Question

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? \begin{equation}\begin{array}{l}{\text { (a) Helium is a monatomic gas, whereas nearly all the molecules }} \\ {\text { that make up air, such as nitrogen and oxygen, are }} \\ {\text { diatomic. }} \\ {\text { (b) The average speed of helium atoms is greater than the }} \\ {\text { average speed of air molecules, and the greater speed }} \\ {\text { of collisions with the balloon walls propels the balloon }} \\ {\text { upward. }}\\\\{\text { (c) Because the helium atoms are of lower mass than the average }} \\ {\text { air molecule, the helium gas is less dense than air. }} \\\ {\text { The mass of the balloon is thus less than the mass of the }} \\\ {\text { air displaced by its volume. }}\\\\{\text { (d) Because helium has a lower molar mass the average }} \\ {\text { air molecule, the helium atoms are in faster motion. This }} \\ {\text { means that the temperature of the helium is greater than }} \\ {\text { the air temperature. Hot gases tend to rise. }}\end{array} \end{equation}

Short answer

The best explanation for the rising behavior of a closed helium balloon in air is statement (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 consistent with the principle of buoyancy, which states that objects with lower density than the surrounding medium will rise in that medium.

Step-by-step solution

Analyze the properties of helium and air molecules

Helium is a monatomic gas, which means it consists of single atoms, while air consists mainly of diatomic molecules like nitrogen (N2) and oxygen (O2). The average mass of helium atoms is lighter compared to the average mass of air molecules.

Refute or confirm statement (a)

Statement (a) says that helium is a monatomic gas, while air mostly consists of diatomic molecules. Although this statement is correct, it has no direct relation to the rising behavior of a helium balloon. So, statement (a) is not the best explanation.

Refute or confirm statement (b)

Statement (b) says that the average speed of helium atoms is greater than the average speed of air molecules, and the collision of helium atoms inside the balloon with its walls propels the balloon upward. While helium atoms are indeed faster due to their lower mass, this explanation is not sufficient to explain the rising behavior of a balloon filled with helium. So, statement (b) is not the best explanation.

Refute or confirm statement (c)

Statement (c) says that because helium atoms have a lower mass than the average air molecule, the helium gas is less dense than air. This causes the balloon's total mass to be less than the mass of the air it displaces. This statement is consistent with the principle of buoyancy; objects with a lower density than the surrounding fluid will rise in that fluid. This statement provides a more direct explanation of why a helium balloon rises in the air. So, statement (c) is the best explanation.

Refute or confirm statement (d)

Statement (d) says that because helium has a lower molar mass than the average air molecule, the helium atoms move faster, which means that the temperature of the helium is greater than the air temperature, causing hot gases to rise. This statement, although partly correct (helium atoms move faster), is not accurate in terms of its effect on rising behavior. The main reason a helium balloon rises is its lower density, as pointed out in statement (c), not due to the temperature difference. So, statement (d) is not the best explanation. Overall, the best explanation for the rising behavior of a closed helium balloon in air is statement (c). It is due to the lower density of helium compared to air, and the principle of buoyancy, which states that objects with lower density than the surrounding medium will rise in that medium.

Key concepts

Helium gas

Helium is a fascinating element with unique properties that set it apart from other gases. It is a noble gas, occupying a position in group 18 of the periodic table. This means it is chemically inert, rarely forming any compounds with other elements. What makes helium particularly interesting is that it is a monatomic gas. This implies that each helium gas particle is composed of a single atom, unlike most gases like nitrogen and oxygen in the air, which are diatomic and composed of two atoms per molecule.

Helium's atomic structure contributes to its lightweight characteristic. With an atomic number of 2, it is one of the lightest elements. Additionally, being monatomic means fewer atomic interactions, which generally leads to lower density and faster diffusion rates. Because of these properties, helium is often used in airships and balloons as it provides lift by being significantly lighter than the atmospheric air.

Density

Density is an intrinsic property of a substance defined as its mass per unit volume. It can be expressed with the equation \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume. The concept of density is crucial in understanding buoyant behavior in fluids.

When comparing helium to air, it's clear that helium's density is much lower. Air mainly consists of nitrogen and oxygen, which are heavier diatomic molecules. Since helium's atoms are lighter and its configuration is monatomic, helium gas has a lower density than air. This characteristic is why a helium-filled balloon rises: the balloon is lighter than the air it displaces, allowing it to ascend according to the principles of buoyancy.

Principle of buoyancy

The principle of buoyancy, also known as Archimedes' Principle, states that any object partially or fully submerged in a fluid experiences an upward force equal to the weight of the fluid it displaces. This principle is applicable to fluids, including gases like air.

When a balloon is filled with helium gas, its total mass becomes less than the mass of the air it displaces, because helium is less dense than the ambient air. Consequently, the balloon experiences a net upward force and rises. This is why a closed balloon filled with helium rises; the buoyant force created is stronger than the weight of the helium-filled balloon itself.

This principle is crucial in predicting and understanding the floating behavior of objects in various fluids, from boats in water to balloons in the air. It highlights the importance of comparing densities and comprehending how different substances interact within the same environment to determine whether an object will float, sink, or rise.