# What is the rms speed of He atoms at 295 K?

##### 1 Answer

The **root-mean-square (RMS) speed** of a gas is:

#\mathbf(upsilon_"RMS" = sqrt((3k_BT)/m) = sqrt((3RT)/(M_m)))# where

#(M_m)/m = R/(k_B)# .

If you feel the need, I do derive where it comes from, here.

#k_B = 1.3806xx10^(-23) "J/K"# is theBoltzmann constant.#R# is theuniversal gas constant, which in this scenario is#"8.314472 J/mol"cdot"K"# .#T# is thetemperaturein#"K"# .#M_m# is themolar massof the gas in#\mathbf("kg/mol")# (NOT#"g/mol"# like it normally would be!!).#m# would be themassofone molecule(or atom) of the gas, in#"kg"# .

Use whichever version floats your boat, but I'm going to use the one on the right because I'm more used to working with relative atomic masses rather than the mass of one atom.

Remember that

#color(blue)(upsilon_"RMS") = sqrt((3RT)/(M_m))#

#= sqrt((3("8.314472 J/mol"cdot"K")("295 K"))/(4.0026xx10^(-3) "kg/mol"))#

#= sqrt((3("8.314472" cancel("kg")cdot"m"^2"/s"^2cdotcancel("mol")cdotcancel("K"))("295" cancel("K")))/(4.0026xx10^(-3) cancel("kg")"/"cancel("mol")))#

#=# #"1355.87 m/s"#

Or to three sig figs,

#=# #color(blue)("1360 m/s")#