# Question 33156

May 14, 2015

The first thing you need to know is that the root-mean-square speed, or ${v}_{\text{rms}}$, is used to express the speed of gas particles and is independent of pressure.

Mathematically, the formula used to calculate ${v}_{\text{rms}}$ is

${v}_{\text{rms}} = \sqrt{\frac{3 R T}{M} _ M}$, 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 ${v}_{\text{rms}}$

v_"rms" = sqrt((3 * 8.314"J"/(cancel("mol") * cancel("K")) * (273.15 + 23)cancel("K"))/(159.808 * 10^(-3)"kg"/cancel("mol"))

${v}_{\text{rms" = 215 sqrt("J"/"kg}}$

Since ${\text{1 Joule" = ("kg" * "m"^2)/"s}}^{2}$, you get

v_"rms" = 215 * sqrt((cancel("kg") * "m"^2)/(cancel("kg") * "s"^2)) = color(green)("215 m/s")#