Question

Water in an open beaker evaporates over time. As the water is evaporating, is the vapor pressure increasing, decreasing, or staying the same? Why?

Short answer

The vapor pressure in an open beaker decreases during evaporation. This is due to water molecules leaving the liquid-gas interface and dispersing into the surrounding environment, resulting in a constant decrease in the water vapor concentration and, consequently, a decrease in vapor pressure.

Step-by-step solution

Understanding Vapor Pressure

Vapor pressure is the pressure exerted by the gas phase of a substance in equilibrium with its liquid phase. The vapor pressure depends on the temperature, and it increases with temperature according to the Clausius-Clapeyron equation. Evaporation occurs when molecules from the surface of a liquid gain enough energy to become gas. In an open system, these gas molecules can disperse into the surrounding environment.

Analyzing Evaporation in an Open Beaker

In the case of an open beaker, the water molecules in the liquid phase, after gaining enough energy, enter the gas phase and disperse into the surrounding environment. Since the beaker is open, the gas molecules are not confined within the container, and they are allowed to leave the liquid-gas interface and mix with the air.

The Effect of Evaporation on Vapor Pressure

As the water is evaporating, the number of gas molecules leaving the liquid-gas interface is greater than the number of molecules returning to the liquid phase from the gas phase. This means that the concentration of water vapor in the air above the liquid is constantly decreasing, which in turn decreases the vapor pressure. So, over time, the vapor pressure of the water in the open beaker is decreasing. So the answer is: The vapor pressure is decreasing during evaporation in an open beaker. This is because as the water evaporates, the molecules leave the liquid-gas interface and disperse into the surrounding environment, causing the concentration of water vapor in the air to decrease and thus decreasing vapor pressure.

Key concepts

Evaporation Process

Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. This process only happens when the partial pressure of the gas produced by evaporation is less than the equilibrium vapor pressure, meaning the atmosphere is not already saturated with the vapor of the liquid.

During evaporation, molecules located near the liquid's surface that possess enough kinetic energy break away from the bonds of liquid water. The energy required for evaporation is typically provided by heat from the surrounding environment. In an open setting like a beaker, as evaporation takes place, the liquid’s vapor spreads out into the air, which effectively reduces its concentration near the liquid surface. Over time, the amount of liquid diminishes as more and more molecules transition to the gas phase, and this process continues until the liquid is entirely vaporized or the environmental conditions change.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation is a fundamental principle within thermodynamics which describes the relationship between the temperature and pressure of a substance at its phase transition points. In the context of vapor pressure, this equation is critical for understanding how pressure varies with temperature. Mathematically, the Clausius-Clapeyron equation is often expressed as: \( \frac{dP}{dT} = \frac{L}{T(V_\text{g} - V_\text{l})} \) where \( P \) represents the pressure, \( T \) the temperature, \( L \) the latent heat of vaporization, and \( V_\text{g} \) and \( V_\text{l} \) the molar volumes of the gas and liquid phases, respectively. The equation shows us that as temperature increases, the vapor pressure does as well. It explains why evaporation is faster at higher temperatures; a higher temperature means a higher vapor pressure, driving the evaporation process more vigorously.

Liquid-Gas Equilibrium

Liquid-gas equilibrium occurs when a liquid and its vapor (gas phase) are in a closed system, and the rate of evaporation equals the rate of condensation. At this stage, the gas phase exerts a pressure on the liquid called the equilibrium vapor pressure, which depends on the temperature of the system. In a closed system, this pressure remains constant because the amount of gas phase is constant, since the gas has no place to escape.

However, in an open system like an open beaker, equilibrium cannot be established as the vapor phase does not remain constant. It continually changes because the gas molecules can leave the liquid-gas interface, dispersing into the surrounding air. Consequently, the number of gas phase molecules is not replenished as in a closed system, and the vapor pressure does not stay constant but decreases as the evaporation progresses.