Compute the root-mean-square speed of H2 molecules in a sample of hydrogen gas at a temperature of 193°C. m s-1 ?

1 Answer
Truong-Son N.
Mar 4, 2018

#v_(RMS) = 2.40 xx 10^3 "m/s"#

Refer to here for a derivation of all the Boltzmann speed expressions, and to here for a derivation of the Maxwell-Boltzmann distribution itself.

The RMS speed is then given by

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

with #R = "8.314472 J/mol"cdot"K"# being the universal gas constant, #T# temperature in #"K"#, and #M# molar mass in #"kg/mol"#.

Thus:

#color(blue)(v_(RMS)) = sqrt((3cdot"8.314472 kg"cdot"m"^2cdot"s"^(-2)cdotcancel("mol"^(-1))cdotcancel("K"^(-1))cdot(193+273.15 cancel"K"))/(2 cdot 1.0079 cancel("g"/"mol") cdot "kg"/(1000 cancel"g")))#

#= color(blue)(2.40 xx 10^3 "m/s")#

Again, be sure you use molar mass in #ul"kg/mol"#... energy units use #"J"#, i.e. #"kg"cdot"m"^2"/s"^2#.

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