Question

A beaker of water is placed in a closed container. Predict the effect on the vapor pressure of the water when (a) its temperature is lowered, (b) the volume of the container is doubled, (c) more water is added to the beaker.

Short answer

(a) Decreases, (b) Stays the same, (c) Stays the same.

Step-by-step solution

Understanding Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid phase at a given temperature in a closed system. It depends on temperature and the nature of the liquid, but not on the volume or the amount of liquid.

Analyzing the Effect of Lower Temperature

When the temperature of the water is lowered, the kinetic energy of the water molecules decreases. This results in fewer molecules having enough energy to escape the liquid phase and enter the vapor phase, thus reducing the vapor pressure.

Examining the Effect of Increased Volume

Doubling the volume of the container does not change the vapor pressure. Since vapor pressure depends only on temperature and not on the volume, the vapor pressure remains the same even when the volume is increased. To maintain equilibrium, the number of vapor molecules may change, but the pressure stays constant.

Investigating the Effect of Adding More Water

Adding more water to the beaker does not affect the vapor pressure unless it changes the temperature. Since vapor pressure is independent of the amount of liquid as long as there is enough liquid to maintain equilibrium, the vapor pressure remains unchanged.

Key concepts

Temperature and Vapor Pressure

Vapor pressure is highly dependent on the temperature of a liquid. When you lower the temperature of water, the molecules in the liquid slow down because they have less kinetic energy.
This decreased energy means fewer molecules can escape from the liquid to become vapor.
As a result, the vapor pressure gets reduced.
The relationship between temperature and vapor pressure is governed by the Clausius-Clapeyron equation, which mathematically describes how vapor pressure changes with temperature. Essentially, it shows that as the temperature decreases, fewer molecules transition into the vapor phase, reducing the pressure exerted by the vapor.

Volume and Vapor Pressure

One might assume that increasing the volume of a container would directly impact vapor pressure, but that's actually not the case.
No matter how much you change the container's volume, if the temperature stays constant, the vapor pressure remains unaffected.
This is because vapor pressure is a property that is dependent on the liquid's nature and temperature, not on the volume of the container.
When the container's volume increases, the number of molecules in the vapor phase may fluctuate to maintain equilibrium, but the vapor pressure itself does not change.

• Vapor pressure is thus constant given a constant temperature and enough liquid to maintain saturation.
• It is important to distinguish between the quantity of vapor and the pressure it exerts, which stays constant with volume changes.

Liquid Quantity and Vapor Pressure

At first glance, you might think that adding more liquid to a beaker would increase vapor pressure.
However, if the temperature doesn't change, the vapor pressure remains constant.
This is because vapor pressure is independent of the amount of liquid, provided there is an adequate quantity to maintain a saturated state.

• The added water serves to replace liquid as it evaporates, ensuring a consistent vapor environment.
• The key factor is maintaining a dynamic equilibrium where evaporation rates are balanced with condensation rates.

Adding more water helps maintain this equilibrium but does not change the intrinsic vapor pressure property.