Question

(a) Give two examples of endothermic processes that are spontaneous. (b) Give an example of a process that is spontaneous at one temperature but nonspontaneous at a different temperature.

Short answer

(a) Two examples of endothermic spontaneous processes are the dissolution of ammonium nitrate in water and the evaporation of water. (b) The melting of ice is a process that is spontaneous at temperatures above \(0^\circ\text{C}\) but nonspontaneous at temperatures below \(0^\circ\text{C}\).

Step-by-step solution

A. Examples of Endothermic Processes That Are Spontaneous

An endothermic process is a process in which the system absorbs energy from its surroundings. Spontaneous processes are those that occur without any external energy input. In this part, we will give two examples of endothermic processes that are spontaneous. 1. Dissolution of Ammonium Nitrate in Water: Dissolving ammonium nitrate (\(\text{NH}_4\text{NO}_3\)) in water is an endothermic process. When ammonium nitrate dissolves in water, it absorbs heat from its surroundings, causing the temperature of the solution to decrease. Despite being endothermic, this process is spontaneous due to its increased entropy, which outweighs the energy-absorbing nature of the reaction. 2. Evaporation of Water: The evaporation of water is another example of an endothermic spontaneous process. When water molecules evaporate, they absorb heat energy from their surroundings and turn from liquid to gas phase. The evaporation of water is spontaneous at room temperature because the increase in entropy (disorder) when water changes from the liquid to gas phase is large enough to offset the energy-absorbing nature of the process.

B. A Process That Is Spontaneous at One Temperature but Nonspontaneous at a Different Temperature

For this part, we have to give an example of a process that is spontaneous at one temperature but nonspontaneous at a different temperature. Melting of Ice: Melting of ice is a process that is spontaneous at certain temperatures and nonspontaneous at others. The melting of ice is an endothermic process because it absorbs heat from its surroundings to break the solid lattice structure and change into a liquid state. At temperatures above \(0^\circ\text{C}\), the melting of ice is spontaneous because the increase in entropy when water changes from the solid to the liquid phase is large enough to offset the energy-absorbing nature of the process. However, at temperatures below \(0^\circ\text{C}\), the melting process becomes nonspontaneous as the absorbed heat is insufficient to overcome the energy required to break the lattice structure. In this case, water molecules in the solid state have lower energy and are more stable than if they were in the liquid state, which is why the melting of ice is nonspontaneous at temperatures below \(0^\circ\text{C}\).

Key concepts

Entropy and Spontaneity

Understanding the intricacy of entropy and spontaneity is crucial when determining why certain processes occur without external input. Entropy refers to the disorder or randomness in a system and is a key factor in the spontaneity of processes. A helpful way to remember this is the phrase 'nature tends towards chaos', which implies that processes aiming to increase chaos (entropy) are often favored.

Spontaneous endothermic reactions, such as the dissolution of ammonium nitrate in water or the evaporation of water, are excellent examples. Although these processes require heat from their surroundings, they happen willingly because the overall entropy of the system increases. This increase in randomness or disorder often becomes the driving force for spontaneity, overriding the need for an energy input from the environment.

When a substance like ammonium nitrate dissolves, its ions dispersed in water increase the system's disorder. Similarly, when water evaporates, molecules move from a structured liquid state to a more disordered gas phase, raising entropy. Hence, while these processes absorb energy, the natural tendency of increasing entropy often makes them spontaneous.

Phase Transition Temperature Dependence

The spontaneity of a phase transition—such as the melting of ice—is intimately linked to temperature dependence. This fascinating relationship is best illustrated by examining when a substance changes its state. Take ice, for example; at temperatures above 0°C, ice melts spontaneously, with the process driven by entropy. The water molecules, when given enough thermal energy, break free from the rigid lattice structure, favoring a more disordered liquid state.

However, as the temperature drops below the freezing point, it lacks sufficient energy to allow for this transition. As a result, the melting of ice becomes nonspontaneous. At colder temperatures, the structured solid state of ice is more stable and has lower energy compared to the liquid state. This example highlights that the spontaneity of phase changes cannot be discussed without considering the temperature’s crucial role.

Dissolution of Ionic Compounds

Let’s delve into the dissolution of ionic compounds, such as when ammonium nitrate dissolves in water—an endothermic but spontaneous process. Ionic compounds consist of positive and negative ions held together by strong electrostatic forces. In dissolution, these ions are separated and surrounded by water molecules, a process that requires energy to overcome the ionic bonds.

The fascinating bit is that despite being energetically unfavorable at the outset due to the need to absorb heat, dissolution can still be spontaneous. This is because the resulting increase in entropy, from an ordered solid to a more disordered solution, plays a significant role. For students, it's critical to recognize that the disintegration of a structured ionic compound lattice into a solution provides a considerable entropy boost, often making the process spontaneous despite its endothermic nature.