Which of the following contains the same number of molecules ?

Options

A. `1g` of `O_(2)`,`2g` of `SO_(2)`
B. `1g` of `CO_(2)` , `1g` of `N_(2)O`
C. `112ml` of `O_(2)` at `STP,` `224 ml` of `He` at `0.5atm` and `273K`
D. All of these

Explanation

To determine which of the following options contains the same number of molecules, we will calculate the number of molecules for each case using the mole concept.

### Step 1: Calculate the number of molecules in 1 gram of O₂

1. **Given Data**:
- Mass of O₂ = 1 gram
- Molar mass of O₂ = 32 g/mol

2. **Calculate Moles of O₂**:
\[ \text{Moles of O₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{1 \text{ g}}{32 \text{ g/mol}} = 0.03125 \text{ mol} \]

3. **Calculate Number of Molecules**:
\[ \text{Number of molecules} = \text{Moles} \times N_A = 0.03125 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.88 \times 10^{22} \text{ molecules} \]

### Step 2: Calculate the number of molecules in 2 grams of SO₂

1. **Given Data**:
- Mass of SO₂ = 2 grams
- Molar mass of SO₂ = 64 g/mol

2. **Calculate Moles of SO₂**:
\[ \text{Moles of SO₂} = \frac{2 \text{ g}}{64 \text{ g/mol}} = 0.03125 \text{ mol} \]

3. **Calculate Number of Molecules**:
\[ \text{Number of molecules} = 0.03125 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.88 \times 10^{22} \text{ molecules} \]

### Step 3: Calculate the number of molecules in 1 gram of CO₂

1. **Given Data**:
- Mass of CO₂ = 1 gram
- Molar mass of CO₂ = 44 g/mol

2. **Calculate Moles of CO₂**:
\[ \text{Moles of CO₂} = \frac{1 \text{ g}}{44 \text{ g/mol}} \approx 0.02273 \text{ mol} \]

3. **Calculate Number of Molecules**:
\[ \text{Number of molecules} = 0.02273 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.37 \times 10^{22} \text{ molecules} \]

### Step 4: Calculate the number of molecules in 1 gram of N₂O

1. **Given Data**:
- Mass of N₂O = 1 gram
- Molar mass of N₂O = 44 g/mol

2. **Calculate Moles of N₂O**:
\[ \text{Moles of N₂O} = \frac{1 \text{ g}}{44 \text{ g/mol}} \approx 0.02273 \text{ mol} \]

3. **Calculate Number of Molecules**:
\[ \text{Number of molecules} = 0.02273 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.37 \times 10^{22} \text{ molecules} \]

### Step 5: Compare the results

- **O₂**: \( \approx 1.88 \times 10^{22} \) molecules
- **SO₂**: \( \approx 1.88 \times 10^{22} \) molecules
- **CO₂**: \( \approx 1.37 \times 10^{22} \) molecules
- **N₂O**: \( \approx 1.37 \times 10^{22} \) molecules

### Conclusion

From the calculations:
- O₂ and SO₂ contain the same number of molecules.
- CO₂ and N₂O contain the same number of molecules.

Thus, the options that contain the same number of molecules are:
1. 1 gram of O₂ and 2 grams of SO₂
2. 1 gram of CO₂ and 1 gram of N₂O

### Final Answer
All options contain the same number of molecules.

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