Question

Find the rms speed of helium atoms when the temperature is 601.016^o C.

Answer 1

μrms = sqrt(3RT/M)

where

μrms = root mean square velocity in m/sec

R = ideal gas constant = 8.3145 (kg·m^2/sec^2) / K·mol

T = absolute temperature in Kelvin

M = mass of a mole of the gas in kilograms

T = 273.15 + 601.016 = 874.166 K

Molar mass of Helium : 4.002 g/mol

(He) is comprised of two helium atoms bonded together. Therefore:

molar mass of He2 = 2 x 4.002

molar mass of He2 = 8.004 g/mol

Convert this to kg/mol:

molar mass of He2 = 32 g/mol x 1 kg/1000 g

molar mass of He = 8.008 x 10^-2 kg/mol

μrms = sqrt(3RT/M)

μrms = sqrt[3(8.3145 (kg·m^2/sec^2)/K·mol)(874.166K) / 8.008 x 10-2 kg/mol]

μrms = sqrt(272287.2 m^2/sec^2)

μrms = 521.8 m/sec