A closed vessel contains a mixture of Neon and Sulphur dioxide gases in a 4:1 molar ratio at a temperature of 300 K. The ratio of the root mean square speed of Neon molecules to that of Sulphur dioxide molecules is : (Atomic mass of Neon = 20 u, Molecular mass of Sulphur dioxide = 64 u)

Step-by-step solution

The root mean square speed of a gas molecule is given by v_ rms = 3RT M , where M is the molar mass of the gas. For Neon, M_ Ne = 20 u. For Sulphur dioxide, M_ SO₂ = 64 u. Since both gases are at the same temperature T = 300 K, the ratio of their root mean square speeds is: v_ rms, Ne v_ rms, SO₂ = M_ SO₂ M_ Ne Substituting the given values: v_ rms, Ne v_ rms, SO₂ = 64 20 = 16 5 = 4 5 The molar ratio of the gases does not affect the root mean square speed. Answer: 4 5