The temperature of an ideal gas is increased from -173 ^ C to 127 ^ C . What is the percentage increase in the root mean square (rms) speed of the gas molecules?

Step-by-step solution

The root mean square (rms) speed of gas molecules is given by v = 3RT M . This implies that v T , where T is the absolute temperature in Kelvin. Initial temperature, T₁ = -173 + 273 = 100 K Final temperature, T₂ = 127 + 273 = 400 K Taking the ratio of the final speed to the initial speed: v₂ v₁ = T₂ T₁ = 400 100 = 4 = 2 This means v₂ = 2v₁ . The percentage increase in the rms speed is: v₂ - v₁ v₁ 100 % = 2v₁ - v₁ v₁ 100 % = 100 % Answer: 100 %