A cylinder of helium is advertised to fill 50 9\" balloons. a. If a 9\" balloon
ID: 894735 • Letter: A
Question
A cylinder of helium is advertised to fill 50 9" balloons.
a. If a 9" balloon can hold a volume of 0.27 cubic feet and the temperature of gas is 25 degrees celcius, what is the mass of helium contained in the full cylinder? You can assume that pressure inside a ballon is equal to 1.01 atm.
b. What is the density of helium in one balloon?
c. What would be the density of a balloon filled with nitrogen if all other factors remained constant
d. Air leaks out of the balloon so that the pressure decreases by a rate of 0.0012 atm per day. How long will it take (in hours) for the balloon to be half of its original size.
Explanation / Answer
If a cylinder of helium is advertised to fill 50 9" balloons then,
a) If a 9" balloon can hold a volume of 0.27 cubic feet and the temperature of gas is 25 degrees celcius at pressure inside a ballon is equal to 1.01 atm. then
Convert the values in one unit. and put in above equation
As we know that, 1 cm3 = 3.531 x 10-5 feet3
Therefor, 0.27 feet3 = 7645.5 cm3
Now, after knowing the volume, pressure, and temperature we can calculate the mass helium gas filled in one ballon.
By appling a Ideal gas equestion,
PV = nRT
P= absolute pressure of gas
V= volume
n= amoun of gas (Usally moles)
R= Ideal gas constant
T= Absolute temperature
By putting the values in ideal gas equation
1.01 x 7645.5 = (mass/ mol. wt.) 8.3145 x 273................................(1)
1.01 x 7645.5 x 4.0 / 8.3145 x 273 = mass
30887.82 / 2269.85 = 13.6 gm (mass of helium gas field in one balloon)
The mass of helium contained in the full cylinder = 50.9 x 13.6 / 9 = 76.91 gm
b) Hence the density of helium in one balloon = mass of helium in balloon / volume of helium gas in balloon
= 13.6 / 7645.5 = 0.0017 gm / ml
c) The density of a balloon filled with nitrogen will be (if all other factors remained constant )
puting the values in equation (1) for nitrogen gas, (molecular wt. =14)
mass = 1.01 x 7645.5 x 14 /8.3145 x 273
= 108107.37 / 2269.85 = 47.62 gm
Density of nitrogen in balloon = 47.62 / 7645.5 = 0.0062 gm/ml
d) If air leaks out of the balloon so that the pressure decreases by a rate of 0.0012 atm per day.
then the time require to become a ballon half to its original size can be calculated as,
= Total pressure of gas/ rate of release of gas per day
= 1.01 / 0.0012
= 841.66 days are reqire to get release all gas then its half time will be 420.83 days
it can be converted in to hours as
= 420.83 x 24 =10099.92 hrs
Total 10099.92 hrs will it takes for the balloon to be half of its original size.
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