Problem 24 - University Physics with Modern Physics

Question

A glass of water at room temperature is left on the kitchen counter overnight. In the morning, the amount of water in the glass is smaller due to evaporation. The water in the glass is below the boiling point, so how is it possible for some of the liquid water to have turned into a gas?

Step-by-Step Solution

Answer

Question: Explain why evaporation occurs at temperatures below the boiling point of water. Answer: Evaporation occurs at temperatures below the boiling point of water due to the distribution of molecular energies and vapor pressure. Some water molecules at the surface have enough energy to overcome the attractive forces from other water molecules and enter the gas phase. This process happens even at room temperature, and as a result, the amount of water in a glass left overnight decreases as water molecules escape the liquid phase and become water vapor.

Step 1: Introduction: Molecular Motion and Evaporation

In liquids, molecules are constantly in motion, and their energy levels are distributed over a range. Some molecules have higher energy levels than others, which allows them to break away from their neighbors and turn into gases. This process is called evaporation, and it can occur at temperatures below a liquid's boiling point.

Step 1: Understanding Evaporation at a Molecular Level

Evaporation is a surface phenomenon. Molecules of water at the surface of the liquid have a higher probability of escaping the liquid phase because there are fewer neighboring water molecules above them applying attractive forces. Therefore, if a water molecule at the surface has enough energy to overcome the attractive forces from other water molecules around it, it can break free and become a water vapor molecule.

Step 2: Energy Distribution Among Molecules

According to the kinetic theory of gases, the distribution of energies among molecules in a sample follows the Maxwell-Boltzmann distribution. This means that there is a range of energy levels present in the sample. A small portion of molecules at the high-energy tail of the distribution may have enough energy to overcome the intermolecular forces and break away from the liquid to enter the gas phase at any given moment.

Step 3: Vapor Pressure

When some molecules of liquid water become water vapor, they exert a pressure on their surroundings, known as the vapor pressure. This pressure depends on the temperature of the liquid: as the temperature rises, the vapor pressure increases because a larger fraction of molecules have enough energy to break free from the liquid phase. When the vapor pressure equals the atmospheric pressure, the liquid reaches its boiling point. However, evaporation can happen before this point, as long as some molecules have enough energy to enter the gas phase.

Step 4: Evaporation at Room Temperature

Over time, the warmer water molecules close to the surface will escape the liquid and move into the gas phase. As a result, the amount of water in the glass decreases due to evaporation. Even though the water in the glass is below its boiling point, there are still some water molecules with enough energy to escape the liquid phase and become water vapor. This is why the amount of water in a glass left overnight decreases even if it's not being heated to the boiling point. In conclusion, evaporation can occur at temperatures below the boiling point of water due to the distribution of molecular energies and vapor pressure. As a result, the amount of water in a glass left on the kitchen counter will gradually decrease overnight as water molecules escape the liquid phase and enter the gas phase.