To determine which pairs of gases contain the same number of molecules, we need to calculate the number of moles for each gas in the given pairs. The number of moles can be calculated using the formula:
\[
\text{Number of moles} = \frac{\text{Given mass (g)}}{\text{Molar mass (g/mol)}}
\]
1. **Option 1: 16 g of O2 and 14 g of N2**
- Calculate moles of O2:
\[
\text{Molar mass of O2} = 32 \, \text{g/mol}
\]
\[
\text{Moles of O2} = \frac{16 \, \text{g}}{32 \, \text{g/mol}} = 0.5 \, \text{moles}
\]
- Calculate moles of N2:
\[
\text{Molar mass of N2} = 28 \, \text{g/mol}
\]
\[
\text{Moles of N2} = \frac{14 \, \text{g}}{28 \, \text{g/mol}} = 0.5 \, \text{moles}
\]
- **Conclusion for Option 1**: Both O2 and N2 have 0.5 moles, thus they contain the same number of molecules.
2. **Option 2: 8 g of O2 and 22 g of CO2**
- Calculate moles of O2:
\[
\text{Moles of O2} = \frac{8 \, \text{g}}{32 \, \text{g/mol}} = 0.25 \, \text{moles}
\]
- Calculate moles of CO2:
\[
\text{Molar mass of CO2} = 12 + 32 = 44 \, \text{g/mol}
\]
\[
\text{Moles of CO2} = \frac{22 \, \text{g}}{44 \, \text{g/mol}} = 0.5 \, \text{moles}
\]
- **Conclusion for Option 2**: O2 has 0.25 moles and CO2 has 0.5 moles, so they do not contain the same number of molecules.
3. **Option 3: 28 g of N2 and 22 g of CO2**
- Calculate moles of N2:
\[
\text{Moles of N2} = \frac{28 \, \text{g}}{28 \, \text{g/mol}} = 1 \, \text{mole}
\]
- Calculate moles of CO2:
\[
\text{Moles of CO2} = \frac{22 \, \text{g}}{44 \, \text{g/mol}} = 0.5 \, \text{moles}
\]
- **Conclusion for Option 3**: N2 has 1 mole and CO2 has 0.5 moles, so they do not contain the same number of molecules.
4. **Option 4: 32 g of CO2 and 28 g of N2**
- Calculate moles of CO2:
\[
\text{Moles of CO2} = \frac{32 \, \text{g}}{44 \, \text{g/mol}} \approx 0.727 \, \text{moles}
\]
- Calculate moles of N2:
\[
\text{Moles of N2} = \frac{28 \, \text{g}}{28 \, \text{g/mol}} = 1 \, \text{mole}
\]
- **Conclusion for Option 4**: CO2 has approximately 0.727 moles and N2 has 1 mole, so they do not contain the same number of molecules.
**Final Answer**: The pair of gases that contains the same number of molecules is **Option 1: 16 g of O2 and 14 g of N2**.
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