Question

Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) dissolves spontaneously and endothermically in water. What can you deduce about the sign of \(\Delta S\) for the solution process?

Short answer

\(\Delta S\) is positive for the solution process.

Step-by-step solution

Understand the Terms Involved

To solve this problem, we first need to understand the key terms: 'endothermic' and 'spontaneous.' An 'endothermic' process absorbs heat, meaning that the system takes in energy from the surroundings. A 'spontaneous' process occurs naturally without needing extra energy input.

Utilize Gibbs Free Energy Equation

The spontaneity of a process at constant temperature and pressure can be explained using Gibbs Free Energy change (\(\Delta G\)). The equation is given by: \[\Delta G = \Delta H - T\Delta S\] where \(\Delta G\) is the change in free energy, \(\Delta H\) is the change in enthalpy, \(T\) is the temperature, and \(\Delta S\) is the change in entropy.

Analyze the Impact of Endothermic Process

Since the process is endothermic, \(\Delta H\) is positive. In an endothermic and spontaneous process, the system absorbs heat, so we expect a positive \(\Delta H\).

Determine Implications for Entropy

For a process to be spontaneous (\(\Delta G < 0\)), and considering that \(\Delta H > 0\), the entropy change \(\Delta S\) must be positive. This means that the entropy of the system increases. Essentially, the increase in entropy compensates for the energy absorbed as heat.

Key concepts

Endothermic Process

An endothermic process is one that absorbs energy in the form of heat from its surroundings. This means that during the process, heat flows into the system from the external environment. Examples of such processes include the melting of ice and the dissolution of ammonium nitrate in water. When a reaction or process is endothermic, it is characterized by a positive change in enthalpy (\(\Delta H > 0\)). Although heat is absorbed, this does not mean the process cannot happen spontaneously. In some instances, other factors, such as increasing entropy, play a crucial role in making an endothermic process spontaneous.

Entropy Change

Entropy (\(S\)) is a measure of the disorder or randomness in a system. Changes in entropy during a process are indicated by \(\Delta S\). If \(\Delta S\) is positive, it signifies an increase in disorder or randomness in the system. This often favors spontaneous processes. Let's consider the example of ammonium nitrate dissolving in water. Here, we deal with the dissolution process where the solid crystals, having a defined structure, dissolve into ions. As the ions disperse in solution, the disorder increases substantially. Thus, \(\Delta S\) is positive. This increase in entropy can make up for the energy input required in an endothermic reaction, allowing it to still progress naturally.

Spontaneous Reaction

A spontaneous reaction is one that occurs naturally without the need for additional energy input. These reactions can be driven by favorable thermodynamic changes. Primarily, spontaneity can be assessed using Gibbs Free Energy, \(\Delta G\).For a reaction to be spontaneous, \(\Delta G\) must be less than zero (\(\Delta G < 0\)). This can occur in several scenarios:

• If both enthalpy (\(\Delta H\)) and entropy change (\(\Delta S\)) are favorable.
• If endothermic (\(\Delta H > 0\)), the entropy change must be significantly positive to make \(\Delta G\) negative by overcoming the heat absorbed.

In the case of dissolving ammonium nitrate, despite the endothermic nature, the positive entropy change drives the reaction to occur spontaneously.

Enthalpy Change

Enthalpy (\(H\)) is a measure of the total energy of a thermodynamic system. When involved in processes, the change in enthalpy (\(\Delta H\)) reflects the heat exchanged with the surroundings.- A positive \(\Delta H\) indicates that the reaction absorbs heat, characteristic of endothermic reactions.- A negative \(\Delta H\) implies that the reaction releases heat, typical of exothermic reactions.In spontaneous processes, the enthalpy change interacts with entropy change and temperature to dictate the spontaneity via the Gibbs Free Energy equation. For endothermic processes to occur spontaneously, there needs to be a substantial positive change in entropy (\(\Delta S\)) to compensate for the absorbed energy, ensuring that \(\Delta G\) remains negative.