Question

A system is divided into two halves separated by a removable divider. Initially, with the divider in place, the left half has only red molecules and the right half has only blue molecules. The divider is removed and equilibrium is reached. Which of the following statements correctly characterizes the system? a. It contains only blue molecules on the left side. b. It contains only red molecules on the left side. c. It contains a mixture of red and blue molecules throughout the system. d. It contains only blue molecules at the bottom of the system. e. It has an equal number of red and blue molecules on each side.

Short answer

c. It contains a mixture of red and blue molecules throughout the system.

Step-by-step solution

Understand the Initial Setup

Initially, the system is divided into two halves by a divider. The left half contains only red molecules, and the right half contains only blue molecules. This separation implies no mixing has occurred yet.

Consider the Action Taken

The removable divider is taken away. This action allows the molecules to mix freely, as the barrier that kept them separated is no longer in place.

Identify the Concept of Equilibrium

After removing the divider, the system is allowed to reach equilibrium. At equilibrium, the properties of the system become uniform throughout, implying that both red and blue molecules will evenly spread out due to random thermal motion.

Analyze the Outcome

Since the system reaches equilibrium, random movement of both red and blue molecules will cause them to mix evenly across the entire system. Neither side will exclusively contain one color of molecules.

Select the Correct Statement

At equilibrium, the mixture of red and blue molecules is uniform throughout the system. This matches option "c. It contains a mixture of red and blue molecules throughout the system."

Key concepts

Molecular Motion

Molecules are in constant motion, and this movement is fundamental in understanding processes like mixing and reaching equilibrium. When considering a system initially separated by a barrier, as in our exercise, each side will have molecules that are only red or only blue. Once the barrier is removed, the molecules start to move freely.

Molecular motion is random and continuous, which means that over time, molecules of different colors - red and blue - will encounter each other frequently. Eventually, their movements help to transform the initially distinct regions into a more blended mix. This behavior is due to their constant and unrestricted motion after the divider is removed.

This mixing effect is an integral part of the concept of equilibrium as molecules diffuse throughout the available space, leading to a uniform distribution.

Thermal Motion

Thermal motion is the random movement of particles resulting from their energy, typically heightened due to temperature. In our example, this type of motion plays a significant role in how molecules blend and reach equilibrium.

As the temperature of the system increases, the energy imparted to the molecules also increases, which enhances their motion. Faster-moving molecules will spread out more quickly. This resulting motion causes molecules to intermingle extensively and helps distribute molecules evenly across the system.

The thorough mixing we observe as a consequence of thermal motion ensures that, over time, the system achieves an even blend, thus perfectly setting the stage for equilibrium to be attained.

Uniform Distribution

When we achieve equilibrium, one of the most inherent properties is a uniform distribution of molecules throughout the system. Uniform distribution means that the concentration of molecules becomes consistent throughout the entire space, regardless of initial conditions.

In the scenario given, after removing the divider, both red and blue molecules will roam freely. Due to their ceaseless and random motion—driven by thermal energy—they spread evenly throughout the space available. Eventually, every part of the system will have a similar mix of red and blue molecules.

This uniform distribution is reached without bias toward any initial side of the system and represents a state where no net change occurs, signifying that equilibrium has been reached.

System Mixing

System mixing is an observable process that occurs when separate substances within a system, like our red and blue molecules, intermingle after barriers to their movement are removed. This intermingling is critical to reaching equilibrium.

The essential driver behind this mixing is the inherent motion of molecules. As the barrier is lifted, these molecules—driven by molecular and thermal motion—begin to explore the space formerly restricted to them. While each molecule moves individually, the collective effect of all molecules moving leads to mixing.

This kind of mixing results in a system where the previously separate components (red and blue molecules) become indistinguishable in their distribution, ultimately leading to a stable, uniformly mixed state throughout the system. This process illustrates the natural trend toward disorder and randomness, often referred to as entropy, which is a fundamental principle underlying equilibrium.