At what temperature is the root mean square speed of helium gas equal to that of oxygen gas at 300. K?
A) 37.5 K
B) 75 K
C) 106 K
D) 292 K
E) 2400. K

Question

Quizplus · Accepted Answer

The root mean square speed of a gas is proportional to the square root of its temperature. Therefore, the root mean square speed of helium gas at a temperature of T will be equal to that of oxygen gas at a temperature of 300 K if T = 300 K * (molar mass of oxygen / molar mass of helium). The molar mass of oxygen is 32 g/mol and the molar mass of helium is 4 g/mol. Therefore, T = 300 K * (32 g/mol / 4 g/mol) = 2400 K.

At What Temperature Is the Root Mean Square Speed of Helium