# Air Balloon ( 5.5 inch diameter) vs Helium gas balloon ( 11 inch diameter )?

1. Nov 30, 2008

### redhot209

1. The problem statement, all variables and given/known data
You blow up an ordinary party balloon with air until it has a diameter of 5.5 inches. Your friend blows up another
balloon with helium gas until it has a diameter of 11 inches. Air consists mostly of O2 and N2 molecules, while
helium gas consists of He atoms. Assume the pressure in each balloon is the same.

(a) Compare the number of helium atoms to the total number of O2 and N2 molecules.
(b) Air is about 80 percent nitrogen and 20 percent oxygen. Which balloon weighs more and by how much? (
Hint: Imagine that there are 80 helium atoms in the helium balloon. Calculate the mass, in atomic mass units,
of this amount of helium, and then compare to the mass of the corresponding number of oxygen and nitrogen
molecules).

2. Relevant equations

3. The attempt at a solution
(A)
For the 5.5 inch balloon the volume is (4/3)*pi*2.75^2 = 31.68in^3
For the 11 inch balloon the volume is (4/3)*pi*5.5^2 = 126.71 in^3

Therefor the ratio of air to Helium is 31.68/126.71 = .25 air molecules for every Helium molecule.

(B)

The atomic mass of Helium is 1 so 4 mols of Helium = 4g
And we know that the 1 mol of air is 80%N and 20%Oxygen so we have .8mols of Nitrogen and .2mols of Oxygen

Oxygen's atomic mass is approx 16 so .2mols of Oxygen = 3.2g
Nitrogen has an atomic mass of approx 14 so .8mols of Nitrogen = 11.2g
The total mass of the air balloon is 3.2 + 11.2 = 14.4g

Therefor the air balloon weighs 3.6 times as much as the helium balloon. (14.4/4)

2. Dec 1, 2008

### horatio89

Part A: Read the question again. What ratio does the question asks for?

Part B: Can I take it that you got part B correct? The working is pretty much OK.