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.

Statement A claims that the helium balloon rises in air because helium is a monatomic gas while nitrogen and oxygen in air are diatomic. While it is true that helium is a monatomic gas and nitrogen and oxygen are diatomic gases, this fact alone does not explain why the closed balloon rises. The relationship between the number of atoms in a molecule and buoyancy is not direct. Therefore, we can rule out statement A as the best explanation.

Statement B suggests that the balloon rises because helium atoms have a greater average speed than air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. While it is true that helium atoms have a higher average speed than air molecules due to their lower mass, this explanation focuses on the kinetic energy of the individual gas particles instead of the properties of the whole gas and its interactions with the surrounding air. Therefore, statement B is not the best explanation.

Statement C posits that the balloon rises because the helium gas is less dense than air, and the mass of the balloon is less than the mass of the air displaced by its volume. This explanation takes into account the buoyancy principle, which states that an object submerged in a fluid will experience an upward force equal to the weight of the fluid it displaces. In this case, the helium gas has a lower density than the air, meaning that the mass of the balloon with the helium is less than the mass of the air it displaces. Because of this, the balloon experiences an upward force, also known as buoyancy, which causes it to rise in the air. Statement C is the most accurate explanation for the given phenomena and takes into account important physical and gas principles.

Statement D claims that the balloon rises because helium has a lower molar mass than air molecules, resulting in faster motion and higher temperature for the helium, causing the hot gas to rise. Although it is true that helium has a lower molar mass and faster motion, it does not necessarily mean that the helium inside the balloon has a higher temperature than the surrounding air. Temperature is a measure of the average kinetic energy of the gas particles, and the statement does not provide any information about the helium gas temperature. Furthermore, the focus on temperature does not directly address the buoyancy principle responsible for the balloon rising in the air. In conclusion, the best explanation for why a closed helium balloon rises in air is Statement C. The lower density of helium gas compared to air, coupled with the buoyancy principle, causes the balloon to experience an upward force and rise in the air.