Which of the following contains greatest number of oxygen atoms ? .

Options

A. 1g of O
B. 1g of `O_(2)`
C. 1g of `O_(3)`
D. All have the same number of atoms

Explanation

To determine which of the given options contains the greatest number of oxygen atoms, we need to calculate the number of moles of oxygen atoms in each option and then convert that to the number of oxygen atoms.

### Step-by-Step Solution:

1. **Identify the options**:
- 1 gram of oxygen (O)
- 1 gram of O2 (oxygen molecule)
- 1 gram of O3 (ozone molecule)
- All have the same number of atoms

2. **Calculate the number of moles for each option**:
- **For 1 gram of O**:
- The atomic weight of oxygen (O) = 16 g/mol
- Number of moles of O = mass / molar mass = 1 g / 16 g/mol = 0.0625 moles of O

- **For 1 gram of O2**:
- The molecular weight of O2 = 32 g/mol
- Number of moles of O2 = mass / molar mass = 1 g / 32 g/mol = 0.03125 moles of O2

- **For 1 gram of O3**:
- The molecular weight of O3 = 48 g/mol
- Number of moles of O3 = mass / molar mass = 1 g / 48 g/mol = 0.02083 moles of O3

3. **Calculate the number of oxygen atoms in each option**:
- **For O**:
- Each mole of O contains 1 mole of oxygen atoms.
- Number of oxygen atoms = 0.0625 moles × Avogadro's number (N_A = 6.022 × 10^23) = 0.0625 × 6.022 × 10^23 ≈ 3.76 × 10^22 oxygen atoms.

- **For O2**:
- Each mole of O2 contains 2 moles of oxygen atoms.
- Number of oxygen atoms = 0.03125 moles × 2 × N_A = 0.03125 × 2 × 6.022 × 10^23 ≈ 3.76 × 10^22 oxygen atoms.

- **For O3**:
- Each mole of O3 contains 3 moles of oxygen atoms.
- Number of oxygen atoms = 0.02083 moles × 3 × N_A = 0.02083 × 3 × 6.022 × 10^23 ≈ 3.76 × 10^22 oxygen atoms.

4. **Compare the number of oxygen atoms**:
- For 1 gram of O: ≈ 3.76 × 10^22 oxygen atoms
- For 1 gram of O2: ≈ 3.76 × 10^22 oxygen atoms
- For 1 gram of O3: ≈ 3.76 × 10^22 oxygen atoms

5. **Conclusion**:
- All three options (1 gram of O, 1 gram of O2, and 1 gram of O3) contain the same number of oxygen atoms.
- Therefore, the correct answer is: **All have the same number of atoms**.