Which of the following statements is/are correct in following reaction.
`As_(2)S_(5)+NO_(3)^(ɵ)toAsO_(4)^(3-)+NO_(2)+SO_(4)^(2-)`

Options

A. The equivalent weight of `As_(2)S_(5) is (M)/(40)`. (`M=` molecular weight of `As_(2)S_(5))`.
B. The equivalent weight of `NO_(3)^(ɵ) is (M)/(3)`.
(`M=` molecular weight of `NO_(3)^(ɵ)` ion)
C. n-factor for the conversion of `As_(2)S_(5)` to `AsO_(4)^(3-)` is zero.
D. n-factor for the conversion of `As_(2)S_(3)` to `SO_(4)^(2-)` is 30.

Explanation

To determine which of the statements regarding the reaction \( \text{As}_2\text{S}_5 + \text{NO}_3^- \rightarrow \text{AsO}_4^{3-} + \text{NO}_2 + \text{SO}_4^{2-} \) are correct, we need to analyze each statement step by step.

### Step 1: Calculate the Equivalent Weight of \( \text{As}_2\text{S}_5 \)

1. **Determine the oxidation states of sulfur in \( \text{As}_2\text{S}_5 \)**:
- In \( \text{As}_2\text{S}_5 \), sulfur has an oxidation state of \(-2\).
- In \( \text{SO}_4^{2-} \), sulfur has an oxidation state of \(+6\).

2. **Calculate the change in oxidation state**:
- The change is from \(-2\) to \(+6\), which is a change of \(8\) for each sulfur atom.
- Since there are \(5\) sulfur atoms, the total change in oxidation state is \(5 \times 8 = 40\).

3. **Calculate the equivalent weight**:
- The equivalent weight is given by the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{n \text{ factor}} \]
- Therefore, the equivalent weight of \( \text{As}_2\text{S}_5 \) is:
\[ \frac{M}{40} \]
- This confirms that the first statement is correct.

### Step 2: Calculate the Equivalent Weight of \( \text{NO}_3^- \)

1. **Determine the oxidation states of nitrogen in \( \text{NO}_3^- \)**:
- In \( \text{NO}_3^- \), nitrogen has an oxidation state of \(+5\).
- In \( \text{NO}_2 \), nitrogen has an oxidation state of \(+4\).

2. **Calculate the change in oxidation state**:
- The change is from \(+5\) to \(+4\), which is a change of \(1\).

3. **Calculate the equivalent weight**:
- The equivalent weight is:
\[ \frac{M}{1} = M \]
- The second statement claims the equivalent weight is \( \frac{M}{3} \), which is incorrect.

### Step 3: Determine the n-factor for the conversion of \( \text{As}_2\text{S}_5 \) to \( \text{AsO}_4^{3-} \)

1. **Determine the oxidation states of arsenic**:
- In \( \text{As}_2\text{S}_5 \), arsenic is at \(+3\) (average).
- In \( \text{AsO}_4^{3-} \), arsenic is at \(+5\).

2. **Calculate the change in oxidation state**:
- The change is from \(+3\) to \(+5\), which is a change of \(2\) for each arsenic atom.
- Since there are \(2\) arsenic atoms, the total change is \(2 \times 2 = 4\).

3. **Determine the n-factor**:
- The statement claims the n-factor is \(0\), which is incorrect. The n-factor is \(4\).

### Step 4: Determine the n-factor for the conversion of \( \text{As}_2\text{S}_3 \) to \( \text{SO}_4^{2-} \)

1. **Determine the oxidation states of sulfur**:
- In \( \text{As}_2\text{S}_3 \), sulfur is at \(-2\).
- In \( \text{SO}_4^{2-} \), sulfur is at \(+6\).

2. **Calculate the change in oxidation state**:
- The change is from \(-2\) to \(+6\), which is a change of \(8\) for each sulfur atom.
- Since there are \(3\) sulfur atoms, the total change is \(3 \times 8 = 24\).

3. **Determine the n-factor**:
- The statement claims the n-factor is \(30\), which is incorrect.

### Conclusion

The correct statements are:
1. The first statement is correct: Equivalent weight of \( \text{As}_2\text{S}_5 \) is \( \frac{M}{40} \).
2. The second statement is incorrect.
3. The third statement is incorrect.
4. The fourth statement is incorrect.

Thus, the only correct statement is the first one.