Pressure of Helium inside a balloon floating in air

1. Dec 11, 2012

yaylee

Pressure of Helium inside a balloon "floating" in air

1. The problem statement, all variables and given/known data
A spherical balloon of radius R = 2.98 m is made from a material of mass M = 3.16 kg and is filled with helium gas at temperature T = 285 K. Assume the thickness of the balloon is negligible compared to the radius of the balloon, and the balloon just floats on air, neither rising nor falling. If the density of the surrounding air is ρ = 1.19 kg/m3, find P, the absolute pressure of the helium inside the balloon.
ASSUME: The balloon material displaces a negligible amount of air, and therefore creates no measurable buoyancy.

2. Relevant equations
Volume of a sphere = (4/3)π(r^3)
Buoyant force of an object "floating": F = (mass object)(g) = (ρliquid)(Vobject)(g), and the "g's" cancel.
PV = nRT
moles = grams/ (grams/mol)

3. The attempt at a solution
First: find the mass of the TOTAL object. We can then subtract the mass of the balloon's material from the Total mass to find the mass of the Helium itself.
Use, Buoyant Force equation, where (ρliquid)(Vobject) = (mass object) = (1.19)(4/3)π(2.98^3) = 131.912 kg.

Then: (mass object) - (mass of balloon material) = mass of Helium = 131.912 - 3.16 = 128.75 kg = 128,750 grams.
number of moles of Helium inside balloon: 128, 750 g/4 g/mol = 32187.50 moles.

Now: can use pv = nRT, or P = nRT/V = 32187.50(8.314)(285)/((4/3)(∏)(2.98^3) = 6.88 x 10^5 Pascals.

The answer key marked me incorrect, however, I believe I have reasoned the problem correctly. Does anyone have any suggestions?

My unlimited thanks in advance!

2. Dec 11, 2012

haruspex

Re: Pressure of Helium inside a balloon "floating" in air

I think you're an order of magnitude out. Check the final calculation.

3. Dec 11, 2012

yaylee

Re: Pressure of Helium inside a balloon "floating" in air

Thanks!

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