# Ideal Gas

## Homework Statement

The ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a
temperature of 300 K.Find the root mean square speed of the gas atoms.

## Homework Equations

p=(1/3)*(Nm/V)*v(squared)

## The Attempt at a Solution

I tried to make v(squared) the subject, but N(the number of atoms) is not given, and when I looked at the answer, it made v(squared) the subject, and omitted N. I don's understand why do they have to omit N, is it because we are suppose to find the speed for one atom?

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cepheid
Staff Emeritus
Gold Member

## Homework Statement

The ideal gas has a density of 2.4 kgm–3 at a pressure of 2.0 × 105 Pa and a
temperature of 300 K.Find the root mean square speed of the gas atoms.

## Homework Equations

p=(1/3)*(Nm/V)*v(squared)

## The Attempt at a Solution

I tried to make v(squared) the subject, but N(the number of atoms) is not given, and when I looked at the answer, it made v(squared) the subject, and omitted N. I don's understand why do they have to omit N, is it because we are suppose to find the speed for one atom?
Well, N/V is the number of particles per unit of volume. If you multiply this by m, the mass per particle, you get the mass per unit volume. What's another name for that?

Thanks

Well, N/V is the number of particles per unit of volume. If you multiply this by m, the mass per particle, you get the mass per unit volume. What's another name for that?
Oh, I get it, so you mean the density is mN/v, right?

Oh, I get it, so you mean the density is mN/v, right?
Yes, he means that in,

P= mnvrms2/3V

Density is mn/V

m=molar mass
n=number of moles

But you have written N=avogadro's number
m=mass of one molecule ?

Are you giving this formula for 1 mole of gas ?

cepheid
Staff Emeritus
Gold Member
Oh, I get it, so you mean the density is mN/v, right?
Yes, that is exactly what I meant :)

cepheid
Staff Emeritus
Gold Member
Yes, he means that in,

P= mnvrms2/3V

Density is mn/V

m=molar mass
n=number of moles

But you have written N=avogadro's number
m=mass of one molecule ?

Are you giving this formula for 1 mole of gas ?
The OP explicitly stated that N was the total number of atoms. So this problem isn't doing anything with moles.