The number of oxygen atoms required to combine with 7 g of `N_2` to form `N_2 O_3` when 80% of `N_2` is converted to `N_2 O_3`.

Options

A. `2.3 xx 10^(23)`
B. `3.6 xx 10^23`
C. `1.8 xx 10^(21)`
D. `5.4 xx 10^(21)`

Answer

To solve the problem of determining the number of oxygen atoms required to combine with 7 g of \( N_2 \) to form \( N_2O_3 \) when 80% of \( N_2 \) is converted to \( N_2O_3 \), we can follow these steps:

### Step 1: Determine the number of moles of \( N_2 \)
The number of moles is calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
For \( N_2 \):
- Given mass = 7 g
- Molar mass of \( N_2 = 28 \, \text{g/mol} \)

Calculating the moles:
\[ \text{Number of moles of } N_2 = \frac{7 \, \text{g}}{28 \, \text{g/mol}} = 0.25 \, \text{moles} \]

### Step 2: Calculate the amount of \( N_2 \) converted to \( N_2O_3 \)
Since 80% of \( N_2 \) is converted:
\[ \text{Moles of } N_2 \text{ converted} = 0.80 \times 0.25 \, \text{moles} = 0.20 \, \text{moles} \]

### Step 3: Write the balanced chemical equation
The balanced equation for the formation of \( N_2O_3 \) is:
\[ N_2 + \frac{3}{2} O_2 \rightarrow N_2O_3 \]

### Step 4: Determine the moles of \( O_2 \) required
From the balanced equation, 1 mole of \( N_2 \) reacts with 1.5 moles of \( O_2 \). Therefore, for 0.20 moles of \( N_2 \):
\[ \text{Moles of } O_2 \text{ required} = 0.20 \, \text{moles} \times 1.5 = 0.30 \, \text{moles} \]

### Step 5: Calculate the number of oxygen molecules
We know that 1 mole of \( O_2 \) contains \( 6.022 \times 10^{23} \) molecules (Avogadro's number). Thus, for 0.30 moles of \( O_2 \):
\[ \text{Number of } O_2 \text{ molecules} = 0.30 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 1.8066 \times 10^{23} \, \text{molecules} \]

### Step 6: Calculate the number of oxygen atoms
Each \( O_2 \) molecule contains 2 oxygen atoms. Therefore, the total number of oxygen atoms is:
\[ \text{Number of oxygen atoms} = 1.8066 \times 10^{23} \, \text{molecules} \times 2 = 3.6132 \times 10^{23} \, \text{atoms} \]

### Final Answer
The number of oxygen atoms required to combine with 7 g of \( N_2 \) to form \( N_2O_3 \) is approximately:
\[ 3.61 \times 10^{23} \, \text{atoms} \]