Question

For the process \(\mathrm{A}(l) \longrightarrow \mathrm{A}(\mathrm{g})\), which direction is favored by changes in energy probability? Positional probability? Explain your answers. If you wanted to favor the process as written, would you raise or lower the temperature of the system? Explain.

Short answer

The process A(l) → A(g) is not favored by energy probability since the liquid phase has lower energy than the gaseous phase. However, the process is favored by positional probability as the gaseous phase has higher positional probability, with more available volume and microstates. To favor the process as written, the temperature of the system should be raised, providing energy to overcome the intermolecular forces in the liquid phase and allowing the transition to the gaseous phase to become more probable.

Step-by-step solution

Understand the process

The given process involves the conversion of substance A from its liquid phase (l) to its gaseous phase (g). It is essential to know which direction is favored by energy probability and positional probability. Step 2: Determine the favored direction by energy probability

Determine the favored direction by energy probability

Energy probability is related to the stability of a system, and it usually favors the direction with lower energy. In the case of this process, the liquid phase typically has lower energy than the gaseous phase due to the intermolecular forces in the liquid state. Therefore, the process A(l) → A(g) is not favored by energy probability. Step 3: Determine the favored direction by positional probability

Determine the favored direction by positional probability

Positional probability is related to the available volume and number of microstates (arrangements) of a system. The gaseous phase has a higher positional probability compared to the liquid phase since the gas molecules can occupy a larger volume and have more microstates. Thus, the process A(l) → A(g) is favored by positional probability. Step 4: Determine the effect of changing temperature on the process

Determine the effect of changing temperature on the process

To favor the process A(l) → A(g) as written, we need to increase the temperature of the system. By raising the temperature, we provide energy to overcome the intermolecular forces in the liquid phase, allowing the molecules of substance A to transition into the gaseous phase. This process becomes more probable as the temperature increases, eventually favoring the formation of the gaseous phase.

Key concepts

Energy Probability

Energy probability is a crucial concept in understanding phase transitions. It refers to the tendency of a system to move towards configurations that require less energy. Systems naturally favor states with lower energy because they are often more stable. For the transition from a liquid to a gas, labeled as \( \text{A(l)} \rightarrow \text{A(g)} \), the liquid state typically has a lower energy due to the presence of intermolecular forces.

These forces hold the molecules closer in the liquid state, resulting in decreased movement and subsequently lower energy levels. When analyzing phase transitions, this means that energy probability would favor remaining as a liquid rather than transitioning to a gas, where the molecules move quickly and have higher energy. Therefore, for the process \( \text{A(l)} \rightarrow \text{A(g)} \), the transition isn’t naturally favored by energy probability.

Positional Probability

Positional probability focuses on the arrangement and distribution of particles within a phase. It relates to the available space and the number of ways that molecules can be positioned. In a gas, molecules have significantly more freedom to move than in a liquid.

This leads to a higher positional probability in the gaseous state due to a greater number of possible microstates. Essentially, there are more configurations and positions that the particles can take in the gas phase compared to the more tightly packed liquid phase. Because of this, the process \( \text{A(l)} \rightarrow \text{A(g)} \) is favored by positional probability. Thus, while the transition may not be favored energetically, it is favored based on spatial considerations, highlighting the significance of positional probability in phase changes.

Temperature Effect on Phase Change

Temperature plays a vital role in facilitating phase changes, particularly when overcoming energy and positional considerations. In the process \( \text{A(l)} \rightarrow \text{A(g)} \), increasing the temperature provides the necessary energy to match or overcome molecular attractions in the liquid state.

Raising the temperature essentially supplies additional energy to the system, enabling molecules in the liquid to gain sufficient energy to escape into the gaseous phase. Higher temperatures result in greater kinetic energy among particles, allowing them to spread apart and form a gas.

• Increased temperature boosts energy probability for gas formation.
• Enables molecules to move freely, supporting the gas phase.

To favor the phase change \( \text{A(l)} \rightarrow \text{A(g)} \), elevating the temperature makes the transition more likely by overcoming the energy deficit and enhancing positional freedom.