Which of the following has possesses maximum rms velocity? All being at same temperature

Options

A. Oxygen
B. Carbon dioxide
C. Hydrogen
D. Helium

Answer

To determine which gas possesses the maximum root mean square (rms) velocity at the same temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for rms velocity**: The rms velocity (V_rms) of a gas is given by the formula:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molar mass of the gas.

2. **Identify the relationship**: From the formula, we can see that the rms velocity is inversely proportional to the square root of the molar mass (M). This means that as the molar mass decreases, the rms velocity increases.

3. **List the molar masses of the given gases**:
- Oxygen (O₂): Molar mass = 32 g/mol
- Carbon dioxide (CO₂): Molar mass = 44 g/mol
- Hydrogen (H₂): Molar mass = 2 g/mol
- Helium (He): Molar mass = 4 g/mol

4. **Compare the molar masses**: To find which gas has the maximum rms velocity, we need to identify the gas with the lowest molar mass:
- Hydrogen (H₂) has the lowest molar mass of 2 g/mol.
- Helium (He) has a molar mass of 4 g/mol.
- Oxygen (O₂) has a molar mass of 32 g/mol.
- Carbon dioxide (CO₂) has a molar mass of 44 g/mol.

5. **Conclusion**: Since hydrogen has the lowest molar mass, it will have the highest rms velocity among the gases listed. Therefore, the gas that possesses the maximum rms velocity at the same temperature is:
\[ \text{Hydrogen (H₂)} \]

### Final Answer:
The gas with the maximum rms velocity is **Hydrogen (H₂)**.