Which one of the following parts of gases contains the same number of molecules?

Options

A. (a)`16g " of "O_(2)and14 g " of "N_(2)`
B. (b)`8g " of "O_(2)and22 g " of " CO_(2)`
C. (c)`28 g " of " N_(2)and 22 g " of " CO_(2)`
D. (d)`32g " of " O_(2)and 32g " of " N_(2)`

Answer

To determine which of the given parts of gases contains the same number of molecules, we need to calculate the number of moles for each gas in the options provided. The number of moles can be calculated using the formula:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molecular mass}} \]

Once we have the number of moles, we can find the number of molecules using Avogadro's number (\(N_A\)), which is approximately \(6.022 \times 10^{23}\) molecules/mole. The relationship is given by:

\[ \text{Number of molecules} = \text{Number of moles} \times N_A \]

Now, let's analyze the options step by step:

### Option A: 16 grams of O2 and 14 grams of N2
1. **Calculate moles of O2**:
- Molecular mass of O2 = 32 g/mol
- Moles of O2 = \( \frac{16 \text{ g}}{32 \text{ g/mol}} = 0.5 \text{ moles} \)

2. **Calculate moles of N2**:
- Molecular mass of N2 = 28 g/mol
- Moles of N2 = \( \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ moles} \)

3. **Calculate number of molecules**:
- For O2: \( 0.5 \text{ moles} \times N_A = 0.5 N_A \)
- For N2: \( 0.5 \text{ moles} \times N_A = 0.5 N_A \)

Since both gases have \(0.5 N_A\) molecules, they contain the same number of molecules.

### Option B: 8 grams of O2 and 22 grams of CO2
1. **Calculate moles of O2**:
- Moles of O2 = \( \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ moles} \)

2. **Calculate moles of CO2**:
- Molecular mass of CO2 = 44 g/mol
- Moles of CO2 = \( \frac{22 \text{ g}}{44 \text{ g/mol}} = 0.5 \text{ moles} \)

3. **Calculate number of molecules**:
- For O2: \( 0.25 \text{ moles} \times N_A = 0.25 N_A \)
- For CO2: \( 0.5 \text{ moles} \times N_A = 0.5 N_A \)

These values are not equal, so this option is incorrect.

### Option C: 28 grams of O2 and 22 grams of CO2
1. **Calculate moles of O2**:
- Moles of O2 = \( \frac{28 \text{ g}}{32 \text{ g/mol}} = 0.875 \text{ moles} \)

2. **Calculate moles of CO2**:
- Moles of CO2 = \( \frac{22 \text{ g}}{44 \text{ g/mol}} = 0.5 \text{ moles} \)

3. **Calculate number of molecules**:
- For O2: \( 0.875 \text{ moles} \times N_A = 0.875 N_A \)
- For CO2: \( 0.5 \text{ moles} \times N_A = 0.5 N_A \)

These values are not equal, so this option is incorrect.

### Option D: 32 grams of O2 and 32 grams of N2
1. **Calculate moles of O2**:
- Moles of O2 = \( \frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole} \)

2. **Calculate moles of N2**:
- Moles of N2 = \( \frac{32 \text{ g}}{28 \text{ g/mol}} \approx 1.14 \text{ moles} \)

3. **Calculate number of molecules**:
- For O2: \( 1 \text{ mole} \times N_A = 1 N_A \)
- For N2: \( 1.14 \text{ moles} \times N_A \approx 1.14 N_A \)

These values are not equal, so this option is incorrect.

### Conclusion:
The only option where the number of molecules is the same is **Option A** (16 grams of O2 and 14 grams of N2).