Question

Solid \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is placed in a beaker containing water at \(25^{\circ} \mathrm{C}\). When the solid has completely dissolved, the temperature of the solution is \(23.5^{\circ} \mathrm{C}.\) (a) Was the process exothermic or endothermic? (b) Was the process spontaneous? (c) Did the entropy of the system increase? (d) Did the entropy of the universe increase?

Short answer

Endothermic, spontaneous, increased system entropy, increased universe entropy.

Step-by-step solution

Evaluate Temperature Change

The initial temperature of the water is \(25^{\circ} \mathrm{C}\), and after dissolving, the temperature is \(23.5^{\circ} \mathrm{C}\). Since the temperature decreased, this indicates that the process absorbed heat from the surroundings.

Determine Process Type (Exothermic or Endothermic)

Because heat is absorbed from the surroundings (evidenced by the temperature drop), the dissolution process is endothermic.

Analyze Process Spontaneity

Even though the process was endothermic, it proceeded without external intervention, indicating that it was spontaneous. Spontaneity can result from an increase in entropy or from entropic favorability that outweighs enthalpy.

Consider System Entropy Change

Dissolution generally leads to an increase in disorder as the solid \(\mathrm{NH}_4 \mathrm{NO}_3\) separates into ions in solution. This suggests an increase in entropy of the system.

Consider Universe Entropy Change

Although the process is endothermic (absorbing heat and decreasing surroundings' entropy), the increase in system entropy due to dissolution is greater, leading to an overall increase in the entropy of the universe.

Key concepts

Endothermic Process

In thermodynamics, an endothermic process is one where energy, typically in the form of heat, is absorbed from the surroundings into the system. This energy is required for the reaction or process to occur. A simple clue that an endothermic process is taking place is a decrease in temperature of the surroundings. This happens because heat from the surrounding environment is being pulled into the system.
In the example of ammonium nitrate (\(\mathrm{NH}_4\mathrm{NO}_3\)), when it dissolves in water, the temperature lowers from \(25^{\circ} \mathrm{C}\) to \(23.5^{\circ} \mathrm{C}\). This indicates that the solution absorbed heat from its immediate environment, confirming that the dissolution is indeed an endothermic process.
It's important to remember that endothermic processes can occur naturally without any input from outside sources. This will tie into the concept of spontaneity, which we will explore further.

Spontaneity

Spontaneity refers to the likelihood of a process occurring without needing external influence. A spontaneous process unfolds naturally because of intrinsic properties, rather than applied forces or catalysts.
In the context of the dissolution of ammonium nitrate, despite the process being endothermic, the molecules spread out into the solvent on their own. This can sometimes be surprising, since energy is being absorbed, but spontaneity doesn't only depend on energy changes.
One critical factor affecting spontaneity is entropy, which often increases when substances dissolve. Thus, while the solution cools due to absorbed heat, the natural tendency towards greater disorder (molecular spreading) helps drive the process forward spontaneously.

Entropy Change

Entropy is all about disorder and randomness. In chemistry, it particularly relates to how energy is dispersed within a system. When a solid like ammonium nitrate dissolves in water, it separates into individual ions: the \(\mathrm{NH}_4^+\) and \(\mathrm{NO}_3^-\) ions.
This dissolution leads to a significant increase in the disorder of the system, primarily because the order of the solid lattice structure is lost as ions disperse into the solution. This randomness indicates an increase in entropy.
A general rule is that when solids dissolve, the disorder tends to increase, as seen in the example of ammonium nitrate. Hence, understanding entropy change helps explain why certain reactions occur without needing extra energy or force.

Dissolution of Ammonium Nitrate

Dissolution involves a solute breaking down into its constituent particles and spreading throughout the solvent. For ammonium nitrate, which dissolves in water, this process is interestingly characterized by a decrease in temperature, setting it apart as an endothermic reaction.
As the crystalline structure of ammonium nitrate breaks down, the resulting ions disperse uniformly in the water. This transition from ordered solid to scattered ions is also accompanied by swelling in randomness, boosting the system's entropy.

• The cooling effect during dissolution is a direct result of energy uptake from the environment.
• The overall increase in disorder supports spontaneity, showing why ammonium nitrate dissolves easily despite being endothermic.

By observing how ammonium nitrate behaves in water, students can gain deeper insights into thermodynamics, especially regarding how energy, entropy, and spontaneous reactions interact.