How many balloons can be filled from the cylinder

[cricket0140]

Homework Statement

:[/B]
A gas cylinder contains 4.00x10⁴cm³ of hydrogen at a pressure of 2.50x10⁷Pa and a temperature of 290 K.
The cylinder is to be used to fill balloons. Each balloon, when filled, contains 7.24x10³cm³ of hydrogen at a pressure of 1.85x10⁵Pa and a temperature of 290K

Calculate the number of balloons that can be filled from the cylinder

Homework Equations

pV=nRT

The Attempt at a Solution

First I calculated how much hydrogen is inside the gas cylinder.
n = pV/RT
n = (2.50x10⁷ x (4x10⁴/100³)) / (8.3 x 290)
n = 415 moles of hydrogen in the gas cylinder ( this is correct from the mark scheme)

However, I feel I have gone wrong with my next steps.

I then found out the number of moles in one balloon of hydrogen.
n = ((1.85x10⁵ x (7.24x10³/100³))/(8.3 x 290)
n = 0.556 moles of hydrogen in one balloon

I then simply did 415/0.556 to find out how many balloons I could fill, which gave me 746mol. The correct answer is actually 741mol.

This has been asked before but I just can't seem to wrap my head around their explanations. Something about there being gas that will be in the cylinder that will be unable to be used to fill the balloons.

Thanks

 

[jedishrfu]

As you release the gas there will come time where the pressure matches the outside pressure and no more gas can be released into the balloon which looks like its when the cylinder is down to 5moles of hydrogen.

 

[cricket0140]

Okay, so I tried to calculate how many moles would be left in the cylinder when the pressure in the cylinder is down to 1.85x10⁵Pa.
So n=pV/RT = (1.85x10⁵ x (4x10⁴/100³)) / 8.3 x 290
But this gives 3.07 instead of 5. I think I'm assuming that the volume will stay constant, which I believe to be wrong. How would I calculate the new volume of gas in the cylinder?

 

[TSny]

your original answer was 746 balloons, not moles. So, you were off by 5 balloons, not 5 moles. Try the calculation again with jedishrfu's suggestion. I think it will work out.

 

[jedishrfu]

Yeah my mistake i saw the moles realized it was really ballons but forgot to mention it as i wrote my post. Thanks Tsny for spotting that.

 

[cricket0140]

Oh, sorry, I did mean 746 balloons. So in my second post I calculated there to be 3.07mol left in the container when the pressures were the same. However, when I convert this to how many balloons I'm missing out on (3.07 / 0.556) I get 5.52. And 746 - 5.52 = 740. Which is still wrong. On the mark scheme it says I lose a mark if I get 740. What am I doing wrong?

Thanks for the help guys.

EDIT EDIT EDIT: Thanks guys, turned out to be a rounding problem. Can't thank you guys enough for the help

 

[SteamKing]

Okay, so I tried to calculate how many moles would be left in the cylinder when the pressure in the cylinder is down to 1.85x10⁵Pa.
So n=pV/RT = (1.85x10⁵ x (4x10⁴/100³)) / 8.3 x 290
But this gives 3.07 instead of 5. I think I'm assuming that the volume will stay constant, which I believe to be wrong. How would I calculate the new volume of gas in the cylinder?

Ask yourself: Will the remaining hydrogen snuggle up in one end of the cylinder? Or will the remaining hydrogen fill the entire volume, regardless of amount?