Finding composition of air (Ideal gas law)

[jricci12]

The problem is as follows:

 

The density of dry air at 1.00 atm and 34.4 degrees Celsius is 1.15g/L. Calculate the composition of air (percent by mass) assuming that it contains only nitrogen and oxygen and behaves like an ideal gas. (Hint: First calculate the "molar mass" of air, then the mole fractions, and then the mass fractions of O2 and N2.)

This is my first time posting here so if I'm breaking any rules please let me know. I'm supposed to answer this problem with the information given and not assuming any values. The answer in the book is O2: 28% and N2: 72%

I have been stuck on this problem for the past few hours and nothing I do seems to get me to the correct answer. Can someone please help me out or at least point me in the right direction? Thanks in advance.

[swansont]

How did you try and solve the problem?

[jricci12]

How did you try and solve the problem?

I've tried a couple different methods. I tried following along with the hint at the end of the problem telling me to first find molar mass of the air, so I took the molar mass of both N2 and O2 and added them together to get 60 g/mol, and wasn't sure this was the correct way to do it. I continued anyways and tried to find mass using PV=nRT to first find the volume and then using the known density and volume to get the mass. Then I took this mass and divided it by the 60 g/mol in order to get mols of the air, and then using this value of moles I found the mass of N2 and O2 by doing mols N2/O2 * molar mass of N2/O2. I then used those masses and divided it by the known mass of the air and multiplied by 100% to get the two mass %'s. This was far off from the right answer. This was only one of many ways I've tried so far, but this is usually the general way I was following with trying some different numbers here and there to try and get closer to the known answer but it wasn't working.

[studiot]

I've tried a couple different methods. I tried following along with the hint at the end of the problem telling me to first find molar mass of the air, so I took the molar mass of both N2 and O2 and added them together to get 60 g/mol, and wasn't sure this was the correct way to do it. I continued anyways and tried to find mass using PV=nRT to first find the volume and then using the known density and volume to get the mass. Then I took this mass and divided it by the 60 g/mol in order to get mols of the air, and then using this value of moles I found the mass of N2 and O2 by doing mols N2/O2 * molar mass of N2/O2. I then used those masses and divided it by the known mass of the air and multiplied by 100% to get the two mass %'s. This was far off from the right answer. This was only one of many ways I've tried so far, but this is usually the general way I was following with trying some different numbers here and there to try and get closer to the known answer but it wasn't working.

 

No adding them together is not the way to do it.

 

Call air 'the gas' (which it of course is) or 'the mixture' or something.

 

You are told P, V, T and I assume R so you can calculate n for the mixture.

 

If you are cute and use the appropriate units for R you will obtain the number of moles.

 

You can then use the mass information and break this down to % as they suggest.

 

Remember that if x = % oxygen then (100-x) = % nitrogen.

Edited September 18, 2016 by studiot

[swansont]

You can't just add the molar masses directly. You have a mixture, so it will be a weighted average of the two.

[jricci12]

 

No adding them together is not the way to do it.

 

Call air 'the gas' (which it of course is) or 'the mixture' or something.

 

You are told P, V, T and I assume R so you can calculate n for the mixture.

 

If you are cute and use the appropriate units for R you will obtain the number of moles.

 

You can then use the mass information and break this down to % as they suggest.

 

Remember that if x = % oxygen then (100-x) = % nitrogen.

The volume isn't given, so how can I calculate n without V or vice-versa? R = .08206 for this I'm fairly confident, but I'm only given P, T, Density, and R (constant)

[studiot]

 

 

1.15g/L.

 

What does this say?

 

Consider one litre of the mixture?

[jricci12]

 

What does this say?

 

Consider one litre of the mixture?

So I only have this post and one more post left that I'm allowed to post, just FYI moving forward.

 

So if I consider one liter of the mixture, I have 1.15g of air, correct? So assuming 1 liter, I could use PV=nRT to find moles of air, right? Would that # of moles be the same for both N2 and O2? Not sure what kind of ratios I'm dealing with here, just assuming its 1:1. Assuming that moles air = moles O2 = moles N2, I could use that # of moles of O2 and N2 to find the mass of both N2 and O2, and then divide by 1.15g of air * 100% to get the mass percentage. Am I on the right track?

 

EDIT: Assumed 1 L of air, I used PV=nRT to get .0396 moles of air. When I assumed it was a 1:1 ratio I multipled .0396 * MW of N2 and O2 and divided by the 1.15g air to try and get mass percentage. This didn't lead me to the right answer.

EDIT2: I feel like I'm missing something with the ratios. Without looking them up, how am I supposed to tell the ratio of N2 : O2? I know in the end that N2 needs to be basically 3x more than O2, but without knowing the answers before hand I'm not sure how I could come to that conclusion. I could be totally wrong and possibly getting further from the answer, but knowing the moles of air is a good start, just not quite sure where to go from there.

EDIT3: Still can't seem to figure this one out. This assignment is due in the morning so any help would be greatly appreciated!!

Edited September 18, 2016 by jricci12

[hypervalent_iodine]

It would probably help you to come up with a mathematical equation for the molecular mass of air, incorporating the molecular mass of O2 and N2.

 

A hint by way of analogy: let's say I have a 20 kg pile of bricks that has some percentage of large bricks that weigh 1kg and some percentage of smaller bricks that weigh 200 g. I know that the mass of the small bricks plus the big bricks adds up to 100% of the mass of bricks that I have, and that 100% of the bricks is equal to 20 kg. I could then come up with an equation to define this, which I will let you figure out. .