Ch.10 - Gases

Problem 6a

Chapter 10, Problem 6a

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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Identify the initial conditions: three containers with different gases (red, blue, green) and two empty containers.

Recognize that when the valves are opened, the gases will mix and distribute evenly due to diffusion.

Understand that the total number of gas particles will be conserved, and they will spread out to occupy all available space.

Calculate the total number of gas particles from all containers and divide by the number of containers to find the average number of particles per container.

Conclude that each container will have an equal number of gas particles, with a mix of red, blue, and green particles in each container.

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Key Concepts

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

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature, pressure, and volume. Key laws include Boyle's Law, Charles's Law, and Avogadro's Law, which collectively explain how gas volume changes with pressure and temperature. Understanding these laws is essential for predicting how gases will behave when allowed to mix or expand in a given system.

Effusion and Diffusion

Effusion is the process by which gas molecules escape from a container through a small opening, while diffusion refers to the mixing of gas molecules due to their random motion. Graham's Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. These concepts are crucial for understanding how gases will distribute themselves in the containers after the valves are opened.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particle motion. It posits that gas particles are in constant, random motion and that their collisions with container walls create pressure. This theory helps to understand how temperature affects the speed of gas particles and, consequently, the distribution of gases in the containers when mixed.

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Related Practice

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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Open Question

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.

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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Open Question

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (d) the rate of effusion through a pinhole leak?

Textbook Question

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?

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