Problem 49 - Chemistry: The Central Science

Question

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Step-by-Step Solution

Answer

The best explanation for why a closed balloon filled with helium gas rises in air is statement (c): Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. This is in line with the buoyancy principle and explains the rising of the helium-filled balloon in air.

Step 1: Statement (a) analysis

Helium is indeed a monatomic gas, while nitrogen and oxygen are diatomic. However, being monatomic or diatomic does not directly explain why the closed balloon filled with helium rises in air confidently.

Step 2: Statement (b) analysis

Helium atoms are lighter and have higher average speed than air molecules, but the greater speed of collisions with the balloon walls does not constantly propel the balloon upward. Simply having a higher collision speed does not guarantee a continuous rising motion.

Step 3: Statement (c) analysis

Helium atoms are of lower mass than the average air molecule, so the helium gas inside the balloon is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. This explanation is in line with the buoyancy principle, making it the most likely reason for why a helium-filled balloon rises in air.

Step 4: Statement (d) analysis

Although helium has a lower molar mass than the average air molecule and can be in faster motion due to lighter atoms, this does not necessarily mean that the helium's temperature is greater than the air temperature. Additionally, hot gases do tend to rise, but this factor alone does not fully explain the rising of the helium-filled balloon in air. In conclusion, the most appropriate explanation for why a closed balloon filled with helium gas rises in air is statement (c): Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume.