of \( A \) that has reacted to form \( A_3 \)). The remaining concentration of \( A \) will be \( C(1 - \alpha) \).

4. **Calculating the Van't Hoff Factor**: The Van't Hoff factor \( i \) is defined as the ratio of the actual number of particles in solution after dissociation to the number of formula units initially dissolved in solution. Initially, we have \( C \) moles of \( A \), which will yield:
- \( C(1 - \alpha) \) moles of unreacted \( A \)
- \( \frac{C \alpha}{3} \) moles of \( A_3 \)

Therefore, the total number of particles after trimerization is:
\[ \text{Total particles} = C(1 - \alpha) + \frac{C \alpha}{3} \]

5. **Expressing the Van't Hoff Factor**:
\[ i = \frac{\text{Total particles}}{\text{Initial concentration}} = \frac{C(1 - \alpha) + \frac{C \alpha}{3}}{C} \]
Simplifying this gives:
\[ i = (1 - \alpha) + \frac{\alpha}{3} = 1 - \alpha + \frac{\alpha}{3} = 1 - \frac{2\alpha}{3} \]

6. **Final Result**: Thus, the Van't Hoff factor \( i \) for the solution is:
\[ i = 1 - \frac{2\alpha}{3} \]