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.

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In the context of vapor pressure, thermodynamics helps us understand how energy is transferred during the phase changes of a substance, like the transition from liquid water to water vapor.

During this phase change, energy is required to break the intermolecular forces that hold the water molecules in a liquid state. This energy comes in the form of heat and is absorbed from the surroundings (or an external source) when the water evaporates. Conversely, when vapor pressure decreases due to a drop in temperature, as mentioned in Part a of the exercise, it is because the average kinetic energy of the water molecules has decreased. With less kinetic energy, fewer molecules can escape into the vapor phase, leading to lower vapor pressure.

In thermal equilibrium, a substance's vapor pressure is determined at a given temperature, regardless of other parameters like the volume of its container or the quantity of the substance, aligning with the solved exercise.

Phase change refers to the transition of a substance from one state of matter to another, such as from solid to liquid (melting), liquid to gas (evaporation), or vice versa (condensation). This is particularly relevant when discussing vapor pressure, which occurs during the phase change of evaporation.

The molecules in a liquid state move at various speeds, and those at the surface with enough kinetic energy can break free and become vapor. Lowering the temperature, as in Part a, diminishes the energy available for these molecules, resulting in few making the phase change, hence the vapor pressure drops. In contrast, with a change in volume or addition of more liquid, as seen in Parts b and c, the phase change dynamics at the molecular level remain unaffected, meaning the vapor pressure stays constant.

Understanding phase change is crucial since it embodies the heart of the vapor pressure concept, which is exclusive to the liquid and gas phases and their equilibrium.

The kinetic molecular theory provides an explanation of how particles in matter behave. It dictates that molecules are in constant random motion and that the temperature of a substance is a measure of the average kinetic energy of its molecules. This theory underpins the explanation for variations in vapor pressure with changes in temperature.

When we talk about the vapor pressure of water in a closed container, as in the given exercise, we are considering the molecules that have enough kinetic energy to escape the liquid phase. Lowering the temperature (Part a) leads to molecules slowing down, thus reducing the number that can vaporize and, consequently, lowering the vapor pressure.

Even if the volume of the container is doubled (Part b) or more water is added to the beaker (Part c), the average kinetic energy of the molecules does not change, provided the temperature remains the same. Hence, according to kinetic molecular theory, the vapor pressure will remain unchanged as well. This theory enables a better grasp of the molecular activity during phase changes and the conditions affecting vapor pressure.