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 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 higher than the air temperature. Hot gases tend to rise.

Short answer

The most appropriate explanation for the rising of helium balloons in the air is option (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 focuses on the buoyancy effect that occurs within the air, causing the less dense helium-filled balloon to rise.

Step-by-step solution

Understand the given options

Let's analyze each of the given options before finding the correct answer: (a) Although it's true that helium is a monatomic gas and the air is formed of diatomic molecules like nitrogen and oxygen, this statement doesn't explain why the balloon filled with helium rises. (b) This statement suggests that the average speed of helium atoms helps propel the balloon upward due to collisions with the walls. However, this is not the primary reason why the balloon rises. (c) This statement refers to the differences in mass between helium atoms and the average air molecule and how that results in different densities. A lower density would lead to the buoyancy effect making the balloon rise. (d) This statement suggests that helium has a higher temperature than the surrounding air, which would, in turn, make it rise. While it's true that the helium atoms are in faster motion due to their lower molar mass, it doesn't necessarily mean that the helium temperature would be higher than the air temperature.

Identify the most appropriate explanation

From the analysis of the four statements, we can deduce that the most appropriate explanation for the rising of helium balloons in the air is option (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 the best explanation because it focuses on the buoyancy effect that occurs within the air. Buoyancy arises due to a difference in densities or, in other terms, a difference in the mass-to-volume ratio between the gas inside the balloon and the air outside of it. The lower mass of helium atoms compared to that of air molecules (mainly nitrogen and oxygen) leads to the helium-filled balloon being less dense than the air, and as a consequence, the balloon rises. So, the correct answer is option (c).

Key concepts

Density Differences in Gases

The concept of density is central to understanding the buoyancy effect in gases. Density is defined as the mass per unit volume of a substance. This physical property is crucial when comparing different gases and their behavior upon interaction with each other.

In the context of our exercise, the density of helium gas compared to air is the determining factor for the helium balloon's ability to rise. Since helium atoms have a lower mass compared to the average mass of air molecules, which consist mostly of nitrogen (N2) and oxygen (O2), the overall mass of a given volume of helium is less than the same volume of air. Thus, the density of helium is lower than that of air.

It's important to note that gases are compressible, meaning their densities can change with pressure and temperature. However, in the case of a helium balloon in normal atmospheric conditions, the differences in density remain significant enough to cause the helium balloon to be buoyant and rise. This illustrates why density differences are so vital to explaining the behavior of gases in various situations.

Helium Gas Buoyancy

The buoyancy of a gas is its ability to float or rise within another medium, such as air. This phenomenon, governed by Archimedes' principle, states that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. For gases, this principle translates to the interplay between the densities of the gas inside an object, like a balloon, and the surrounding air.

In the example provided in the textbook exercise, a balloon filled with helium rises because helium is less dense than air. When the balloon displaces a volume of air, the weight of that displaced air is more than the weight of the helium inside the balloon. The difference in weight creates an upward buoyant force that causes the balloon to ascend. This is similar to how a cork floats on water; the cork is less dense than the water it displaces, leading to the upward force.

Buoyancy in gases is also why hot air balloons rise. Heated air within the balloon expands and becomes less dense, thus displacing colder, denser air outside, resulting in an upward buoyant force. This principle is widely used in various applications, from meteorological balloons to recreational and transport uses in hot air ballooning.

Molar Mass and Gas Behavior

The molar mass of a substance is the mass of one mole of that substance, essentially a measure of the mass of the molecules or atoms that make it up. In gases, the molar mass is key to understanding the behavior of the gas under different conditions, as it relates directly to the Ideal Gas Law represented by the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.

Because helium has a lower molar mass compared to most components of air, the behavior of helium under the same conditions of temperature and pressure is different from that of air. For instance, helium atoms will move faster on average than air molecules at the same temperature because they are lighter, leading to a concept known as kinetic molecular theory. Although this faster movement doesn't directly cause buoyancy, as was incorrectly suggested in options (b) and (d) of the exercise, it's a related aspect of gas behavior that's important for a comprehensive understanding of how gases differ in their physical properties.

Additionally, the lower molar mass of helium explains why it diffuses faster than air and why it has a distinctive high-pitched effect on the human voice when inhaled. This demonstrates how the molar mass affects various characteristics of gas behavior, ranging from its buoyancy to other physical and chemical properties.