The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube closed at both ends.
a. How many blue gas molecules are in the left container?
b. How many red gas molecules are in the middle container?
c. When the valves are opened and the gases are allowed to mix at constant temperature, how many atoms of each type of gas end up in the originally empty container? Assume that the containers are of equal volume and ignore the volume of the connecting tube. [Section 10.4]

Verified step by step guidance

1. <Step 1: Understand the initial setup.> Identify that there are two gas-filled containers and one empty container, all of equal volume, connected by a tube. The left container has blue gas molecules, and the middle container has red gas molecules.
2. <Step 2: Determine the initial number of molecules.> Count the number of blue gas molecules in the left container and the number of red gas molecules in the middle container from the given diagram or description.
3. <Step 3: Consider the mixing process.> When the valves are opened, the gases will mix. Since the containers are of equal volume and the temperature is constant, the gases will distribute evenly across all three containers.
4. <Step 4: Calculate the distribution of molecules.> Divide the total number of blue gas molecules by three to find out how many blue molecules will be in each container after mixing. Do the same for the red gas molecules.
5. <Step 5: Conclude the distribution.> State the number of blue and red gas molecules that will end up in the originally empty container after the gases have mixed.>

Key Concepts

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. Key laws include Boyle's Law, which states that pressure and volume are inversely related at constant temperature, and Charles's Law, which states that volume is directly proportional to temperature at constant pressure. Understanding these laws is essential for predicting how gases will behave when mixed or when conditions change.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the amount of substance to the number of particles, such as atoms or molecules. One mole of any substance contains Avogadro's number (approximately 6.022 x 10²³) of particles. This concept is crucial for calculating the number of molecules in each container and for understanding how they will distribute when mixed.

Diffusion of Gases

Diffusion is the process by which gas molecules spread from areas of higher concentration to areas of lower concentration. In the context of the question, when the valves are opened, the gases will diffuse into the empty container until the concentration is uniform. This concept is important for predicting the final distribution of gas molecules in the containers after mixing.