Density and r.m.s of an ideal gas

[Apothem]

Homework Statement

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)

Homework Equations

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

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!

 

[SteamKing]

Homework Statement

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

Homework Equations

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

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!

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

The mass of the gas (the molecular mass is stated as 28)

 

[Apothem]

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

Sorry I have added it now.

 

[ehild]

Homework Statement

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)

Homework Equations

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

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!

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

 

[HalfLostAndSearching]

Yes, you are on the right track. For the root mean squared speed, you can use the equation you provided: r.m.s=sqrt(3kT/m). However, you need to convert the mass from grams to kilograms in order to get the correct units for the speed. So the correct calculation would be: r.m.s=sqrt(3kT/(m*0.001)). And yes, for the density, you can use the equation: density=molar mass x P/R x T. Just make sure to convert the pressure from kPa to Pa before plugging it into the equation.