Read the following statements carefully: (A) If the temperature of a gas in ^ C is doubled, its rms speed increases by a factor of 2 . (B) To increase the rms speed of a gas by 50 % , its absolute temperature must be increased by 125 % . (C) At a given temperature, the rms speed of SO ₂ gas is half that of CH ₄ gas. (D) If the volume of a given mass of gas is halved at constant temperature, its rms speed is doubled.

Step-by-step solution

Statement (A) is incorrect because the rms speed is proportional to the square root of absolute temperature (in Kelvin), not temperature in ^ C . Statement (B) is correct. Let initial speed be v and absolute temperature be T . The new speed v' = v + 0.5v = 1.5v . Since v T , T' (v')^2 = (1.5v)^2 = 2.25 v^2 . Thus, T' = 2.25T . The percentage increase in temperature is 2.25T - T T 100 % = 125 % . Statement (C) is correct. v_ rms = 3RT M . At constant temperature, v_ rms 1 M . Molar mass of SO ₂ = 64 g/mol and CH ₄ =