# How is density linked to mass and mols?

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.

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

Kurdt
Staff Emeritus
Science Advisor
Gold Member
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.

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

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

correcto

Kurdt
Staff Emeritus
Science Advisor
Gold Member
Yes units are fine.

Brilliant. Thanks for the help.