Calculate RMS speed of hydrogen molecules in a sample of hydrogen gas at 300 K?

1 Answer
Dec 14, 2017

The RMS speed of any homogeneous gas sample is given by:

#v_(RMS) = sqrt((3RT)/M)#,

where #R# is the universal gas constant in #"J/mol"cdotK"#, #T# is temperature in #"K"#, and #M# is molar mass in #"kg/mol"#.

Thus,

#color(blue)(v_(RMS)) = sqrt((3 cdot "8.314472 J/mol"cdot"K" cdot "300. K")/("0.0020158 kg/mol"))#

#=# #color(blue)("1930 m/s")#

to three sig figs. Why did we have to use molar masses in #"kg/mol"#? Why not #"g/mol"#?