Question

Consider a tank that contains a saturated liquid vapor mixture of water in equilibrium. Some vapor is now allowed to escape the tank at constant temperature and pressure. Will this disturb the phase equilibrium and cause some of the liquid to evaporate?

Short answer

Answer: Yes, allowing vapor to escape the tank will disturb the phase equilibrium and cause some liquid to evaporate. This happens because the system aims to re-establish equilibrium by either increasing the rate of evaporation and/or decreasing the rate of condensation.

Step-by-step solution

Understand the behavior of saturated mixtures in equilibrium

When a saturated liquid-vapor mixture is in equilibrium, it means that the rate of evaporation of water molecules from the liquid phase equals the rate of condensation of water molecules back into the liquid phase from the vapor phase. This balance is maintained by the constant temperature and pressure in the system.

Analyze the effect of vapor escaping the tank

When the vapor is allowed to escape the tank, the balance between evaporation and condensation is disrupted. The loss of vapor results in a decrease in the number of water molecules in the vapor phase, which would tend to disrupt the phase equilibrium.

Determine the response of the system to the disturbance

Since the number of water molecules in the vapor phase has decreased, it means that the rate of evaporation must increase, and/or the rate of condensation must decrease, in order to re-establish phase equilibrium at the same temperature and pressure. This implies that some of the liquid water must evaporate, increasing the mole fraction of the water vapor in the system, ultimately re-establishing the equilibrium between the liquid and vapor phases.

Conclusion

Allowing vapor to escape the tank at constant temperature and pressure will disturb the phase equilibrium and cause some of the liquid to evaporate. This is because the system needs to compensate for the loss of vapor molecules by increasing the rate of evaporation and/or decreasing the rate of condensation in order to maintain phase equilibrium under the given conditions.

Key concepts

Saturated Liquid-Vapor Mixture

Understanding a saturated liquid-vapor mixture is essential when dealing with substances that can exist in both liquid and gaseous phases under certain conditions of temperature and pressure. A classic example involves a closed container partly filled with water and the space above the water occupied by water vapor. In this enclosed system, water molecules are continuously evaporating and condensing.

At saturation point, the rate of evaporation equals the rate of condensation, leading to phase equilibrium in the mixture. It's a delicate balance - a dynamic process where individual molecules transition between phases, but the overall quantity in each phase remains constant. No net increase in vapor or liquid will be observed as long as the temperature and pressure are unaltered. This state is characteristic of a saturated liquid-vapor mixture.

When the equilibrium is disturbed, such as by allowing vapor to escape, the system responds to reinstate balance. This automatic adjustment highlights the system's inherent drive to maintain equilibrium, which will be further discussed when exploring thermodynamic equilibrium.

Evaporation and Condensation Rates

The rates of evaporation and condensation are pivotal in understanding phase changes in a system. Evaporation is the process where molecules transition from the liquid to the vapor state, typically on the surface of the liquid. For water in a closed container, as the temperature increases, more water molecules gain the energy needed to overcome intermolecular forces and become vapor.

In contrast, condensation is the reverse process, where vapor molecules lose energy, bond together, and transition back to the liquid state. In a saturated liquid-vapor mixture, these two rates are equal, resulting in no net change in the amount of liquid or vapor - a key aspect of phase equilibrium.

If vapor is removed from the system (like from the exercise described), the condensation rate temporarily exceeds evaporation, disturbing equilibrium. The system will react by accelerating evaporation to restore the balance of evaporation and condensation rates, thereby upholding the principle that systems tend to move towards equilibrium.

Thermodynamic Equilibrium

Thermodynamic equilibrium is a broad concept referring to a state where all macroscopic changes have ceased in a system, indicating a balance in various types of equilibria, including mechanical, thermal, and phase equilibrium. Concerning phase equilibrium specifically, a system reaches this state when the properties such as temperature and pressure are uniform throughout and no further changes occur in phase proportions without external interference.

From our exercise, when vapor is allowed to escape from a tank containing a saturated liquid-vapor mixture, the phase equilibrium is indeed disrupted. However, thermodynamic systems inherently strive to return to equilibrium. When the vapor leak occurs, adjustments in the rates of evaporation and condensation take place, prompting the liquid to evaporate and hence counteract the disturbance.

This example illustrates how dynamic processes within the thermodynamic framework are self-regulating to maintain equilibrium conditions. It is fundamental to understand that maintaining equilibrium doesn't necessarily mean that the microscale actions (like molecules evaporating or condensing) cease; instead, they continue in a balanced way that sustains the overall stable condition of the system.