Question

At a given temperature, arrange the gases hydrogen, oxygen, nitrogen in the order of maximum rms speeds:

• A. Hydrogen>Nitrogen>Oxygen
• B. Nitrogen>Hydrogen>Oxygen
• C. Oxygen>Nitrogen>Hydrogen
• D. Hydrogen = Nitrogen = Oxygen

Hint:

Remember that the root mean square speed is inversely proportional to the square root of the molar mass. Hence, lighter gases have higher speeds.

Answer 1

The Correct Option is A

The root mean square (rms) speed of a gas is given by the formula:

\[ v_{{rms}} = \sqrt{\frac{3kT}{m}} \] Where: - \( k \) is the Boltzmann constant,
- \( T \) is the temperature,
- \( m \) is the molar mass of the gas.

At a given temperature, the rms speed is inversely proportional to the square root of the molar mass. Therefore, lighter gases will have higher rms speeds.

The molar masses of the gases are as follows:
- Hydrogen (H\(_2\)): 2 g/mol,
- Nitrogen (N\(_2\)): 28 g/mol,
- Oxygen (O\(_2\)): 32 g/mol.

Hence, the order of gases based on the maximum rms speed is: \[ \text{Hydrogen} > \text{Nitrogen} > \text{Oxygen} \] Thus, the correct answer is: Hydrogen > Nitrogen > Oxygen.