How to find the answer and what is it?

Question

The average kinetic energy of the molecules in a gas sample depends only on the temperature, 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‾‾‾‾‾√

where 𝑅=8.314 J/(mol⋅K) and ℳ 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 Cl2 molecules at 333 K?

rms speed: 

What is the rms speed of He atoms at 333 K?

rms speed:

Answer 1

RMS speed = √3RT/M

For Cl₂, molar mass = 70.9 g = 0.0709 kg

RMS = √(3)(8.314)(333) / 0.0709

RMS = 342 m/s

For He, molar mass 4 g = 0.004 kg

RMS √(3)(8.314)(333) / 0.004

RMS = 1441 m/s