Calculate Nitrogen Gas Density at 1.7 Atm, 332K

[LostInScience]

Homework Statement

What is the density of nitrogen gas (molecular mass = 28 u) at a pressure of 1.7 atmospheres and a temperature of 332 K?

Homework Equations

You must convert pressure from atmospheres to Pascals. I'vedone this using the conversion 1 atmosphere = 1.01*10^5 pascals.
I was also told that I needed to convert molecular mass into kilograms. Given a molecular mass of 28u. I calculated the mass in kilograms to be 0.00002799 kg/mole of Nitrogen.

The Attempt at a Solution

1 molecule of Nitrogen = 28u
28u * 1.066*10^-27=4.648*10^-26 grams per molecule.
1 mole = 6.022*10^23 molecules therefore 1 mole = 0.027990256 grams.
There are 1000 grams in 1 kg. So 1 mole = 0.00002799 kg of Nitrogen.
volume=nRt/p
If I assume 1 mole and am given R=8.31 t=332k and p=1.7 atmospheres
My equation should come to be volume = (1)(8.31)(332)/171700.

This gave me a volume of approximately 0.01607

If I then divide my mass in kilograms by this I get 0.00175 as my density which is wrong.

Am I missing a step?

Am I using the wrong equations?

Thanks in advance for any help you can offer!

 

[mgb_phys]

1 atmoshere is 101.4 KPa ( a useful number to remember)
You have the mass wrong, 1 mole of a substance is it's atomic mass in grams.
So N2 = 2*14 = 28g/mole or 0.028 kg/mole.
Don't work in individual atoms, work in moles - makes the numbers more reasonable.

Then you need PV = nRT to tell you how many moles are in a given volume at a given temp/pressure.
See http://en.wikipedia.org/wiki/Pv=nrt for values / units.

Hint - another useful number to know is that 1 mole of a gas at stp is 22.4 litres, this comes out of the above equation.

 

[Urmi Roy]

A quick question-

"Hint - another useful number to know is that 1 mole of a gas at stp is 22.4 litres, this comes out of the above equation."

...Then what is the volume of 1 kilogram mole of an ideal gas?

 

[Borek]

...Then what is the volume of 1 kilogram mole of an ideal gas?

What is kilogram mole? How is it related to just a mole?

Note that STP is ambiguous and in different contexts means different things.

 

[Urmi Roy]

kilogram mole is supposed to be the amount of a substance containing as many elementary particles as there is in 12kg C12 isotope.

 

[Urmi Roy]

If 1 gram mole of an ideal gas has a volume of 22.4 metre cube,then perhaps 1 kg-mole has a volume of 22.4x10^3 metre cube??

 

[Borek]

If 1 gram mole of an ideal gas has a volume of 22.4 metre cube,then perhaps 1 kg-mole has a volume of 22.4x10^3 metre cube??

Yes and no.

Yes - your thinking is correct. No - 22.4 cubic meters is a wrong value to start with.

 

[Urmi Roy]

Then I guess the volume of 1 gram mole is 22.4 litres and that of 1 kg-mole is 22.4 metre-cube??

 

[Borek]

Yes.

 

[Urmi Roy]

Thanks.