# How many balloons can be filled from the cylinder

• cricket0140
In summary: If the remaining hydrogen fills the entire volume, then there would be zero moles remaining in 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

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

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.

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?

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.

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.

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

cricket0140 said:
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?

## 1. How do you determine how many balloons can be filled from a cylinder?

To determine how many balloons can be filled from a cylinder, you first need to know the volume of the cylinder. Then, you can divide the volume of the cylinder by the volume of one balloon to calculate the maximum number of balloons that can be filled.

## 2. What is the volume of a cylinder?

The volume of a cylinder is calculated by multiplying the area of the circular base by the height of the cylinder. The formula for volume is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

## 3. How do you measure the volume of a cylinder?

The volume of a cylinder can be measured using a graduated cylinder or by using a ruler to measure the height and diameter of the cylinder and then calculating the volume using the formula V = πr^2h.

## 4. Can the volume of a cylinder change?

The volume of a cylinder can change if the height or radius is altered. The volume will increase if the height or radius is increased, and it will decrease if the height or radius is decreased.

## 5. Are there any factors that can affect the number of balloons that can be filled from a cylinder?

Yes, there are a few factors that can affect the number of balloons that can be filled from a cylinder. These include the size and shape of the balloons, the size and shape of the cylinder, and the pressure and temperature of the gas being used to fill the balloons.

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