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.

Short answer

The best explanation for why a closed helium balloon rises in air is Statement C. The helium gas is less dense than air, making the mass of the balloon less than the mass of the air it displaces. This causes the balloon to experience an upward force, known as buoyancy, which results in the balloon rising.

Step-by-step solution

(1. Analyzing Statement A)

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.

(2. Analyzing Statement B)

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.

(3. Analyzing Statement C)

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.

(4. Analyzing Statement D)

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.

Key concepts

Helium Gas

Helium gas is a fascinating subject and plays a key role in understanding why balloons float. It is a noble gas, which means it doesn't react easily with other elements. Helium is a monatomic gas, consisting of single atoms rather than molecules. This is different from air, which is primarily made up of nitrogen and oxygen molecules that are diatomic, meaning they consist of two atoms.

A key characteristic of helium is its very low density compared to air. Helium's low density makes it lighter, and thus plays a crucial role in making balloons rise. Its properties are leveraged in many practical applications beyond balloons, such as in airships and even in scientific equipment, due to its stable, non-reactive nature.

Density

Density is a fundamental concept in physics, especially when discussing why objects float or sink. The density of a substance is defined as its mass per unit volume. This physical property has a direct relationship with whether an object will float or sink in a fluid.

• If an object is less dense than the fluid it is in, it will float.
• Conversely, if an object is more dense, it will sink.

The reason a helium-filled balloon rises in the air is due to helium gas having a much lower density than the surrounding air. When a balloon filled with helium displaces a volume of air, the weight of the air displaced is greater than the weight of the helium inside the balloon.

This difference causes buoyancy, an upward force, making the balloon rise.

Gas Laws

Gas laws help us understand the behavior of gases under different conditions. These laws describe how gases interact with changes in pressure, volume, and temperature, and are key to explaining the behavior of helium in balloons.

One relevant concept is the Ideal Gas Law, expressed as \( PV = nRT \), where \( P \) represents pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is temperature. This equation is fundamental in predicting how a change in one of the variables will affect the others.

For helium balloons, the laws suggest that if temperature or pressure changes, the volume of the helium inside might adjust accordingly. However, since a balloon is often at constant temperature and pressure with the outside air, the overriding reason helium balloons rise is due to differences in density, highlighting how buoyancy (related to density) often trumps temperature and pressure effects when it comes to floating.