You place an online order for 13 perfectly round Latex Cryst

You place an online order for 13 perfectly round Latex Crystal-tone Color Balloons (diameter of 1.000 ft) which completely inflate at a pressure of 1.5 atm, 2 packages of Quickie Balloon Clips (they only come in packages of 12), and a roll of White Curling Ribbon (you opt for the special deal of the 500-yd roll). To enhance your savings, you use your knowledge about gas laws to figure out how much helium you would actually need. There are four sizes of helium gas cartridges available: 2.125 L at 120 atm, 2.500 L at 125 atm, 3.000 L at 110 atm, and 3.250 L at 100 atm. The price is calculated according to pressure times volume. Which one will make your wallet happy?

Extra info:

(A) Room temp = 25 degrees Celcius

(B) Helium may be considered ideal only at low pressures

(C) It is relatively easy to solve the Van der Waals equation for pressure, solving it for volume or number of moles leads to cubic equations.

(D) Van der Waals constants for He: a = 0.03502 L^2 atm mol^-2, b = 0.0237 L/mol

Solution

There are 13 round balloons.

The diameter of each balloon is 1 ft which is equal to 30.48 cm.Therefore the radius is 30.48/2= 15.24 cm.

The volume of each balloon is ((4/3) * * r³) = 14.81 L = 0.01481 m³

The volume of helium needed to fill one balloon is 14.81 L * 1.5 = 22.215 L = 0.022215 m3

The volume of helium needed to fill 13 balloons is .0222 * 13 = 0.288 m³

The volume of helium present in each cylinder are the following:

1) 2.125 L* 120 = 255 L =0.255 m³

2) 2.500 L* 125 = 312.5 L =0.312 m³

3) 3 L * 110 = 330 L =0.330 m³

4) 3.250 L * 100 = 325 L =0.325 m³

The second cylinder is the perfect one.