Question is in the description

Question

The average kinetic energy of the molecules in a gas sample depends only on the temperature, 𝑇.T. However, given the same kinetic energies, a lighter molecule will move faster than a heavier molecule, as shown in the equation for rms speed

rms speed=3𝑅𝑇ℳ⎯⎯⎯⎯⎯⎯⎯⎯⎯√rms speed=3RTℳ

where 𝑅=8.314 J/(mol⋅K)R=8.314 J/(mol⋅K) and ℳℳ is molar mass in kilograms per mole. Note that a joule is the same as a kilogram‑meter squared per second squared (kg·m²/s²).

What is the rms speed of O2O2 molecules at 411 K?

What is the rms speed of HeHe atoms at 411411 K?

Answer 1

rms speed = √3RT/M not the way you have it written

For O2, M = 32 g / mol x 1 kg / 1000 g = 0.032 kg

rms speed = √(3)(8.314)(411) / 0.032

rms speed = 565 m/s

For He, M = 4 g / mol x 1 kg / 1000 g = 0.004 kg

do the same math as above, but substitute 0.004 in the denominator