# Pressure ratio problem

## Homework Statement

Calculate the pressure ratio of He to N2 at which helium would have the same density as nitrogen if their temperatures were the same.

I used D = m/v

## The Attempt at a Solution

DHe = mHe/v
DN2 = mN2/v
Both gases occupy the same volume, so just v for both.

Since DHe = DN2,
mHr/v = mN2/v and mHe = mN2

For some x and y,
x mol He(4.003 g/mol He) = mHe
y mol N2(28.01 g/mol N2) = mN2

4.003x g = 28.01y g
x = 7y

To me it looks like there are 7 times as many moles of He as N2 but I doubt that would directly apply to their pressure ratios. I think I'd have to use PV = nRT but I'm not sure how I'd put it in.
I was actually helping some chemistry students earlier today with this and am hoping I can have the answer ready for them tomorrow morning. Last edited:

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Borek
Mentor
Honestly, I have no idea what the question asks. Oxygen? And why do you use neon in your calculations?

Could be what you did is OK, but with all these typos/inconsistencies it is not.

I fixed the Ne and oxygen; I have an older edition of the book than that which the students are using and I hadn't quite changed everything to match the problem in their book. Should be alright now.

Borek
Mentor
OK.

Now, knowing ratio of numbers of moles try to calculate ratio of pressures using PV=nRT. Don't be surprised if everything cancels out I think I got it now (don't know why I didn't look at it like this before)

I found that nHe/nN2 = 7/1, and using P = nRT/V,

PHe/PN2 = (nHeRT/V)/(nN2RT/V)
PHe/PN2 = nHe/nN2 = 7/1