Question regarding the Pressure of a gas flowing from a cylinder into balloons

[zee123]

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 290 K.
Calculate the number of balloons that can be filled.
Below is the solution but I can't seem to understand it.

Relevant Equations

PV=nRT, P1V1=P2V2

P1V1=P2V2
(2.5x10^7x4x10^4)/1.85x10^5 , V2 = 5.41x10^6 cm^3
5.41x10^6=4x10^4+7.24x10^3 N
N= 741

 

[TSny]

Welcome to PF!

The rules here at the forum require that you show some work of your own. To get some discussion going, let me ask the following:

After the last balloon has been filled, is there any gas remaining in the tank?

 

[zee123]

Welcome to PF!

The rules here at the forum require that you show some work of your own. To get some discussion going, let me ask the following:

After the last balloon has been filled, is there any gas remaining in the tank?

There might be, as gas takes up the volume of the container. It wasn't mentioned in the question tho.

 

[TSny]

There might be, as gas takes up the volume of the container. It wasn't mentioned in the question tho.

The question intends for you to deduce from physics principles whether or not there will be any gas remaining in the tank.

 

[zee123]

The question intends for you to deduce from physics principles whether or not there will be any gas remaining in the tank.

But how much gas will flow into the balloons, will the gas stop flowing once the pressure inside the cylinder is 1.85x10^5 Pa?

 

[TSny]

But how much gas will flow into the balloons, will the gas stop flowing once the pressure inside the cylinder is 1.85x10^5 Pa?

Yes. Good.

 

[Lnewqban]

But how much gas will flow into the balloons, will the gas stop flowing once the pressure inside the cylinder is 1.85x10^5 Pa?

The original mass of compressed hydrogen (high pressure) is shared by n-number of ballons plus the same cylinder at a lower common pressure.
Because of that you have:

Initial conditions inside cylinder = Final conditions inside cylinder + [Number of balloons x Final conditions inside each balloon]

$$P_{ci}V_{ci}=nP_bV_b+P_{cf}V_{cf}$$
where $V_{ci}=V_{cf}$, since the cylinder has solid walls and constant volume.

Then,
$$n= \frac{V_c(P_{ci}-P_{cf})}{P_bV_b}=741~balloons$$