Root Mean Square Speed of Helium

Question

At what temperature in kelvin is the root mean square speed of helium

atoms (atomic weight = 4.00) equal to that of oxygen molecules (molecular

weight = 32.00) at 300. K?

Please include all steps.

Answer 1

The formula for calculating the root mean square velocity is u_rms = √3RT/M

u_rms = root mean square velocity

R = 8.314 J/molK

T = 300K

M = molar mass

For He: u_rms = √3RT_He / M_He

For O2: u_rms = √3RT_O2 / M_O2

Setting these equal to each other, we have...

√3RT_He / M_He = √3RT_O2 / M_O2

Squaring both sides...

3RT_He / M_He = 3RT_O2 / M_O2

Since both sides contain the common R and 3, this reduces to...

RT_He = RT_O2

Solving for T_He we have...

T_He = T_O2M_He / M_O2

T_He = (300K)(4.00) / (32.00)

T_He = = 37.5K