Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 9a

Chapter 10, Problem 9a

Consider the following graph. (a) If curves A and B refer to two different gases, He and O2, at the same temperature, which curve corresponds to He?

Verified step by step guidance

Step 1: Understand the context of the problem. The problem involves comparing two gases, helium (He) and oxygen (O2), at the same temperature.

Step 2: Recall the concept of molecular speed distribution. At a given temperature, lighter gas molecules move faster than heavier ones. This is described by the Maxwell-Boltzmann distribution.

Step 3: Identify the key difference between He and O2. Helium is a lighter gas compared to oxygen, which means its molecules will have higher average speeds at the same temperature.

Step 4: Analyze the graph. The curve that is more spread out and shifted towards higher speeds corresponds to the lighter gas, which in this case is helium (He).

Step 5: Conclude which curve corresponds to He. Based on the analysis, the curve that shows higher average speeds and a broader distribution is the one that represents helium.

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Key Concepts

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

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that gas particles are far apart, move freely, and collide elastically. This theory helps in understanding how different gases, like helium (He) and oxygen (O2), exhibit different properties such as speed and energy at the same temperature.

Molar Mass and Gas Behavior

Molar mass significantly influences the behavior of gases. Lighter gases, such as helium, have lower molar masses compared to heavier gases like oxygen. At the same temperature, lighter gases move faster than heavier ones, which is crucial for determining which curve in the graph corresponds to He.

Graph Interpretation of Gas Properties

Graphs depicting gas properties often illustrate relationships such as speed versus temperature or pressure. Understanding how to interpret these graphs is essential for identifying which gas is represented by each curve. In this case, recognizing that the curve for He will be steeper due to its higher average speed compared to O2 is key to answering the question.

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Related Practice

Textbook Question

Consider the following graph. (b) If A and B refer to the same gas at two different temperatures, which represents the higher temperature?

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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rank

Textbook Question

Consider the following samples of gases:

If the three samples are all at the same temperature, rank them with respect to (a) total pressure

Textbook Question

Consider the following graph. (c) For each curve, which speed is highest: the most probable speed, the root-mean-square speed, or the average speed?

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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