Which of the following pairs of gases will have identical rate of effusion under similar conditions?

Options

A. Dideuterium and Helium
B. Diprotium and Dideuterium
C. Propene and Propane
D. Nitrogen dioxide and Carbon dioxide

Answer

To determine which pair of gases will have identical rates of effusion under similar conditions, we can use Graham's law of effusion. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Therefore, for two gases to have the same rate of effusion, their molar masses must be identical.

### Step-by-Step Solution:

1. **Identify the Gases and Their Molar Masses**:
- **Deuterium (D2)**: The molar mass of deuterium (D) is approximately 2 g/mol. Thus, for D2, it is \(2 \times 2 = 4 \, \text{g/mol}\).
- **Helium (He)**: The molar mass of helium is approximately 4 g/mol.
- **Diprotein (H2)**: The molar mass of hydrogen (H) is approximately 1 g/mol. Thus, for H2, it is \(2 \times 1 = 2 \, \text{g/mol}\).
- **Diduterium (D2)**: As calculated earlier, D2 is 4 g/mol.
- **Propene (C3H6)**: The molar mass is calculated as \( (12 \times 3) + (1 \times 6) = 36 + 6 = 42 \, \text{g/mol}\).
- **Propane (C3H8)**: The molar mass is calculated as \( (12 \times 3) + (1 \times 8) = 36 + 8 = 44 \, \text{g/mol}\).
- **Nitrogen Dioxide (NO2)**: The molar mass is calculated as \(14 + (16 \times 2) = 14 + 32 = 46 \, \text{g/mol}\).
- **Carbon Dioxide (CO2)**: The molar mass is calculated as \(12 + (16 \times 2) = 12 + 32 = 44 \, \text{g/mol}\).

2. **Compare Molar Masses**:
- **Pair 1**: Deuterium (4 g/mol) and Helium (4 g/mol) → Identical molar masses.
- **Pair 2**: Diprotein (2 g/mol) and Diduterium (4 g/mol) → Different molar masses.
- **Pair 3**: Propene (42 g/mol) and Propane (44 g/mol) → Different molar masses.
- **Pair 4**: Nitrogen Dioxide (46 g/mol) and Carbon Dioxide (44 g/mol) → Different molar masses.

3. **Conclusion**:
The only pair of gases with identical molar masses is Deuterium and Helium. Therefore, they will have identical rates of effusion under similar conditions.

### Final Answer:
The pair of gases that will have identical rates of effusion under similar conditions is **Deuterium (D2) and Helium (He)**.

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