# Homework Help: Density and r.m.s of an ideal gas

1. Sep 10, 2014

### Apothem

1. The problem statement, all variables and given/known data

A can which is sealed of a volume 0.035m3 contains an ideal gas with a pressure of 150kPa, at a temperature of 350K.
Calculate the gas density and the root mean squared speed of the gas molecules
(P.S. the molecular mass is stated as 28)

2. Relevant equations

r.m.s=sqrt(3kT/m) density=molar massxP/RxT

3. The attempt at a solution

So before this I calculated the number of moles: (150x103)*(0.035)/(8.31*350)= 1.81 moles (3.s.f)
The number of molecules: N=n*Na=(1.80....)*(6.023x1023)=1.09x1024 molecules (3.s.f)
The mass of the gas (the molecular mass is stated as 28) mass=n*M=(1.80...)(28)=50.5g (3.s.f)

For r.m.s, do I simply just have to put the mass I just calculated into the equation? For the density, do I just put the molar mass as 28?

Thanks for any help in advance!

Last edited: Sep 10, 2014
2. Sep 10, 2014

### SteamKing

Staff Emeritus
It seems like the following should have been put into the Problem Statement:

3. Sep 10, 2014

### Apothem

Sorry I have added it now.

4. Sep 10, 2014

### ehild

In the formula for the rms speed, m is the mass of one molecule.

As for the density, you calculated the mass of the gas already: it is 50.5 g. The volume of the gas is given. And you certainly know how the density is defined with mass and volume ?

ehild