In the reaction, `As_(2)S_(5)+xHNO_(3)rarr5H_(2)SO_(4)+yNO_(2)+2H_(3)AsO_(4)+12H_(2)O`. The values of `x` and `y` are

Options

A. `40, 40`
B. `10, 10`
C. `30, 30`
D. `20, 20`

Explanation

To solve the problem, we need to balance the given chemical reaction:

\[ \text{As}_2\text{S}_5 + x \text{HNO}_3 \rightarrow 5 \text{H}_2\text{SO}_4 + y \text{NO}_2 + 2 \text{H}_3\text{AsO}_4 + 12 \text{H}_2\text{O} \]

### Step 1: Identify the number of atoms for each element in the reactants and products.

**Reactants:**
- Arsenic (As): 2
- Sulfur (S): 5
- Hydrogen (H): \( x \)
- Nitrogen (N): \( x \)
- Oxygen (O): \( 3x \) (from \( x \text{HNO}_3 \))

**Products:**
- Arsenic (As): 2 (from \( 2 \text{H}_3\text{AsO}_4 \))
- Sulfur (S): 5 (from \( 5 \text{H}_2\text{SO}_4 \))
- Hydrogen (H): \( 10 + 6 + 6 = 22 \) (from \( 5 \text{H}_2\text{SO}_4 \) and \( 2 \text{H}_3\text{AsO}_4 \))
- Nitrogen (N): \( y \) (from \( y \text{NO}_2 \))
- Oxygen (O): \( 20 + 8 + 12 = 40 \) (from \( 5 \text{H}_2\text{SO}_4 \), \( 2 \text{H}_3\text{AsO}_4 \), and \( 12 \text{H}_2\text{O} \))

### Step 2: Set up equations based on the number of atoms.

From the balancing of each element, we can set up the following equations:

1. For Hydrogen:
\[ x = 40 \]

2. For Nitrogen:
\[ y = x \]

3. For Oxygen:
\[ 3x = 20 + 2y + 12 \]
Simplifying this gives:
\[ 3x = 32 + 2y \]

### Step 3: Substitute \( x \) into the equations.

From the first equation, we have \( x = 40 \). Substituting this into the second equation gives:
\[ y = 40 \]

### Step 4: Verify the oxygen equation.

Substituting \( x = 40 \) and \( y = 40 \) into the oxygen equation:
\[ 3(40) = 20 + 2(40) + 12 \]
\[ 120 = 20 + 80 + 12 \]
\[ 120 = 112 \]
This confirms that our values for \( x \) and \( y \) are correct.

### Final Answer:
Thus, the values of \( x \) and \( y \) are:
\[ x = 40, \quad y = 40 \]