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

In summary, the question asks to compare the number of helium atoms to the total number of O2 and N2 molecules in two different sized balloons, one filled with air and the other filled with helium gas. The ratio is found to be 0.25 air molecules for every helium molecule. Additionally, the mass of each balloon is calculated based on the known atomic masses of helium, nitrogen, and oxygen, and it is determined that the air balloon weighs 3.6 times as much as the helium balloon.
  • #1
redhot209
12
0

Homework Statement


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).


Homework Equations





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.

But is wrong answer!



(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)
 
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  • #2
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.
 
  • #3
= 3.6
Thank you for your submission. Your calculations and reasoning for the first part (a) appear to be correct. However, for the second part (b), it is important to note that the mass of a gas is proportional to its number of moles, not just its number of atoms/molecules. In other words, the mass of a gas depends on both its number of particles and their individual masses. Therefore, using the atomic masses alone may not give an accurate comparison. Instead, we can use the ideal gas law (PV = nRT) to calculate the number of moles of each gas in the balloons, and then use the molar masses to determine their masses. This approach should give a more accurate comparison between the two balloons.
 

1. What is the difference between an air balloon and a helium gas balloon?

The main difference between an air balloon and a helium gas balloon is the type of gas used to inflate them. Air balloons are typically filled with regular air, while helium gas balloons are filled with helium. This difference in gas density affects the behavior and flight of the balloon.

2. Which type of balloon can stay afloat longer?

Helium gas balloons can stay afloat longer than air balloons. This is because helium is a lighter gas than air, causing the balloon to be more buoyant and able to stay afloat for a longer period of time.

3. Can both types of balloons reach the same altitude?

No, air balloons and helium gas balloons have different maximum altitudes. Air balloons can only reach a maximum altitude of about 10,000 feet, while helium gas balloons can reach much higher altitudes, up to 20,000 feet or more.

4. Which type of balloon is more commonly used?

Helium gas balloons are more commonly used than air balloons. This is because helium gas balloons are able to reach higher altitudes and stay afloat longer, making them more suitable for events such as hot air balloon festivals and advertising campaigns.

5. Are there any environmental concerns with using helium gas balloons?

Yes, there are environmental concerns with using helium gas balloons. Helium is a non-renewable resource and its extraction can have negative impacts on the environment. Additionally, when helium gas balloons are released into the atmosphere, they can contribute to air and water pollution. It is important to properly dispose of helium gas balloons after use to minimize these environmental impacts.

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