The rms velocity of the gas molecule at 327^ C is same as the rms velocity of the oxygen molecules at 27^ C . If the molecular weight of oxygen is 32 then the molecular weight of the given gas molecule is:

Step-by-step solution

The root mean square velocity of a gas is given by the formula v_ rms = 3RT M , where R is the universal gas constant, T is the absolute temperature in Kelvin, and M is the molar mass of the gas. Given that the rms velocity of the gas at T₁ = 327^ C is equal to the rms velocity of oxygen at T₂ = 27^ C , we have: 3RT₁ M₁ = 3RT₂ M₂ Squaring both sides and simplifying, we get: T₁ M₁ = T₂ M₂ Convert the temperatures to Kelvin: T₁ = 327 + 273 = 600 K T₂ = 27 + 273 = 300 K The molar mass of oxygen M₂ = 32 . Substituting