The answer is 215 m/s.
The first thing you need to know is that the root-mean-square speed, or #v_"rms"#, is used to express the speed of gas particles and is independent of pressure.
Mathematically, the formula used to calculate #v_"rms"# is
#v_("rms") = sqrt((3RT)/M_M)#, where
#R# - the universal gas constant - expressed in Joules per mol K;
#T# - the temperature of the gas in Kelvin;
#M_M# - the molar mass of the gas - expressed in kg permol!
The molar mass of bromine gas is 159.808 g/mol, which is equal to
#159.808cancel("g")/"mol" * (10^(-3)"kg")/(1cancel("g")) = 159.808 * 10^(-3)"kg/mol"#
Plug your data into the equation for root-mean-square speed and solve for #v_"rms"#
#v_"rms" = sqrt((3 * 8.314"J"/(cancel("mol") * cancel("K")) * (273.15 + 23)cancel("K"))/(159.808 * 10^(-3)"kg"/cancel("mol"))#
#v_"rms" = 215 sqrt("J"/"kg"#
Since #"1 Joule" = ("kg" * "m"^2)/"s"^2#, you get
#v_"rms" = 215 * sqrt((cancel("kg") * "m"^2)/(cancel("kg") * "s"^2)) = color(green)("215 m/s")#
