`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. `(M.wt.)/(2)`
B. `(M.wt.)/(4)`
C. `(M.wt.)/(24)`
D. `(M.wt.)/(28)`

Explanation

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

### Step 1: Identify the change in oxidation states
In the reaction, we need to determine the oxidation states of arsenic (As) and sulfur (S) in As₂S₃ and in the products.

- In As₂S₃, arsenic (As) has an oxidation state of +3, and sulfur (S) has an oxidation state of -2.
- In the product, AsO₄³⁻, arsenic has an oxidation state of +5.

### Step 2: Calculate the change in oxidation state
The change in oxidation state for arsenic (As) from +3 to +5 is:
\[ \Delta \text{Oxidation state of As} = +5 - (+3) = +2 \]

Since there are 2 arsenic atoms in As₂S₃, the total change in oxidation state for arsenic in the reaction is:
\[ 2 \times 2 = 4 \]

### Step 3: Determine the number of moles of As₂S₃
From the balanced equation, we see that 3 moles of As₂S₃ are consumed.

### Step 4: Calculate the total change in moles of electrons
The total change in moles of electrons (n) can be calculated as:
\[ n = \text{moles of As}_2\text{S}_3 \times \text{total change in oxidation state} \]
\[ n = 3 \times 4 = 12 \]

### 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)

Thus, the molar mass of As₂S₃ is:
\[ \text{Molar mass of As}_2\text{S}_3 = 2 \times 74.92 + 3 \times 32.07 = 149.84 + 96.21 = 246.05 \, \text{g/mol} \]

### Step 6: Calculate the equivalent mass
The equivalent mass (E) is given by the formula:
\[ E = \frac{\text{Molar mass}}{n} \]
Substituting the values:
\[ E = \frac{246.05 \, \text{g/mol}}{12} = 20.504 \, \text{g/equiv} \]

### Final Answer
The equivalent mass of As₂S₃ in the given reaction is approximately **20.50 g/equiv**.

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