Question

At what temperature average speed of nitrogen will be same as the RMS speed of oxygen at 300 kelvin?

Answer 1

avg speed = v = sqrt(8RT/pi*M)
r_rms = sqrt (3RT/M)

Solve v equation for T
Solve rms sped for T
Set v = vrms = to each other.
Substitute values and solve for T
Post your work if you gets stuck.

Answer 2

RMS = [158(Kelvin Temp/Mol Wt)^1/2]meters/sec

RMS O2 = 158(300/32)^1/2 m/sec
= 484 m/sec

Kelvin Temp for N2 RMS to equal O2 RMS @300K = M(RMS/158)^2
=28(484/158)^2 = 263 Kelvin

Check ...
RMS N2 = 158(263/28)^1/2 m/sec
=484 m/sec