Ch.10 - Gases

Problem 6b

Chapter 10, Problem 6b

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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Identify the number of gas particles in each container. The left container has green particles, and the right container has brown particles.

Count the number of green particles in the left container and the number of brown particles in the right container.

Assume that the containers are of equal volume and that the temperature is constant.

Use the ideal gas law, PV = nRT, to understand that the pressure is directly proportional to the number of particles (n) when volume (V) and temperature (T) are constant.

Compare the number of particles in each container to determine which gas has the greater partial pressure after the valves are opened.

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Key Concepts

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

Partial Pressure

Partial pressure is the pressure exerted by a single gas in a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas. This concept is crucial for understanding how gases behave in a shared volume, especially when valves are opened to allow gas to mix.

Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and the number of moles of a gas. The Ideal Gas Law (PV=nRT) is particularly relevant here, as it relates these variables in a way that helps predict how gases will behave when conditions change, such as when the valves in the apparatus are opened.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific gas to the total number of moles of all gases present. Understanding mole fraction is essential for determining the partial pressures of the gases in the containers after the valves are opened, as it directly influences the distribution of pressure in the system.

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Related Practice

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. 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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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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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?

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