Calculate the number of oxygen atoms requried to combine with `7.0 g` of `N_(2)` to form `N_(2) O_(3)` if 82% of `N_(2)` is converted into products.
`N_(2) + (3)/(2) O_(2) rarr N_(2) O_(3)`

Options

A. `3.24 xx 10^(23)`
B. `3.6 xx 10^(23)`
C. `18 xx 10^(23)`
D. `6.02 xx 10^(23)`

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction is:
\[ N_2 + \frac{3}{2} O_2 \rightarrow N_2O_3 \]

### Step 2: Calculate the molar mass of \( N_2 \)
The molar mass of nitrogen (\( N \)) is approximately \( 14 \, \text{g/mol} \). Therefore, the molar mass of \( N_2 \) is:
\[ 2 \times 14 = 28 \, \text{g/mol} \]

### Step 3: Determine the amount of \( N_2 \) that reacts
Given that \( 7.0 \, \text{g} \) of \( N_2 \) is used and \( 82\% \) of it is converted into products, we first find the moles of \( N_2 \) that react:
1. Calculate the moles of \( N_2 \):
\[ \text{Moles of } N_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{7.0 \, \text{g}}{28 \, \text{g/mol}} = 0.25 \, \text{mol} \]
2. Calculate the moles of \( N_2 \) that actually react:
\[ \text{Moles of } N_2 \text{ that reacts} = 0.25 \, \text{mol} \times \frac{82}{100} = 0.205 \, \text{mol} \]

### Step 4: Calculate the moles of \( O_2 \) required
From the balanced equation, \( 1 \, \text{mol} \) of \( N_2 \) reacts with \( \frac{3}{2} \, \text{mol} \) of \( O_2 \). Therefore, the moles of \( O_2 \) required for \( 0.205 \, \text{mol} \) of \( N_2 \) is:
\[ \text{Moles of } O_2 = 0.205 \, \text{mol} \times \frac{3}{2} = 0.3075 \, \text{mol} \]

### Step 5: Calculate the number of molecules of \( O_2 \)
Using Avogadro's number (\( 6.022 \times 10^{23} \, \text{molecules/mol} \)):
\[ \text{Number of molecules of } O_2 = 0.3075 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.85 \times 10^{23} \, \text{molecules} \]

### Step 6: Calculate the number of oxygen atoms
Since each molecule of \( O_2 \) contains 2 oxygen atoms, the total number of oxygen atoms is:
\[ \text{Number of oxygen atoms} = 1.85 \times 10^{23} \, \text{molecules} \times 2 = 3.70 \times 10^{23} \, \text{atoms} \]

### Final Answer
The number of oxygen atoms required to combine with \( 7.0 \, \text{g} \) of \( N_2 \) to form \( N_2O_3 \) is approximately:
\[ \boxed{3.70 \times 10^{23}} \]