A molecule M associates in a given solvent according to the equation `M hArr (M)_(n)`. For a certain concentration of M, the van't Hoff factor was found to be `0.9` and the fraction of asscoiated molecules was `0.2`. The value of n is:

Options

A. 2
B. 4
C. 5
D. 3

Explanation

To solve the problem, we need to find the value of \( n \) based on the given information about the molecule \( M \) that associates in a solvent. We are provided with the van't Hoff factor \( i = 0.9 \) and the degree of association \( \alpha = 0.2 \).

### Step-by-Step Solution:

1. **Understanding the Association**:
The association of the molecule \( M \) can be represented by the equation:
\[ M \rightleftharpoons (M)_n \]
Here, \( n \) represents the number of molecules that associate together.

2. **Using the Van't Hoff Factor**:
The van't Hoff factor \( i \) is related to the degree of association \( \alpha \) and the number of molecules that associate \( n \) by the formula:
\[ i = 1 - \alpha + n \cdot \alpha \]
Substituting the known values:
\[ 0.9 = 1 - 0.2 + n \cdot 0.2 \]

3. **Rearranging the Equation**:
Simplifying the equation:
\[ 0.9 = 0.8 + 0.2n \]
Subtract \( 0.8 \) from both sides:
\[ 0.1 = 0.2n \]

4. **Solving for \( n \)**:
Now, solve for \( n \):
\[ n = \frac{0.1}{0.2} = 0.5 \]

5. **Finding the Value of \( n \)**:
Since we need to express \( n \) in terms of whole numbers, we can multiply both sides by 2:
\[ n = 2 \]

### Final Answer:
The value of \( n \) is \( 2 \).