A compound X undergoes tetramerisation in a given organic solvent. The Van't Hoff factor i is calculated as 0.05Y.
Find Y (Assuming 100% association).

Answer

To solve the problem, we need to determine the value of Y given that the Van't Hoff factor \( i \) is calculated as \( 0.05Y \) and that the compound X undergoes tetramerization.

### Step-by-Step Solution:

1. **Understanding Tetramerization**:
- Tetramerization means that four moles of a compound combine to form one mole of a tetramer.
- In this case, we can represent the reaction as:
\[ 4X \rightarrow X_4 \]
- Here, \( X_4 \) is the tetramer formed from 4 moles of \( X \).

2. **Defining the Van't Hoff Factor \( i \)**:
- The Van't Hoff factor \( i \) is defined as:
\[ i = \frac{\text{Total number of moles of particles after association or dissociation}}{\text{Number of moles of particles before association or dissociation}} \]

3. **Calculating Moles Before and After Association**:
- Before association, we have 4 moles of \( X \).
- After tetramerization, we have 1 mole of \( X_4 \).
- Therefore, the total number of moles of particles after association is 1, and before association is 4.

4. **Calculating the Van't Hoff Factor \( i \)**:
- Substituting the values into the formula:
\[ i = \frac{1}{4} \]

5. **Setting Up the Equation**:
- According to the problem, we have:
\[ i = 0.05Y \]
- So we can set up the equation:
\[ 0.05Y = \frac{1}{4} \]

6. **Solving for \( Y \)**:
- To find \( Y \), we rearrange the equation:
\[ Y = \frac{1}{4 \times 0.05} \]
- Calculating the denominator:
\[ 4 \times 0.05 = 0.2 \]
- Therefore:
\[ Y = \frac{1}{0.2} = 5 \]

### Final Answer:
Thus, the value of \( Y \) is \( 5 \).

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