The mole fraction of solute in some solution is `1//n`. If `50%` of the solute molecules dissociates into two parts and remaining `50%` get dimerized now mole fractions of solvent become `4/5`. Find value of `n`.

Explanation

To solve the problem step by step, let's break it down:

### Given:
- Mole fraction of solute = \( \frac{1}{n} \)
- 50% of solute dissociates into 2 parts.
- 50% of solute dimerizes.
- Mole fraction of solvent = \( \frac{4}{5} \)

### Step 1: Understand the dissociation and dimerization
Let’s denote the initial number of solute molecules as \( x \).

- After dissociation:
- 50% of \( x \) dissociates into 2 parts, so the number of particles from dissociation = \( 0.5x \times 2 = x \).

- After dimerization:
- The remaining 50% of \( x \) dimerizes, which means \( 0.5x \) forms \( \frac{0.5x}{2} = 0.25x \) dimers (since each dimer consists of 2 molecules).

### Step 2: Calculate total number of solute particles
Now, the total number of solute particles after these processes is:
- From dissociation: \( x \)
- From dimerization: \( 0.25x \)

Total number of solute particles = \( x + 0.25x = 1.25x \).

### Step 3: Determine mole fraction of solute and solvent
The mole fraction of the solvent is given as \( \frac{4}{5} \). Therefore, the mole fraction of the solute is:
\[ 1 - \text{mole fraction of solvent} = 1 - \frac{4}{5} = \frac{1}{5} \]

### Step 4: Set up the equation for mole fraction
We know that the mole fraction of solute is also given by:
\[ \text{Mole fraction of solute} = \frac{\text{number of solute particles}}{\text{number of solute particles} + \text{number of solvent particles}} \]
Let’s denote the number of solvent particles as \( y \).

Thus, we have:
\[ \frac{1.25x}{1.25x + y} = \frac{1}{5} \]

### Step 5: Solve for \( y \)
Cross-multiplying gives:
\[ 5 \times 1.25x = 1.25x + y \]
\[ 6.25x = 1.25x + y \]
\[ y = 6.25x - 1.25x = 5x \]

### Step 6: Substitute into the mole fraction of solute
Now, substituting back into the mole fraction equation:
\[ \frac{1}{n} = \frac{1.25x}{1.25x + 5x} \]
\[ \frac{1}{n} = \frac{1.25x}{6.25x} \]
\[ \frac{1}{n} = \frac{1.25}{6.25} \]
\[ \frac{1}{n} = \frac{1}{5} \]

### Step 7: Solve for \( n \)
From the equation above, we can see that:
\[ n = 5 \]

### Conclusion
Thus, the value of \( n \) is:
\[ \boxed{6} \]