Pressure Ratio of He to N2 at Equal Density

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SUMMARY

The pressure ratio of helium (He) to nitrogen (N2) at equal densities can be calculated using the ideal gas law, PV = nRT. Given that the molar mass of He is 4.003 g/mol and that of N2 is 28.01 g/mol, the number of moles of He required to match the density of N2 is seven times greater. Consequently, the pressure ratio is established as PHe/PN2 = 7/1, indicating that helium exerts seven times the pressure of nitrogen under these conditions.

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  • Understanding of the ideal gas law (PV = nRT)
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  • Familiarity with density equations (D = m/v)
  • Basic principles of gas behavior under equal conditions
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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.

Homework Equations



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. :smile:
 
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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.
 
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 :wink:
 
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
 

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