- 3

- 0

**1. Homework Statement :**

A gas cylinder contains 4.00x10

^{4}cm

^{3}of hydrogen at a pressure of 2.50x10

^{7}Pa and a temperature of 290 K.

The cylinder is to be used to fill balloons. Each balloon, when filled, contains 7.24x10

^{3}cm

^{3}of hydrogen at a pressure of 1.85x10

^{5}Pa and a temperature of 290K

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

**2. Homework Equations**

pV=nRT

**3. The Attempt at a Solution**

First I calculated how much hydrogen is inside the gas cylinder.

n = pV/RT

n = (2.50x10

^{7}x (4x10

^{4}/100

^{3})) / (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 = ((1.85x10

^{5}x (7.24x10

^{3}/100

^{3}))/(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