The stoichiometric constants for the reaction `pCu+qHNO_(3) rarr rCu(NO_(3))_(2)+sNO+tH_(2)O` p, q, r, s and t respectively are

Options

A. 3, 3, 3, 2, 3
B. 3, 2, 3, 2, 4
C. 3, 8, 3, 2, 4
D. 2, 3, 3, 3, 2

Explanation

To solve the question regarding the stoichiometric constants for the reaction \( pCu + qHNO_3 \rightarrow rCu(NO_3)_2 + sNO + tH_2O \), we will follow these steps:

### Step 1: Write the unbalanced reaction
The unbalanced reaction can be written as:
\[ Cu + HNO_3 \rightarrow Cu(NO_3)_2 + NO + H_2O \]

### Step 2: Determine oxidation states
- **Copper (Cu)**: In elemental form, the oxidation state is 0.
- **Nitrogen in HNO3**: Let the oxidation state be \( x \). The equation is:
\[ x + 1 + 3(-2) = 0 \implies x - 5 = 0 \implies x = +5 \]
- **Copper in Cu(NO3)2**: The oxidation state of Cu is +2 (since the nitrate ion \( NO_3^- \) has a charge of -1 and there are two of them).
- **Nitrogen in NO**: Let the oxidation state be \( y \). The equation is:
\[ y - 2 = 0 \implies y = +2 \]

### Step 3: Identify oxidation and reduction
- **Oxidation**: Copper goes from 0 to +2 (loses electrons).
- **Reduction**: Nitrogen goes from +5 in HNO3 to +2 in NO (gains electrons).

### Step 4: Balance the reaction
To balance the reaction, we need to ensure that the number of atoms of each element is the same on both sides.

1. **Balance Copper (Cu)**:
- We have 1 Cu on the left and 1 Cu in \( Cu(NO_3)_2 \) on the right.

2. **Balance Nitrogen (N)**:
- We have 1 N in \( HNO_3 \) and 1 N in \( NO \) and 2 N in \( Cu(NO_3)_2 \).
- To balance, we can use 4 \( HNO_3 \) to provide 4 N (2 for \( Cu(NO_3)_2 \) and 2 for 2 \( NO \)).

3. **Balance Hydrogen (H)**:
- From 4 \( HNO_3 \), we have 4 H, which will require 2 \( H_2O \) on the product side.

4. **Balance Oxygen (O)**:
- Count the O atoms:
- Left: \( 4 \times 3 = 12 \) from \( HNO_3 \).
- Right: \( 3 \times 2 = 6 \) from \( Cu(NO_3)_2 \) + \( 2 \) from \( 2NO \) + \( 2 \) from \( 2H_2O \) = 10.
- Adjust to balance O by ensuring the total equals 12.

### Final balanced equation
After balancing, the equation becomes:
\[ 3Cu + 8HNO_3 \rightarrow 3Cu(NO_3)_2 + 2NO + 4H_2O \]

### Step 5: Identify stoichiometric coefficients
From the balanced equation:
- \( p = 3 \)
- \( q = 8 \)
- \( r = 3 \)
- \( s = 2 \)
- \( t = 4 \)

### Conclusion
The stoichiometric constants for the reaction are:
- \( p = 3 \)
- \( q = 8 \)
- \( r = 3 \)
- \( s = 2 \)
- \( t = 4 \)