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:
Benzoic acid undergoes dimerization in bezene solution. The Van't Hoff factor `i` for the solutions is

Options

A. `i=2-alpha`
B. `i=1+(alpha/3)`
C. `i=1-(alpha/2)`
D. `i=1+(alpha/2)`

Explanation

To find the Van't Hoff factor \( i \) for benzoic acid undergoing dimerization in benzene solution, we can follow these steps:

### Step 1: Understand Dimerization
Benzoic acid (\( C_6H_5COOH \)) can dimerize in solution, meaning two molecules of benzoic acid combine to form a dimer. The reaction can be represented as:
\[ 2 C_6H_5COOH \rightleftharpoons (C_6H_5COOH)_2 \]

### Step 2: Define Initial Concentration
Let the initial concentration of benzoic acid be \( C \). When dimerization occurs, some of the benzoic acid will form dimers.

### Step 3: Define Degree of Dimerization
Let \( \alpha \) be the degree of dimerization, which represents the fraction of benzoic acid that has dimerized. Thus, the concentration of the dimer formed will be \( \frac{C\alpha}{2} \) (since two molecules of benzoic acid form one dimer).

### Step 4: Calculate Remaining Monomers
The concentration of the remaining monomeric benzoic acid after dimerization will be:
\[ C(1 - \alpha) \]

### Step 5: Calculate Total Number of Particles
The total number of particles in the solution after dimerization consists of the remaining monomers and the dimers:
- Remaining monomers: \( C(1 - \alpha) \)
- Dimers: \( \frac{C\alpha}{2} \)

Thus, the total number of particles \( n \) in solution is:
\[ n = C(1 - \alpha) + \frac{C\alpha}{2} \]

### Step 6: Express Total Number of Particles
Now, we can express this as:
\[ n = C(1 - \alpha) + \frac{C\alpha}{2} = C \left(1 - \alpha + \frac{\alpha}{2}\right) = C \left(1 - \frac{\alpha}{2}\right) \]

### Step 7: Calculate Van't Hoff Factor \( i \)
The Van't Hoff factor \( i \) is defined as:
\[ i = \frac{\text{Actual number of particles in solution}}{\text{Number of formula units initially dissolved}} \]
In this case, the number of formula units initially dissolved is \( C \).

Thus,
\[ i = \frac{C \left(1 - \frac{\alpha}{2}\right)}{C} = 1 - \frac{\alpha}{2} \]

### Final Answer
The Van't Hoff factor \( i \) for benzoic acid undergoing dimerization in benzene solution is:
\[ i = 1 - \frac{\alpha}{2} \]