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Chapter 10: Problem 47

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 balloon thus weighs less than 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

Expert verified
The correct explanation for why a closed balloon filled with helium gas rises in the air is statement (c). Helium atoms have a lower mass than the average air molecules, making helium gas less dense than air. According to Archimedes' principle, the buoyant force acting on the balloon is equal to the weight of the air displaced by the balloon. Since the weight of the helium within the balloon is less than the weight of the displaced air, there is a net upward force on the balloon, causing it to rise.

Step by step solution

01

Statement (a)

Helium is indeed a monatomic gas, whereas nitrogen and oxygen, which are the primary components of air, are diatomic gases. However, this fact alone does not explain why the balloon rises in the air. We need to look for a statement that connects the properties of helium with buoyancy.
02

Statement (b)

It is true that the average speed of helium atoms is higher than the average speed of air molecules due to their lighter mass. However, this does not lead to higher speed collisions with the balloon walls providing upward force strong enough to make the balloon rise. Therefore, this statement does not provide an adequate explanation for the phenomenon.
03

Statement (c)

This statement is correct. The helium atoms have a lower mass than the average air molecules, which makes helium gas less dense than air. According to Archimedes' principle, the buoyant force acting on the balloon is equal to the weight of the air displaced by the balloon. Since the weight of the helium within the balloon is less than the weight of the displaced air, there is a net upward force on the balloon, causing it to rise.
04

Statement (d)

This statement is incorrect. Although helium atoms have a lower molar mass than the average air molecule, it does not mean that the temperature of the helium inside the balloon is higher than the air temperature. Both the balloon and the air around it would have the same temperature under normal conditions, and the hot gas rising concept does not apply in this case. Based on our analysis, the correct statement is (c). This statement explains how the lower density of helium gas compared to air results in a helium-filled balloon rising in the air due to buoyancy.

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Most popular questions from this chapter

Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose \(120.00 \mathrm{~kg}\) of \(\mathrm{N}_{2}(g)\) is stored in a \(1100.0\) - \(\mathrm{L}\) metal cylinder at \(280^{\circ} \mathrm{C}\). (a) Calculate the pressure of the gas, assuming ideal-gas behavior. (b) By using data in Table 10.3, calculate the pressure of the gas according to the van der Waals equation. (c) Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions?

A sample of \(1.42 \mathrm{~g}\) of helium and an unweighed quantity of \(\mathrm{O}_{2}\) are mixed in a flask at room temperature. The partial pressure of helium in the flask is \(42.5\) torr, and the partial pressure of oxygen is 158 torr. What is the mass of the oxygen in the container?

How does a gas differ from a liquid with respect to each of the following properties: (a) density, (b) compressibility, (c) ability to mix with other substances of the same phase to form homogeneous mixtures?

(a) What are the mole fractions of each component in a mixture of \(5.08 \mathrm{~g}\) of \(\mathrm{O}_{2}, 7.17 \mathrm{~g}\) of \(\mathrm{N}_{2}\), and \(1.32 \mathrm{~g}\) of \(\mathrm{H}_{2}\) ? (b) What is the partial pressure in \(a \operatorname{tm}\) of each component of this mixture if it is held in a 12.40-L vessel at \(15^{\circ} \mathrm{C} ?\)

Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and thus has a boiling point at atmospheric pressure of \(-164^{\circ} \mathrm{C}\). One possible strategy is to oxidize the methane to methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), which has a boiling point of \(65^{\circ} \mathrm{C}\) and can therefore be shipped more readily. Suppose that \(10.7 \times 10^{9} \mathrm{ft}^{3}\) of methane at atmospheric pressure and \(25^{\circ} \mathrm{C}\) are oxidized to methanol. (a) What volume of methanol is formed if the density of \(\mathrm{CH}_{3} \mathrm{OH}\) is \(0.791 \mathrm{~g} / \mathrm{mL} ?\) (b) Write balanced chemical equations for the oxidations of methane and methanol to \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). Calculate the total enthalpy change for complete combustion of the \(10.7 \times 10^{9} \mathrm{ft}^{3}\) of methane described above and for complete combustion of the equivalent amount of methanol, as calculated in part (a). (c) Methane, when liquefied, has a density of \(0.466 \mathrm{~g} / \mathrm{mL} ;\) the density of methanol at \(25^{\circ} \mathrm{C}\) is \(0.791 \mathrm{~g} / \mathrm{mL}\). Compare the enthalpy change upon combustion of a unit volume of liquid methane and liquid methanol. From the standpoint of energy production, which substance has the higher enthalpy of combustion per unit volume?
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