Question

You have a 25.0 L cylinder of helium at a pressure of 132 atm and a temperature of 19 ∞C. The He is used to fill balloons to a volume of 2.50 L at 732 mm Hg and 27 ∞C. How many balloons can be filled with He? Assume that the cylinder can provide He until its internal pressure reaches 1.00 atm (i.e., there are 131 atmospheres of usable He in the cylinder).

Answer 1

Answer:

1406 balloons

Explanation:

First of all, we calculate the number of moles of helium gas contained in the 25.0 L cylinder, by using the equation of state for an ideal gas:

$pV=nRT$

where

p = 132 atm is the pressure

V = 25.0 L is the volume

$R=0.082 atm\cdot L / (mol \cdot K)$ is the gas constant

$T=19^{\circ}C+273=292 K$ is the temperature

Solving for n, we find the number of moles:

$n=\frac{pV}{RT}=\frac{(132)(25.0)}{(0.082)(292)}=137.8 mol$

Now we can find using the same equation how many moles of gas can be contained in 1 balloons, which has:

V = 2.50 L (volume)

$p=732 mm Hg =0.963 atm$ is the pressure

$T=27^{\circ}C+273=300 K$ is the temperature

Therefore,

$n_1 = \frac{pV}{RT}=\frac{(0.963)(2.50)}{(0.082)(300)}=0.098 mol$

So, the total number of balloon that can be filled is:

$N=\frac{n}{n_1}=\frac{137.8}{0.098}=1406$