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}

Step by step solution

01

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.

02

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.

03

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.

04

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.

05

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.

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