One mole of `As_(2)S_(3)` is oxidized by `HNO_(3)` to `H_(3)AsO_(4)` and `H_(2)SO_(4). HNO_(3)` is converted into NO. The moles of `HNO_(3) `required are `:`

Options

A. 3
B. 28
C. 14
D. 9.33

Explanation

To solve the problem of how many moles of `HNO3` are required to oxidize one mole of `As2S3` to `H3AsO4` and `H2SO4`, we will follow these steps:

### Step 1: Identify the oxidation states
- In `As2S3`, arsenic (As) has an oxidation state of -3 and sulfur (S) has an oxidation state of -2.
- In `H3AsO4`, arsenic has an oxidation state of +5.
- In `H2SO4`, sulfur has an oxidation state of +6.
- In `HNO3`, nitrogen has an oxidation state of +5, and it is reduced to NO where nitrogen has an oxidation state of +2.

### Step 2: Calculate the change in oxidation states
- For arsenic:
- From `-3` (in `As2S3`) to `+5` (in `H3AsO4`).
- Change = \( +5 - (-3) = +8 \) (for 2 As atoms, total change = \( 2 \times 8 = 16 \)).

- For sulfur:
- From `-2` (in `As2S3`) to `+6` (in `H2SO4`).
- Change = \( +6 - (-2) = +8 \) (for 3 S atoms, total change = \( 3 \times 8 = 24 \)).

### Step 3: Total change in oxidation states
- Total change in oxidation states for `As2S3`:
- Total increase = 16 (from As) + 24 (from S) = 40 electrons lost.

### Step 4: Calculate the reduction of `HNO3`
- For `HNO3` to `NO`:
- Change in oxidation state from +5 (in `HNO3`) to +2 (in `NO`).
- Change = \( +2 - (+5) = -3 \) (for each N atom).

### Step 5: Determine the moles of `HNO3` required
- Each mole of `HNO3` can accept 3 electrons (as it goes from +5 to +2).
- To balance the total of 40 electrons lost from `As2S3`, we need:
\[ \text{Moles of } HNO3 = \frac{\text{Total electrons lost}}{\text{Electrons gained per mole of } HNO3} = \frac{40}{3} \approx 13.33 \text{ moles of } HNO3 \]

### Final Answer
Thus, the moles of `HNO3` required to oxidize one mole of `As2S3` is approximately **13.33 moles**.

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