# What is the volume?

## A 19.0-L helium tank is pressurized to 22.0 atm. When connected to this tank, a balloon will inflate because the pressure inside the tank is greater than the atmospheric pressure pushing on the outside of the balloon. Assuming the balloon could expand indefinitely and never burst, the pressure would eventually equalize causing the balloon to stop inflating. What would the volume of the balloon be when this happens? Assume atmospheric pressure is 1.00 atm. Also assume ideal behavior and constant temperature.

Nov 17, 2016

This problem can be solved assuming that the elasticity of the baloon is negiligible.

Let the volume of the baloon after inflation be $V L$ at 1atm.
The total mass and temperature of the gas being constant we can apply Boyle's law and write

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

Here

${P}_{1} = 22 a t m$

${V}_{1} = 19 L$

${P}_{2} = 1 a t m$

${V}_{2} = \left(19 + V\right) L$

So

$22 \times 19 = 1 \times \left(V + 19\right)$

$\implies V = \left(22 \times 19 - 19\right) L = 21 \times 19 L = 399 L$