Out of following , which molecules has same weight under identical volume at STP ?

Options

A. `.^(14)CO_(2)`
B. `NO_(2)`
C. `.^(13)CO_(2)`
D. `CO_(2)^(18)`

Answer

To determine which molecules have the same weight under identical volume at Standard Temperature and Pressure (STP), we need to calculate the molecular weights of the given molecules: carbon-14 (C-14), carbon dioxide (CO2), nitrogen dioxide (NO2), carbon dioxide with carbon-13 (C-13), and carbon dioxide with oxygen-18 (O-18).

### Step-by-Step Solution:

1. **Calculate the Molecular Weight of Carbon-14 (C-14)**:
- Atomic weight of Carbon (C) = 14 g/mol.
- Since C-14 is a single atom, its molecular weight = 14 g/mol.

2. **Calculate the Molecular Weight of Carbon Dioxide (CO2)**:
- Molecular weight of CO2 = Atomic weight of Carbon + 2 × Atomic weight of Oxygen.
- Atomic weight of Oxygen (O) = 16 g/mol.
- Therefore, molecular weight of CO2 = 14 + 2 × 16 = 14 + 32 = 46 g/mol.

3. **Calculate the Molecular Weight of Nitrogen Dioxide (NO2)**:
- Atomic weight of Nitrogen (N) = 14 g/mol.
- Therefore, molecular weight of NO2 = Atomic weight of Nitrogen + 2 × Atomic weight of Oxygen.
- Molecular weight of NO2 = 14 + 2 × 16 = 14 + 32 = 46 g/mol.

4. **Calculate the Molecular Weight of Carbon Dioxide with Carbon-13 (C-13)**:
- Atomic weight of C-13 = 13 g/mol.
- Therefore, molecular weight of CO2 with C-13 = Atomic weight of C-13 + 2 × Atomic weight of Oxygen.
- Molecular weight = 13 + 2 × 16 = 13 + 32 = 45 g/mol.

5. **Calculate the Molecular Weight of Carbon Dioxide with Oxygen-18 (O-18)**:
- Atomic weight of O-18 = 18 g/mol.
- Therefore, molecular weight of CO2 with O-18 = Atomic weight of Carbon + 2 × Atomic weight of O-18.
- Molecular weight = 12 + 2 × 18 = 12 + 36 = 48 g/mol.

### Summary of Molecular Weights:
- C-14 = 14 g/mol
- CO2 (C-14) = 46 g/mol
- NO2 = 46 g/mol
- CO2 (C-13) = 45 g/mol
- CO2 (O-18) = 48 g/mol

### Conclusion:
The molecules that have the same weight under identical volume at STP are:
- Carbon Dioxide (CO2 with C-14) and Nitrogen Dioxide (NO2), both having a molecular weight of 46 g/mol.

### Final Answer:
**Carbon Dioxide (C-14) and Nitrogen Dioxide (NO2)**.

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