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. **Write the Unbalanced Equation:**
\[ xHNO_3 + yH_2S \rightarrow aNO_2 + bH_2O + S \]

2. **Identify the Atoms to Balance:**
We need to balance the following elements: Nitrogen (N), Hydrogen (H), Oxygen (O), and Sulfur (S).

3. **Count Atoms on Both Sides:**
- **Reactants:**
- Nitrogen: \( x \) (from \( HNO_3 \))
- Hydrogen: \( 2y \) (from \( H_2S \))
- Oxygen: \( 3x \) (from \( HNO_3 \))
- Sulfur: \( y \) (from \( H_2S \))
- **Products:**
- Nitrogen: \( a \) (from \( NO_2 \))
- Hydrogen: \( b \) (from \( H_2O \))
- Oxygen: \( b \) (from \( H_2O \)) + \( 2a \) (from \( NO_2 \))
- Sulfur: \( 1 \) (from \( S \))

4. **Set Up the Balancing Equations:**
From the above counts, we can set up the following equations:
- For Nitrogen: \( x = a \)
- For Hydrogen: \( 2y = b \)
- For Oxygen: \( 3x = 2a + b \)
- For Sulfur: \( y = 1 \)

5. **Substituting Known Values:**
From the sulfur balance, we find:
\[ y = 1 \]
Substitute \( y = 1 \) into the hydrogen equation:
\[ 2(1) = b \Rightarrow b = 2 \]
Now substitute \( b = 2 \) into the oxygen equation:
\[ 3x = 2a + 2 \]
Since \( x = a \), we can replace \( a \) with \( x \):
\[ 3x = 2x + 2 \]
Rearranging gives:
\[ 3x - 2x = 2 \Rightarrow x = 2 \]

6. **Final Values:**
Now we have:
- \( x = 2 \)
- \( y = 1 \)
- \( b = 2 \)

Thus, the values of \( x \), \( y \), and \( b \) are \( 2 \), \( 1 \), and \( 2 \) respectively.

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

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