If a solute undergoes dimerisation and trimerisation, the minimum values of the van't Hoff factors are

Options

A. 0.5 and 1.50
B. 1.5 and 1.33
C. 0.5 and 0.33
D. 0.25 and 0.67

Answer

To determine the minimum values of the van't Hoff factors for a solute that undergoes dimerization and trimerization, we can follow these steps:

### Step 1: Understand Dimerization
Dimerization is a process where two moles of a solute (A) combine to form one molecule of a dimer (A2). This can be represented as:
\[ 2A \rightarrow A_2 \]

### Step 2: Calculate the van't Hoff Factor for Dimerization
The van't Hoff factor (i) is defined as the ratio of the number of particles in solution after dissociation to the number of formula units initially dissolved. In the case of dimerization:
- Initially, we have 2 moles of A.
- After dimerization, we have 1 mole of A2.

Thus, the van't Hoff factor (i) for dimerization is:
\[ i = \frac{\text{number of particles after dimerization}}{\text{number of particles before dimerization}} = \frac{1}{2} = 0.5 \]

### Step 3: Understand Trimerization
Trimerization is a process where three moles of a solute (A) combine to form one molecule of a trimer (A3). This can be represented as:
\[ 3A \rightarrow A_3 \]

### Step 4: Calculate the van't Hoff Factor for Trimerization
Similarly, for trimerization:
- Initially, we have 3 moles of A.
- After trimerization, we have 1 mole of A3.

Thus, the van't Hoff factor (i) for trimerization is:
\[ i = \frac{\text{number of particles after trimerization}}{\text{number of particles before trimerization}} = \frac{1}{3} \approx 0.33 \]

### Step 5: Conclusion
The minimum values of the van't Hoff factors for a solute undergoing dimerization and trimerization are:
- For dimerization: \( i = 0.5 \)
- For trimerization: \( i \approx 0.33 \)

### Final Answer
The minimum values of the van't Hoff factors are 0.5 and 0.33.

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