The substance A when dissolved in solvent B shows the molecular mass corresponding to `A_(3)`. The vant Hoffs factor will be:

Options

A. 1
B. 2
C. 3
D. `1//3`

Explanation

To solve the problem of finding the Van't Hoff factor (i) for substance A when it forms a complex A3 upon dissolution in solvent B, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Dissolution Process**:
- When substance A is dissolved in solvent B, it forms a complex A3. This means that three moles of A combine to form one mole of A3.

2. **Setting Up Initial Conditions**:
- Let's assume that initially, we have 1 mole of substance A and 0 moles of A3.
- At time t, let α be the fraction of A that has reacted to form A3.

3. **Calculating Moles at Time t**:
- The moles of A that have reacted to form A3 will be α moles.
- Therefore, the moles of A remaining will be (1 - α).
- The moles of A3 formed will be α/3 (since 3 moles of A form 1 mole of A3).

4. **Total Number of Particles**:
- The total number of particles in solution at time t will be the sum of the remaining moles of A and the moles of A3 formed:
\[ \text{Total particles} = (1 - α) + \frac{α}{3} \]

5. **Simplifying the Expression**:
- To simplify, we can express the total number of particles as:
\[ \text{Total particles} = 1 - α + \frac{α}{3} = 1 - α + \frac{1}{3}α = 1 - \frac{2}{3}α \]

6. **Calculating the Van't Hoff Factor (i)**:
- The Van't Hoff factor (i) is defined as the ratio of the total number of particles in solution after dissolution to the number of moles of the solute initially dissolved.
- Therefore, we have:
\[ i = \frac{\text{Total particles}}{\text{Initial moles of A}} = 1 - \frac{2}{3}α \]

7. **Considering Complete Reaction**:
- If we assume that all of substance A reacts (i.e., α = 1), then:
\[ i = 1 - \frac{2}{3}(1) = 1 - \frac{2}{3} = \frac{1}{3} \]

8. **Final Answer**:
- Thus, the Van't Hoff factor (i) for the substance A when dissolved in solvent B is:
\[ i = \frac{1}{3} \]