Which of the following has number of molecules present equal to those present in 16 grams of oxygen

Options

A. `16g O_(3)`
B. `32g SO_(2)`
C. `16gSO_(2)`
D. All the above

Answer

To solve the problem of determining which substance has the same number of molecules as those present in 16 grams of oxygen, we will follow these steps:

### Step 1: Calculate the number of moles in 16 grams of oxygen (O₂).
- The molecular mass of oxygen (O₂) is calculated as:
\[ \text{Molecular mass of O}_2 = 2 \times 16 \, \text{g/mol} = 32 \, \text{g/mol} \]
- Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{16 \, \text{g}}{32 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 2: Determine the number of moles in each option provided.
1. **For 16 grams of ozone (O₃)**:
- The molecular mass of ozone (O₃) is:
\[ \text{Molecular mass of O}_3 = 3 \times 16 \, \text{g/mol} = 48 \, \text{g/mol} \]
- Calculate the number of moles:
\[ \text{Number of moles} = \frac{16 \, \text{g}}{48 \, \text{g/mol}} = \frac{1}{3} \, \text{moles} \]

2. **For 32 grams of sulfur dioxide (SO₂)**:
- The molecular mass of sulfur dioxide (SO₂) is:
\[ \text{Molecular mass of SO}_2 = 32 \, \text{g/mol (S)} + 2 \times 16 \, \text{g/mol (O)} = 64 \, \text{g/mol} \]
- Calculate the number of moles:
\[ \text{Number of moles} = \frac{32 \, \text{g}}{64 \, \text{g/mol}} = 0.5 \, \text{moles} \]

3. **For 16 grams of sulfur dioxide (SO₂)**:
- Using the same molecular mass of SO₂:
- Calculate the number of moles:
\[ \text{Number of moles} = \frac{16 \, \text{g}}{64 \, \text{g/mol}} = \frac{1}{4} \, \text{moles} \]

### Step 3: Compare the number of moles.
- From our calculations:
- 16 grams of O₂ = 0.5 moles
- 16 grams of O₃ = \( \frac{1}{3} \) moles
- 32 grams of SO₂ = 0.5 moles
- 16 grams of SO₂ = \( \frac{1}{4} \) moles

### Conclusion:
The substance that has the same number of moles (and thus the same number of molecules) as 16 grams of oxygen is **32 grams of sulfur dioxide (SO₂)**.