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 finding 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 will follow these steps:

### Step 1: Write the Balanced Chemical Equation
The balanced chemical equation for the formation of \( N_2O_3 \) from \( N_2 \) and \( O_2 \) is:
\[ 2 N_2 + 3 O_2 \rightarrow 2 N_2O_3 \]

### Step 2: Calculate Moles of \( N_2 \)
To find the moles of \( N_2 \) in 7 g, we first need the molar mass of \( N_2 \):
- The atomic mass of nitrogen (N) is 14 g/mol.
- Therefore, the molar mass of \( N_2 \) is \( 2 \times 14 = 28 \) g/mol.

Now, calculate the moles of \( N_2 \):
\[ \text{Moles of } N_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{7 \text{ g}}{28 \text{ g/mol}} = \frac{1}{4} \text{ mol} \]

### Step 3: Determine the Amount of \( N_2 \) Converted to \( N_2O_3 \)
Since 80% of \( N_2 \) is converted to \( N_2O_3 \):
\[ \text{Moles of } N_2 \text{ converted} = 0.8 \times \frac{1}{4} = \frac{0.2}{1} \text{ mol} \]

### Step 4: Use Stoichiometry to Find Moles of \( O_2 \) Required
From the balanced equation, we see that:
- 2 moles of \( N_2 \) react with 3 moles of \( O_2 \).

Using the stoichiometric ratio:
\[ \text{Moles of } O_2 \text{ required for } 0.2 \text{ mol of } N_2 = 0.2 \text{ mol } N_2 \times \frac{3 \text{ mol } O_2}{2 \text{ mol } N_2} = 0.3 \text{ mol } O_2 \]

### Step 5: Calculate the Number of Oxygen Molecules
To find the number of molecules of \( O_2 \):
\[ \text{Number of } O_2 \text{ molecules} = 0.3 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.8066 \times 10^{23} \text{ molecules of } O_2 \]

### Step 6: Calculate the Number of Oxygen Atoms
Since each molecule of \( O_2 \) contains 2 oxygen atoms:
\[ \text{Number of oxygen atoms} = 1.8066 \times 10^{23} \text{ molecules} \times 2 \text{ atoms/molecule} = 3.6132 \times 10^{23} \text{ atoms} \]

### Final Answer
The number of oxygen atoms required is approximately:
\[ 3.61 \times 10^{23} \text{ atoms} \]