Density and r.m.s of an ideal gas

AI Thread Summary
The discussion focuses on calculating the density and root mean squared (r.m.s) speed of an ideal gas contained in a sealed can with a volume of 0.035 m³, pressure of 150 kPa, and temperature of 350 K. The user has already calculated the number of moles (1.81 moles) and the total mass of the gas (50.5 g) using the molecular mass of 28. Clarification is sought on whether to use the calculated mass in the r.m.s speed formula and if the molar mass should be directly applied for density calculations. It is confirmed that the r.m.s speed formula requires the mass of a single molecule, while density can be derived from the total mass and volume. The discussion emphasizes the importance of correctly applying the formulas for ideal gas properties.
Apothem
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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!
 
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Apothem said:

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

Sorry I have added it now.
 
Apothem said:

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
 
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