Question

If liquid water is introduced into an evacuated (zero pressure) flask, the pressure will begin to rise. (a) Eventually, the pressure will stop rising and reach a constant value. Why does it stop rising? (b) What do we call this pressure? (c) What will happen to this pressure if we increase the temperature of the flask? Why does it happen?

Short answer

(a) The pressure stops rising because the number of water molecules entering the gas phase equals the number returning to the liquid phase, reaching an equilibrium. (b) This constant pressure is called the vapor pressure. (c) If the temperature of the flask increases, the vapor pressure will also increase because a larger number of water molecules have enough energy to escape the liquid phase and enter the gas phase, shifting the equilibrium and resulting in a higher vapor pressure.

Step-by-step solution

(a) Reason for pressure stop rising

When liquid water is introduced into an evacuated flask, the water molecules start to move and collide with the walls of the flask, causing the pressure to rise. However, as more and more water molecules escape the liquid phase and enter the gas phase, a point is reached where the number of water molecules entering the gas phase equals the number returning to the liquid phase. At this point, the pressure inside the flask no longer changes and reaches a constant value.

(b) Name of the pressure

The constant pressure reached inside the flask when the number of water molecules entering the gas phase equals the number returning to the liquid phase is called the vapor pressure. The vapor pressure depends on the temperature and the substance itself.

(c) The effect of temperature on the pressure

If we increase the temperature of the flask, the vapor pressure of the liquid water will also increase. This occurs because, as the temperature rises, the average kinetic energy of the water molecules increases, and a larger number of molecules have enough energy to escape the liquid phase and enter the gas phase. Consequently, the equilibrium between the number of molecules in the gas and liquid phases shifts, resulting in a higher vapor pressure at higher temperatures.

Key concepts

Equilibrium in Gas and Liquid Phases

When we introduce liquid water into an evacuated flask, an interesting phenomenon occurs. The water molecules begin to evaporate, and as they do, they collide with the flask's walls, leading to an increase in pressure. However, this process doesn't go on indefinitely. What actually happens is that an equilibrium is established between the liquid water and its vapor.

At equilibrium, the rate at which water molecules evaporate (change from the liquid phase to the gas phase) is equal to the rate at which they condense (change from the gas phase back to the liquid phase). This is a dynamic process, meaning that individual molecules are constantly switching between being part of the liquid and being part of the vapor, but the overall number of molecules in each phase remains constant, hence the pressure stabilizes. Such a state is crucial to understand in various applications ranging from chemical reactions to the preservation of food products.

Dynamic Equilibrium

It's important to distinguish this from static equilibrium, where nothing seems to be happening at all. In the case of the water in the evacuated flask, both evaporation and condensation are occurring at the same rate, but they are very much happening, making it a dynamic equilibrium.

Kinetic Energy of Molecules

Kinetic energy is fundamentally associated with the motion of molecules. In the context of the vapor pressure scenario, molecules in the liquid water have varying levels of energy. At any given moment, some molecules have enough kinetic energy to overcome the intermolecular forces binding them to the other molecules in the liquid and escape into the gas phase—this process is known as evaporation.

Conversely, gas-phase water molecules that have lost energy due to collisions with other molecules or the walls of the flask can transition back to the liquid phase through condensation. This balance between evaporation and condensation ensures that at equilibrium, the kinetic energies of the molecules are distributed in such a way that the phase transition rates are equal.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution in thermodynamics describes the spread of kinetic energies among molecules. At a given temperature, most molecules have moderate kinetic energies, with fewer molecules having very high or very low kinetic energies. The higher the temperature, the broader this distribution becomes, with a larger fraction of molecules having higher kinetic energies sufficient to vaporize.

Effects of Temperature on Vapor Pressure

Temperature plays a pivotal role in determining the vapor pressure of a liquid. This is because temperature affects the kinetic energy of molecules, as outlined in the kinetic theory of gases. As the temperature of the system increases, the average kinetic energy of the water molecules also increases, which means more molecules are capable of escaping the liquid and turning into vapor.

The result of this is an increase in vapor pressure; this pressure can be measured and is commonly referred to as the saturation vapor pressure. It's important to note that at higher temperatures, the rate at which molecules enter the gas phase increases, leading to a new equilibrium where the vapor pressure is higher than it was at the lower temperature.

Practical Implications

Understanding the relationship between temperature and vapor pressure is crucial, not only for scientific experiments but also for real-life applications such as predicting weather patterns, designing refrigeration systems, or understanding the behavior of engines. This concept helps explain why water boils at a lower temperature at high altitudes where the atmospheric pressure is lower.