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.

Verified step by step guidance

1. First, let's understand the principle of buoyancy. According to Archimedes' principle, an object immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object. If the weight of the object is less than the weight of the fluid it displaces, the object will float or rise in the fluid.
2. Option (a) states that helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. While this is true, it doesn't explain why helium rises in air.
3. Option (b) suggests that 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. This is not the reason why helium balloons rise. The speed of gas molecules does not directly affect the buoyancy of an object.
4. Option (c) states that 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 statement is correct and aligns with the principle of buoyancy. The helium-filled balloon is less dense than the air it displaces, so it rises.
5. Option (d) suggests that 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. While it's true that hot gases rise, this is not the primary reason why a helium balloon rises. The temperature of the helium in the balloon is not necessarily higher than the surrounding air temperature.

Key Concepts

Density and Buoyancy

Density is defined as mass per unit volume. An object will float or rise in a fluid if it is less dense than the fluid. In this context, helium is less dense than the surrounding air, which allows the balloon to rise due to buoyant forces acting on it.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It states that lighter gas particles, like helium, move faster than heavier particles, such as those in air. This increased speed contributes to the buoyancy of helium-filled balloons.

Archimedes' Principle

Archimedes' Principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. For the balloon, the weight of the air displaced is greater than the weight of the helium and the balloon, resulting in an upward force that causes it to rise.