Question

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (\( V_{\text{rms}} \)) and choose the correct answer from the options given below:

• A. \( V_{\text{rms}} \text{(mono)}>V_{\text{rms}} \text{(dia)}>V_{\text{rms}} \text{(poly)} \)
• B. \( V_{\text{rms}} \text{(dia)}<V_{\text{rms}} \text{(poly)}<V_{\text{rms}} \text{(mono)} \)
• C. \( V_{\text{rms}} \text{(mono)}<V_{\text{rms}} \text{(dia)}<V_{\text{rms}} \text{(poly)} \)
• D. \( V_{\text{rms}} \text{(mono)} = V_{\text{rms}} \text{(dia)} = V_{\text{rms}} \text{(poly)} \)

Hint:

The root mean square speed decreases as the molar mass of the gas increases.

Answer 1

The Correct Option is A

The root mean square speed \( V_{\text{rms}} \) is given by: \[ V_{\text{rms}} = \sqrt{\frac{3RT}{m}} \] Since the gases are at the same temperature and pressure, the root mean square speed depends on the molar mass \( m \). For neon (monoatomic), chlorine (diatomic), and uranium hexafluoride (polyatomic), the molar mass increases in the order: \[ V_{\text{rms}} \text{(mono)}>V_{\text{rms}} \text{(dia)}>V_{\text{rms}} \text{(poly)} \] Thus, the correct answer is \( V_{\text{rms}} \text{(mono)}>V_{\text{rms}} \text{(dia)}>V_{\text{rms}} \text{(poly)} \).