How to calculate the root mean square speed, vrms, in m·s^-1 at 227 Celsius and 900 torr, of a gas having a molar mass of 16.0 g·mol^-1 ?

1 Answer
Stefan V.
Feb 28, 2015

There are two important things to look out for when doing root-mean-square speed calculations

  1. You must use the value for R expressed in Joules per mol K → R=8.31446Jmol⋅K;
  2. You must use molar mass in kilograms;

Using these units will get you to the required units for gas velocity, m⋅s−1.

So, root-mean-square speed allows you to have some measure on the speed of particles in a gas. Mathematically, the equation looks like this

vrms=√3RTMm, where

R - the universal gas constant;
T - the temperature of the gas in Kelvin;
Mm - the molar mass of the gas;

I'll convert the molar mass from g per mole to kg per mole first, and then plug all the value into the equation for root-mean-square speed

16.0gmol⋅1 kg1000 g=0.016kgmol

Therefore,

vrms= ⎷3⋅8.31446Jmol⋅K⋅(273.15+227)K0.016kgmol

vrms=883.01⋅√Jkg

Use the fact that Joule=kg⋅m2s2 to get

vrms=883.01⋅√kg⋅m2kg⋅s2=883.01ms=111.7 m⋅s−1

Rounded to three sig figs, the answer will be

vrms=883 m⋅s−1

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