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")#