Question

On the basis of the distribution of kinetic energies of the molecules of a liquid, explain why increasing the liquid's temperature increases the rate of evaporation.

Short answer

Raising the temperature of a liquid increases the average kinetic energy of its molecules, which causes more molecules to have sufficient energy to overcome intermolecular forces and evaporate, thus increasing the rate of evaporation.

Step-by-step solution

Understanding Kinetic Energy Distribution

The kinetic energies of molecules in a liquid are not all the same; they are distributed over a range of values. At any given temperature, this distribution can be represented by the Maxwell-Boltzmann distribution curve. Some molecules will have low kinetic energies, while others will have enough kinetic energy to overcome the intermolecular forces and exit the liquid phase to become gas, which is the process of evaporation.

Effect of Temperature on Kinetic Energy

As the temperature of a liquid is increased, the average kinetic energy of its molecules increases. This shift means that a greater number of molecules will have kinetic energies that are higher than the threshold energy required for evaporation to occur.

Increase in Evaporation Rate

Since more molecules have higher kinetic energies with the increase in temperature, more molecules are able to overcome the intermolecular forces holding them in the liquid. As a result, the rate of evaporation increases because more molecules have the necessary energy to escape into the gas phase.

Key concepts

Kinetic Energy Distribution

When we delve into the concept of kinetic energy distribution, we're exploring the range of energy levels that the molecules of a substance possess. Imagine a crowded room where some people are sitting still while others are dancing energetically. Similarly, in a liquid, some molecules are moving slowly, and others quickly. This variation is due to the different amounts of kinetic energy the molecules have.

Why does this matter? Well, molecules with higher kinetic energy are like the energetic dancers, more likely to 'break free' from the crowd and escape into the gas phase. In contrast, those with lower energy remain in the liquid state, akin to the people sitting quietly. This diversity in energy levels is crucial for understanding processes like evaporation, where only the 'liveliest' molecules with enough energy to overcome the attraction to their neighbors can evaporate.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution provides a statistical view of the kinetic energies of particles in a substance. Picture a graph where the horizontal axis represents kinetic energy and the vertical axis shows the number of molecules. The curve on this graph—the Maxwell-Boltzmann distribution—peaks at the most probable kinetic energy but shows a spread of energies from low to high.

The 'tail' of this curve to the right represents molecules with enough energy to evaporate. As the substance heats up, this tail stretches further to the right, indicating that more molecules have attained the energy level needed for escape. It’s much like heating up our room of dancers: as the energy—temperature, in this case—increases, more people start to dance, and similarly, more molecules can vaporize.

Intermolecular Forces

Intermolecular forces are the forces of attraction and repulsion between molecules. Think of them as the 'social bonds' that keep the molecules together in the liquid phase. They can be thought of as hands holding the molecules together. The strength of these 'hands' depends on the type of molecules and dictates whether they stick together in a liquid or break apart to turn into gas—the latter occurring during evaporation.

When a molecule gains enough kinetic energy, it's as though it has received an invitation to leave the party—the liquid phase. If this energy surpasses the strength of the intermolecular forces, the molecule can 'let go of the hands' and transition to the gas phase, contributing to evaporation.

Temperature and Evaporation

Now let’s connect temperature to the rate of evaporation. As we increase the temperature, we're essentially turning up the heat on our metaphorical dance floor. This energy boost makes our once sedentary individuals more active. Similarly, heating up a liquid injects energy into it, increasing the average kinetic energy of its molecules.

As more molecules start moving with greater energy, more are able to break away from the pull of their neighbors—overcoming the intermolecular forces. An increase in temperature leads to a higher fraction of molecules with enough energy to transition from liquid to gas, hence accelerating the rate of evaporation. This is why a hot summer day dries a wet pavement faster than a cold one.