Density and r.m.s of an ideal gas

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Homework Help Overview

The discussion revolves around calculating the density and root mean squared (r.m.s) speed of an ideal gas contained in a sealed can. The problem provides specific values for volume, pressure, temperature, and molecular mass, and participants are exploring how to apply relevant equations to derive the required quantities.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculations for the number of moles and the number of molecules, as well as the mass of the gas based on the molecular mass. There are questions about the correct application of the r.m.s formula and the definition of density in relation to the calculated mass and volume.

Discussion Status

The discussion is ongoing, with some participants providing guidance on the interpretation of the formulas and the definitions involved. There is a focus on ensuring that the correct mass is used in the r.m.s calculation and clarifying the relationship between mass, volume, and density.

Contextual Notes

Participants note the importance of correctly identifying the mass of one molecule in the r.m.s formula and emphasize the need to understand how density is defined in terms of mass and volume. There is also mention of the original problem statement and its completeness.

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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