For the balanced chemical reaction
`xHNO_(3)+yH_(2)S rarr aNO_2 +bH_(2)O+S`
What are the values of x, y, and b respectively?

Options

A. 2,1,2
B. 3,1,2
C. 3,2,2
D. 1,2,3

Answer

To solve the balanced chemical reaction \( xHNO_3 + yH_2S \rightarrow aNO_2 + bH_2O + S \), we need to determine the values of \( x \), \( y \), and \( b \).

### Step-by-Step Solution:

1. **Identify the Reactants and Products:**
The reactants are \( HNO_3 \) and \( H_2S \), and the products are \( NO_2 \), \( H_2O \), and \( S \).

2. **Balance Sulfur (S) Atoms:**
- On the left side, the number of sulfur atoms is \( y \) (from \( H_2S \)).
- On the right side, there is 1 sulfur atom (from \( S \)).
- Therefore, we have the equation:
\[ y = 1 \]

3. **Balance Hydrogen (H) Atoms:**
- On the left side, the number of hydrogen atoms is \( x + 2y \) (from \( xHNO_3 \) and \( yH_2S \)).
- On the right side, the number of hydrogen atoms is \( 2b \) (from \( bH_2O \)).
- Substituting \( y = 1 \) into the equation gives:
\[ x + 2(1) = 2b \implies x + 2 = 2b \]

4. **Balance Nitrogen (N) Atoms:**
- On the left side, the number of nitrogen atoms is \( x \) (from \( xHNO_3 \)).
- On the right side, the number of nitrogen atoms is \( a \) (from \( aNO_2 \)).
- Thus, we have:
\[ x = a \]

5. **Balance Oxygen (O) Atoms:**
- On the left side, the number of oxygen atoms is \( 3x \) (from \( xHNO_3 \)).
- On the right side, the number of oxygen atoms is \( 2a + b \) (from \( aNO_2 \) and \( bH_2O \)).
- Therefore, we have:
\[ 3x = 2a + b \]

6. **Substituting Values:**
- From \( x = a \), substitute \( a \) into the oxygen equation:
\[ 3x = 2x + b \implies 3x - 2x = b \implies x = b \]

7. **Final Relationships:**
- We have established:
- \( y = 1 \)
- \( x = b \)
- From \( x + 2 = 2b \), substituting \( b = x \):
\[ x + 2 = 2x \implies 2 = x \]
- Thus, \( x = 2 \) and \( b = 2 \).

8. **Values of \( x \), \( y \), and \( b \):**
- \( x = 2 \)
- \( y = 1 \)
- \( b = 2 \)

### Conclusion:
The values of \( x \), \( y \), and \( b \) are \( 2, 1, 2 \) respectively.