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 determine the stoichiometric constants \( p, q, r, s, \) and \( t \) for the reaction

\[ p \text{Cu} + q \text{HNO}_3 \rightarrow r \text{Cu(NO}_3)_2 + s \text{NO} + t \text{H}_2\text{O} \]

we will follow these steps:

### Step 1: Write the unbalanced equation
The unbalanced equation is given as:

\[ \text{Cu} + \text{HNO}_3 \rightarrow \text{Cu(NO}_3)_2 + \text{NO} + \text{H}_2\text{O} \]

### Step 2: Identify the oxidation states
- Copper (Cu) in elemental form has an oxidation state of 0.
- In \(\text{Cu(NO}_3)_2\), the oxidation state of Cu is +2.
- In \(\text{HNO}_3\), nitrogen (N) has an oxidation state of +5, and in \(\text{NO}\), nitrogen has an oxidation state of +2.
- Oxygen (O) is -2 in both compounds.

### Step 3: Determine the changes in oxidation states
- Cu is oxidized from 0 to +2 (loss of 2 electrons).
- N is reduced from +5 in \(\text{HNO}_3\) to +2 in \(\text{NO}\) (gain of 3 electrons).

### Step 4: Balance the copper atoms
Since 1 mole of Cu produces 1 mole of \(\text{Cu(NO}_3)_2\), we have:

\[ p = 1 \quad \text{and} \quad r = 1 \]

### Step 5: Balance the nitrogen atoms
For every 1 mole of \(\text{Cu(NO}_3)_2\) produced, we need 2 moles of \(\text{HNO}_3\) to provide 2 moles of nitrate ions. Additionally, for each mole of \(\text{NO}\) produced, we need 1 mole of \(\text{HNO}_3\). Therefore, we can write:

\[ q = 4 \quad \text{(2 for } \text{Cu(NO}_3)_2 \text{ and 2 for } \text{NO)} \]

### Step 6: Balance the hydrogen and oxygen atoms
Now, we need to balance the water produced. From the balanced equation, we have:

- 4 moles of oxygen from 4 moles of \(\text{HNO}_3\) (2 from \(\text{Cu(NO}_3)_2\) and 1 from \(\text{NO}\)) and 2 moles of water produced. Thus, we have:

\[ t = 2 \]

### Step 7: Write the final balanced equation
Putting it all together, we have:

\[ 1 \text{Cu} + 4 \text{HNO}_3 \rightarrow 1 \text{Cu(NO}_3)_2 + 2 \text{NO} + 2 \text{H}_2\text{O} \]

Thus, the stoichiometric constants are:

\[ p = 1, \quad q = 4, \quad r = 1, \quad s = 2, \quad t = 2 \]

### Final Answer
The stoichiometric constants are \( p = 1, q = 4, r = 1, s = 2, t = 2 \).

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