How is density linked to mass and mols?

[JosephF]

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 can't 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,

 

[Kurdt]

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.

 

[Chewy0087]

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

 

[JosephF]

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

 

[Chewy0087]

correcto

 

[Kurdt]

Yes units are fine.

 

[JosephF]

Brilliant. Thanks for the help.