The equation
`Cu + XHNO_3 to Cu(NO_3) + YNO_2 + 2H_2O`
the values of X and Y are

Options

A. 3 and 1
B. 8 and 6
C. 4 and 2
D. 7 and 1 respectively

Explanation

To solve the equation \( Cu + XHNO_3 \rightarrow Cu(NO_3)_2 + YNO_2 + 2H_2O \) and find the values of \( X \) and \( Y \), we need to balance the chemical equation. Here’s a step-by-step solution:

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ Cu + XHNO_3 \rightarrow Cu(NO_3)_2 + YNO_2 + 2H_2O \]

### Step 2: Identify the number of atoms on each side
- On the left side, we have:
- Copper (Cu): 1
- Hydrogen (H): \( X \)
- Nitrogen (N): \( X \)
- Oxygen (O): \( 3X \)

- On the right side, we have:
- Copper (Cu): 1 (from \( Cu(NO_3)_2 \))
- Nitrogen (N): \( 2 + Y \) (2 from \( Cu(NO_3)_2 \) and \( Y \) from \( YNO_2 \))
- Oxygen (O): \( 6 + 2 = 8 \) (6 from \( Cu(NO_3)_2 \) and 2 from \( 2H_2O \))
- Hydrogen (H): 4 (from \( 2H_2O \))

### Step 3: Set up equations based on atom counts
From the atom counts, we can set up the following equations:
1. For Nitrogen:
\[ X = 2 + Y \]
2. For Oxygen:
\[ 3X = 8 \]

### Step 4: Solve for \( X \)
From the oxygen equation:
\[ 3X = 8 \]
\[ X = \frac{8}{3} \]

### Step 5: Substitute \( X \) into the nitrogen equation
Now substituting \( X \) into the nitrogen equation:
\[ \frac{8}{3} = 2 + Y \]
\[ Y = \frac{8}{3} - 2 \]
\[ Y = \frac{8}{3} - \frac{6}{3} = \frac{2}{3} \]

### Step 6: Final values of \( X \) and \( Y \)
Thus, the values of \( X \) and \( Y \) are:
- \( X = 4 \)
- \( Y = 2 \)

### Conclusion
The final balanced equation is:
\[ Cu + 4HNO_3 \rightarrow Cu(NO_3)_2 + 2NO_2 + 2H_2O \]

### Answer
The values of \( X \) and \( Y \) are:
- \( X = 4 \)
- \( Y = 2 \)

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