Solving Ideal Gas Question: Calculating Total Hydrogen and # of Balloons

[jiayingsim123]

Homework Statement

A gas cylinder contains 4.00 × 10^4cm^3 of hydrogen at a pressure of 2.50 × 10^7Pa and a
temperature of 290K.
The cylinder is to be used to fill balloons. Each balloon, when filled, contains
7.24 × 10^3cm^3 of hydrogen at a pressure of 1.85 × 10^5Pa and a temperature of 290 K.
Calculate, assuming that the hydrogen obeys the equation: PV = constant x T,
(i) the total amount of hydrogen in the cylinder,
(I've calculated this to be 415 moles, which is the right answer.)

(ii)the number of balloons that can be filled from the cylinder.

Homework Equations

P1V1=P2V2
PV=nRT

The Attempt at a Solution

The part I'm having problems with is b(ii). What I did was I divided the number of moles of the gas contained in the cylinder by the number of moles each balloon should contain when filled, but the answer I got is 746 whilst the correct answer is 741. The mark scheme says that I'm supposed to find out what the volume of the gas is at the reduced pressure of 1.85x10^5Pa and then subtract that volume by the volume of hydrogen in the gas to find out the total volume that is filled into the balloons. I don't see the rationale behind doing this so I'm hoping you guys can help me figure it out!

Thanks! :)

 

[voko]

I think you should take into account that some gas will be left in the cylinder, which you can't use to fill balloons.