Find the RMS speed of #"H"_2# at #"273.15 K"# and #"293.15 K"#? The density at STP is #"0.08988 g/L"#.
1 Answer
Feb 15, 2018
The density given doesn't matter. The RMS speed is:
#v_(RMS) = sqrt((3RT)/M)# where
#R# is the universal gas constant in energy units,#T# is in#"K"# , and#M# is the molar mass in#"kg/mol"# .
Since you are given the temperatures, and since density varies with temperature anyway, ignore the density.
#color(blue)(v_(RMS1)) = sqrt((3RT_1)/M)#
#= sqrt((3cdot"8.314472 kg"cdot"m"^2"/s"^2"/mol"cdot"K" cdot "273.15 K")/("0.0028014 kg/mol"))#
#=# #color(blue)("1560 m/s")#
#color(blue)(v_(RMS2)) = sqrt((3RT_2)/M)#
#= sqrt((3cdot"8.314472 kg"cdot"m"^2"/s"^2"/mol"cdot"K" cdot "293.15 K")/("0.0028014 kg/mol"))#
#=# #color(blue)("1620 m/s")#
