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How is density linked to mass and mols?

  • Thread starter JosephF
  • Start date
  • #1
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Apologies for numerous posts today, I'm trying to catch up from work I missed last term, and my uni is on holiday at the moment so cant get help from lecturers.

I've got these two questions. I think I've correctly worked them out however I'm currently stuck on the last part. How is density linked to mass and mols?

Homework Statement



1 A gas cylinder contains 0.12 m3 of a gas at a pressure of 4545 kPa. What volume would it occupy if it was all released into a pressure of 101 kPa? Assume the temperature remains constant.

2 A car tyre of volume 1.0 * 10-2 m3 contains air at a pressure of 300 kPa and at a temperature of 17oC. The mass of one mole of air is 2.9 *10-2 kg. Assuming that the air behaves as an ideal gas, calculate;
i. the amount of air in moles,
ii. the mass of the air,
iii. the density of the air.


Homework Equations



pV=k

pV=nRT

The Attempt at a Solution



1) pV=k

4545kPa x 0.12m3=545.4

Therefore:

101Pa x V = 545.3

V = 5.4m3

2)i) Assuming ideal gas.

pV=nRT

n=[(4545x103Pa)(1x10-2m3)] / [(8.31Jmol-1K-1)(290.15K)]

n=18.84995375mol

ii) mass of gas = 18.84995375mol x 2.9x10-2

=0.546648658

=0.547 (3dp) kg

iii) Please see above comments.

Thanks,
 

Answers and Replies

  • #2
Kurdt
Staff Emeritus
Science Advisor
Gold Member
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How do you normally work out density? You're given the mass of one mole and you've worked out how many moles there are.
 
  • #3
370
0
Density = Mass / Volume

I've not really read through all of your work but seems right

edit: sorry >.< i'll try to be more constructive next time
 
  • #4
14
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Is it just the mass of the total gas / volume. So;

Density = 0.546648658 / 1.0x10-2

=54.66486586kg/m3

Have I got the unit correct?

Thanks
 
  • #5
370
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correcto
 
  • #6
Kurdt
Staff Emeritus
Science Advisor
Gold Member
4,812
6
Yes units are fine.
 
  • #7
14
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Brilliant. Thanks for the help.
 

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