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 higher than the average speed of air molecules, and the higher 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 balloon thus weighs less than 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 higher than the air temperature. Hot gases tend to rise.

Short answer

The correct explanation for why a closed balloon filled with helium gas rises in the air is statement (c). Helium atoms have a lower mass than the average air molecules, making helium gas less dense than air. According to Archimedes' principle, the buoyant force acting on the balloon is equal to the weight of the air displaced by the balloon. Since the weight of the helium within the balloon is less than the weight of the displaced air, there is a net upward force on the balloon, causing it to rise.

Step-by-step solution

Statement (a)

Helium is indeed a monatomic gas, whereas nitrogen and oxygen, which are the primary components of air, are diatomic gases. However, this fact alone does not explain why the balloon rises in the air. We need to look for a statement that connects the properties of helium with buoyancy.

Statement (b)

It is true that the average speed of helium atoms is higher than the average speed of air molecules due to their lighter mass. However, this does not lead to higher speed collisions with the balloon walls providing upward force strong enough to make the balloon rise. Therefore, this statement does not provide an adequate explanation for the phenomenon.

Statement (c)

This statement is correct. The helium atoms have a lower mass than the average air molecules, which makes helium gas less dense than air. According to Archimedes' principle, the buoyant force acting on the balloon is equal to the weight of the air displaced by the balloon. Since the weight of the helium within the balloon is less than the weight of the displaced air, there is a net upward force on the balloon, causing it to rise.

Statement (d)

This statement is incorrect. Although helium atoms have a lower molar mass than the average air molecule, it does not mean that the temperature of the helium inside the balloon is higher than the air temperature. Both the balloon and the air around it would have the same temperature under normal conditions, and the hot gas rising concept does not apply in this case. Based on our analysis, the correct statement is (c). This statement explains how the lower density of helium gas compared to air results in a helium-filled balloon rising in the air due to buoyancy.