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Ch.10 - Gases
All textbooksBrown 14th EditionCh.10 - GasesProblem 5
Chapter 10, Problem 5

Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? (a) Because Xe is a noble gas, there is less tendency for the Xe atoms to repel one another, so they pack more densely in the gaseous state. (b) Xe atoms have a higher mass than N2 molecules. Because both gases at STP have the same number of molecules per unit volume, the Xe gas must be denser. (c) The Xe atoms are larger than N2 molecules and thus take up a larger fraction of the space occupied by the gas. (d) Because the Xe atoms are much more massive than the N2 molecules, they move more slowly and thus exert less upward force on the gas container and make the gas denser.

Verified step by step guidance
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Step 1: Understand the concept of density in gases. Density is defined as mass per unit volume. At Standard Temperature and Pressure (STP), all gases occupy the same volume per mole, which is 22.4 liters.
Step 2: Recall Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. Therefore, at STP, 1 mole of any gas will have the same volume.
Step 3: Consider the molar mass of the gases. Nitrogen gas (N2) has a molar mass of approximately 28 g/mol, while xenon (Xe) has a molar mass of approximately 131 g/mol.
Step 4: Compare the masses of the gases. Since both gases occupy the same volume at STP, the gas with the higher molar mass will have a greater mass in that volume, making it denser.
Step 5: Evaluate the options. Option (b) correctly states that Xe atoms have a higher mass than N2 molecules, and since both gases have the same number of molecules per unit volume at STP, the Xe gas must be denser.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density and Molar Mass

Density is defined as mass per unit volume. In gases, density can be influenced by the molar mass of the gas particles. A higher molar mass typically results in a higher density if the volume is constant. Therefore, comparing the molar masses of nitrogen (N2) and xenon (Xe) is crucial to understanding their relative densities at standard temperature and pressure (STP).
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Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T). At STP, gases behave ideally, meaning their properties can be predicted using this law. The law implies that for a given volume and temperature, the density of a gas is directly proportional to its molar mass, which is essential for comparing the densities of N2 and Xe.
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Kinetic Molecular Theory

Kinetic Molecular Theory explains the behavior of gases in terms of particle motion. It states that gas particles are in constant motion and that their speed is related to temperature. Heavier gas particles, like Xe, move more slowly than lighter ones, like N2, which affects their density and how they occupy space. Understanding this theory helps clarify why Xe is denser than N2 despite being a noble gas.
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Related Practice
Textbook Question

You have a sample of gas in a container with a movable piston, such as the one in the drawing. (b) Redraw the container to show what it might look like if the external pressure on the piston is increased from 101.3 kPa to 202.7 kPa while the temperature is kept constant.

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Textbook Question

Consider the sample of gas depicted here. What would the drawing look like if the volume and temperature remained constant while you removed enough of the gas to decrease the pressure by a factor of 2? (a) It would contain the same number of molecules. (b) It would contain half as many molecules. (c) It would contain twice as many molecules. (d) There is insufficient data to say.

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Textbook Question

Imagine that the reaction 2 CO1g2 + O21g2¡2 CO21g2 occurs in a container that has a piston that moves to maintain a constant pressure when the reaction occurs at constant temperature. Which of the following statements describes how the volume of the container changes due to the reaction: (a) the volume increases by 50%, (b) the volume increases by 33%, (c) the volume remains constant, (d) the volume decreases by 33%, (e) the volume decreases by 50%.

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Textbook Question

The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube. When the valves are opened and the gases are allowed to mix at constant temperature, what is the distribution of atoms in each container?

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Textbook Question

The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube. Assume that the containers are of equal volume and ignore the volume of the connecting tube. Which gas has the greater partial pressure after the valves are opened?

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