A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O₂), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?

Question

Quizplus · Accepted Answer

The root-mean-square velocity of a gas particle is given by:

v(RMS) = sqrt[(3kT)/m]

where k is Boltzmann's constant, T is the temperature, and m is the molar mass of the gas.

To compare the root-mean-square speeds of helium and oxygen, we can take their ratio:

v(RMS)He / v(RMS)O2 = [sqrt((3kT)/(mHe))]/[sqrt((3kT)/(mO2))]
= sqrt(mO2/mHe)
= sqrt((16.0 g/mol)/(4.0 g/mol))
= sqrt(4)
= 2

Therefore, the ratio of the root-mean-square velocities of helium to oxygen is 2. The correct answer is choice C).

A 50-Liter Gas Tank Holds 1