`28 NO_(3)^(-)+3As_(2)S_(3)+4H_(2)O rarr 6AsO_(4)^(3-)+28NO+9SO_(4)^(2-)+H^(+)` What will be the equivalent mass of As_(2)S_(3)` in the above reaction?

Options

A. `(3M)/(28)`
B. `(M)/(4)`
C. `(M)/(24)`
D. `(M)/(28)`

Explanation

To find the equivalent mass of As₂S₃ in the given reaction, we will follow these steps:

### Step 1: Identify the oxidation states of arsenic and sulfur in As₂S₃.
- In As₂S₃, arsenic (As) has an oxidation state of +3 and sulfur (S) has an oxidation state of -2.

### Step 2: Determine the oxidation states in the products.
- In the products, arsenic is present as AsO₄³⁻, where arsenic has an oxidation state of +5.
- Sulfur is present as SO₄²⁻, where sulfur has an oxidation state of +6.

### Step 3: Calculate the change in oxidation states for arsenic and sulfur.
- For arsenic:
- Change from +3 to +5 = 2 electrons (for each As atom).
- Since there are 2 arsenic atoms, total change = 2 x 2 = 4 electrons.

- For sulfur:
- Change from -2 to +6 = 8 electrons (for each S atom).
- Since there are 3 sulfur atoms, total change = 3 x 8 = 24 electrons.

### Step 4: Calculate the total change in oxidation number (n).
- Total change in oxidation number (n) = Change from arsenic + Change from sulfur = 4 + 24 = 28.

### Step 5: Calculate the molar mass of As₂S₃.
- The molar mass of As₂S₃ can be calculated as follows:
- Molar mass of As = 74.92 g/mol (approximately).
- Molar mass of S = 32.07 g/mol (approximately).
- Molar mass of As₂S₃ = (2 x 74.92) + (3 x 32.07) = 149.84 + 96.21 = 246.05 g/mol.

### Step 6: Calculate the equivalent mass of As₂S₃.
- Using the formula for equivalent mass:
\[ \text{Equivalent mass} = \frac{\text{Molar mass of As}_2\text{S}_3}{n} \]
\[ \text{Equivalent mass} = \frac{246.05 \, \text{g/mol}}{28} \approx 8.79 \, \text{g/equiv}. \]

### Final Answer:
The equivalent mass of As₂S₃ in the reaction is approximately **8.79 g/equiv**.

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