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 find the values of \( x \) and \( y \) in the reaction

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

we will balance the equation step by step.

### Step 1: Identify the elements involved
In the reaction, we have the following elements:
- Arsenic (As)
- Sulfur (S)
- Hydrogen (H)
- Nitrogen (N)
- Oxygen (O)

### Step 2: Count the number of atoms on the left side
From the reactants:
- Arsenic: 2 (from \(\text{As}_2\text{S}_5\))
- Sulfur: 5 (from \(\text{As}_2\text{S}_5\))
- Hydrogen: \( x \) (from \(\text{HNO}_3\))
- Nitrogen: \( x \) (from \(\text{HNO}_3\))
- Oxygen: \( 3x \) (from \(\text{HNO}_3\))

### Step 3: Count the number of atoms on the right side
From the products:
- Arsenic: 2 (from \(2 \text{H}_3\text{AsO}_4\))
- Sulfur: 5 (from \(5 \text{H}_2\text{SO}_4\))
- Hydrogen: \( 10 + 6 + 24 = 40 \) (10 from \(5 \text{H}_2\text{SO}_4\), 6 from \(2 \text{H}_3\text{AsO}_4\), and 24 from \(12 \text{H}_2\text{O}\))
- Nitrogen: \( y \) (from \(y \text{NO}_2\))
- Oxygen: \( 20 + 2y + 12 = 32 + 2y \) (20 from \(5 \text{H}_2\text{SO}_4\), \(2y\) from \(y \text{NO}_2\), and 12 from \(12 \text{H}_2\text{O}\))

### Step 4: Set up equations based on the balanced atoms
From the hydrogen balance:
\[ x = 40 \]

From the nitrogen balance:
\[ y = x = 40 \]

From the oxygen balance:
\[ 3x = 32 + 2y \]

### Step 5: Substitute \( x \) and \( y \) into the oxygen balance equation
Substituting \( x = 40 \) and \( y = 40 \):
\[ 3(40) = 32 + 2(40) \]
\[ 120 = 32 + 80 \]
\[ 120 = 112 \quad \text{(This is incorrect, indicating a need to check the calculations)} \]

### Step 6: Re-evaluate the oxygen balance
Revisiting the oxygen balance:
\[ 3x = 32 + 2y \]
Substituting \( x = 40 \):
\[ 3(40) = 32 + 2y \]
\[ 120 = 32 + 2y \]
\[ 2y = 120 - 32 \]
\[ 2y = 88 \]
\[ y = 44 \]

### Final Answer
Thus, the values of \( x \) and \( y \) are:
\[ x = 40, \quad y = 44 \]