# Root Mean Square Speed Units Question

## Homework Statement

"At 273 K and 1.00x10^-2 atm, the density of a gas is 1.24x10^-5 g/cm^3.

A.) Find the Vrms for the gas molecules
B.) Find the molar mass and identify the gas (Choose from H2, He, H20, N2, O2, or CO2)"

Vrms = √(3RT/Mm)
pV = nRT

## The Attempt at a Solution

n = mass/Mm
pV = mass/Mm *RT
Mm = mass*RT/(pV)
Mm = ρRT/p

Vrms = √(3RT/(ρRT/p)) = √(3p/ρ)

So I have the solution up until this point, the main thing I am worried about is the units of my answer. I have pressure in atm, which is some form of Force/Area. I have density in g/cm^3. So pressure/density will be some form of (distance/time)^2, which of course is taken care of with the radical. The only thing I can not come up with is what exact units it will be in. Any help here would be greatly appreciated. Thanks in advance.

• Htet Htet Bo

A rule of thumb is that if you use SI units for every term in an expression, you can expect the answer to be in SI units. You can do a dimensional analysis to verify this as well. Converting atm to Pascals and g/cm^3 to Kg/m^3, should give you m/s for Vrms.

Ok, that makes sense. Thanks a lot!

SteamKing
Staff Emeritus