8 g of `O_(2)` has the same number of oxygen atoms as

Options

A. `11g CO_(2)`
B. 14 g of CO
C. 32 g of `SO_(2)`
D. 8g `O_(3)`

Explanation

To solve the problem of how many grams of a substance contain the same number of oxygen atoms as 8 g of \( O_2 \), we will follow these steps:

### Step 1: Calculate the number of moles of \( O_2 \)
The molecular weight of \( O_2 \) (oxygen gas) is calculated as follows:
- Each oxygen atom has an atomic weight of 16 g/mol.
- Therefore, the molecular weight of \( O_2 \) is \( 2 \times 16 = 32 \) g/mol.

Now, we can calculate the number of moles of \( O_2 \) in 8 g:
\[ \text{Moles of } O_2 = \frac{\text{mass}}{\text{molecular weight}} = \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 2: Calculate the number of oxygen atoms in \( O_2 \)
Each mole of \( O_2 \) contains 2 moles of oxygen atoms. Therefore, the number of moles of oxygen atoms in 0.25 moles of \( O_2 \) is:
\[ \text{Moles of oxygen atoms} = 0.25 \text{ moles of } O_2 \times 2 = 0.5 \text{ moles of oxygen atoms} \]

### Step 3: Convert moles of oxygen atoms to the number of atoms
Using Avogadro's number (\( 6.022 \times 10^{23} \) atoms/mole), we can find the total number of oxygen atoms:
\[ \text{Number of oxygen atoms} = 0.5 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 3.011 \times 10^{23} \text{ atoms} \]

### Step 4: Find substances that contain the same number of oxygen atoms
Now, we need to find other substances that also contain \( 0.5 \) moles of oxygen atoms, which corresponds to \( 3.011 \times 10^{23} \) oxygen atoms.

1. **For \( CO_2 \)**:
- Molar mass of \( CO_2 \) = 12 (C) + 2 × 16 (O) = 44 g/mol.
- Moles of \( CO_2 \) in 11 g:
\[ \text{Moles of } CO_2 = \frac{11 \text{ g}}{44 \text{ g/mol}} = 0.25 \text{ moles} \]
- Moles of oxygen atoms = \( 0.25 \times 2 = 0.5 \text{ moles} \).

2. **For \( CO \)**:
- Molar mass of \( CO \) = 12 (C) + 16 (O) = 28 g/mol.
- Moles of \( CO \) in 14 g:
\[ \text{Moles of } CO = \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ moles} \]
- Moles of oxygen atoms = \( 0.5 \) moles.

3. **For \( SO_2 \)**:
- Molar mass of \( SO_2 \) = 32 (S) + 2 × 16 (O) = 64 g/mol.
- Moles of \( SO_2 \) in 32 g:
\[ \text{Moles of } SO_2 = \frac{32 \text{ g}}{64 \text{ g/mol}} = 0.5 \text{ moles} \]
- Moles of oxygen atoms = \( 0.5 \times 2 = 1 \text{ mole} \) (not valid).

4. **For \( O_3 \)**:
- Molar mass of \( O_3 \) = 3 × 16 = 48 g/mol.
- Moles of \( O_3 \) in 8 g:
\[ \text{Moles of } O_3 = \frac{8 \text{ g}}{48 \text{ g/mol}} = 0.1667 \text{ moles} \]
- Moles of oxygen atoms = \( 0.1667 \times 3 = 0.5 \text{ moles} \).

### Conclusion
The substances that have the same number of oxygen atoms as 8 g of \( O_2 \) are:
- 11 g of \( CO_2 \)
- 14 g of \( CO \)
- 8 g of \( O_3 \)