A 12-liter tank contains helium gas pressurized to 160 \rm atm.How many 3-liter balloons could the 12-L helium tank fill? Keep in mind that an "exhausted" helium tank is not empty. In other words, once the gas inside the tank reaches atmospheric pressure, it will no longer be able to fill balloons.
If we assume that helium gas follows an ideal gas behaviour, we can use the ideal gas law to solve this problem as follows:
We consider two different states, the initial given by the conditions of the problem statement and the final, when the tank reaches atmospheric pressure and it's no longer able to fill balloons:[tex]P_{1}=160 atm\\V_{1}=12 L\\P_{2}=1 atm\\V_{2}= ?[/tex]
To find out what would be this volume 2, we use the Boyle's Law: [tex]P_{1}V_{1}=P_{2}V_{2}\\V_{2}=\frac{P_{1}V_{1}}{P_{2}} \\V_{2}=\frac{160 atm \times 12L}{1 atm}\\V_{2}=1920 L[/tex]
Now we find the available volume to fill the balloons by substracting both, volume 2 and volume 1: [tex]V_{b}=V_{2}-V_{1}=1920L-12L=1908 L[/tex]
Finally, we determine the quantity of ballons by dividing that available volume between the volume of each ballon:[tex]B=\frac{1908L}{3L} =636 balloons[/tex]
