Question

A vessel contains 5900 oxygen molecules at 520 K having Maxwell-Boltzman distrubution function. The universal gas constant is 8.31451 J/K mol. Determine the most probable speed if the molecular mass of oxygen is 0.032 kg/ mol. Answer is m/s.

Find the average speed for the molecules of the gas in m/s.

Find the root-mean-square speed for the particles in the gas in m/s.

I added more points since this is multiple questions. Thanks!

Answer 1

a) most probable speed is given by

$v_{p} =\sqrt{\frac{2RT}{M}}$

R = 8.31451J/K

M= 0.032kg/Mol

T = 520 K

that gives

Vp = 519.8 m/s

b) Average speed is given by

$v_{ave} =\sqrt{\frac{8RT}{\pi M}}$

plugging in the values we get

Vave = 586.7 m/s

C) Root mean square speed is given by

$v_{rms} =\sqrt{\frac{3RT}{\ M}}$

Vrms = 636.7m/s