Which of the following have same mass ?

Options

A. `0.1` mol of `O_(2)` gas
B. `0.1 " mol of " SO_(2)` gas
C. `6.02 xx 10^(23) " molecules of " O_(2)` gas
D. `1.204 xx 10^(23) " molecules of " O_(2)` gas

Answer

To determine which of the given options have the same mass, we will calculate the mass for each option using the formula:

\[ n = \frac{m}{M} \]

Where:
- \( n \) = number of moles
- \( m \) = mass (in grams)
- \( M \) = molar mass (in grams per mole)

### Step-by-Step Solution:

1. **Calculate mass for Option 1: 0.1 mole of O₂ gas**
- Molar mass of O₂ = 32 g/mol
- Using the formula:
\[ m = n \times M = 0.1 \, \text{mole} \times 32 \, \text{g/mol} = 3.2 \, \text{grams} \]

2. **Calculate mass for Option 2: 0.1 mole of SO₂ gas**
- Molar mass of SO₂ = 64 g/mol
- Using the formula:
\[ m = n \times M = 0.1 \, \text{mole} \times 64 \, \text{g/mol} = 6.4 \, \text{grams} \]

3. **Calculate mass for Option 3: 6.02 × 10²³ molecules of O₂ gas**
- This is equivalent to 1 mole (since 6.02 × 10²³ is Avogadro's number).
- Molar mass of O₂ = 32 g/mol
- Using the formula:
\[ m = n \times M = 1 \, \text{mole} \times 32 \, \text{g/mol} = 32 \, \text{grams} \]

4. **Calculate mass for Option 4: 1.204 × 10²³ molecules of O₂ gas**
- This is equivalent to 0.2 moles (since \( \frac{1.204 \times 10^{23}}{6.02 \times 10^{23}} = 0.2 \)).
- Molar mass of O₂ = 32 g/mol
- Using the formula:
\[ m = n \times M = 0.2 \, \text{mole} \times 32 \, \text{g/mol} = 6.4 \, \text{grams} \]

### Summary of Masses:
- Option 1: 3.2 grams
- Option 2: 6.4 grams
- Option 3: 32 grams
- Option 4: 6.4 grams

### Conclusion:
Options 2 and 4 both have the same mass of 6.4 grams.