Question

Which of the following processes are spontaneous and which are nonspontaneous at a given temperature? (a) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) saturated soln (b) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) unsaturated soln (c) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) supersaturated soln

Short answer

(a) Nonspontaneous, (b) Spontaneous, (c) Nonspontaneous.

Step-by-step solution

Understanding Spontaneity

A process is spontaneous if it occurs without needing to add external energy. In chemistry, spontaneous processes often involve an increase in entropy (disorder) or are influenced by enthalpy changes.

Defining System Scenarios

We need to examine the state of the solution: saturated, unsaturated, and supersaturated. These conditions affect whether the dissolution of a solid into a solution is spontaneous.

Analyzing Saturated Solution (a)

In a saturated solution, the solvent holds the maximum amount of solute that can dissolve at that temperature. Adding more of the same solute will not dissolve spontaneously because the solution is at equilibrium.

Analyzing Unsaturated Solution (b)

In an unsaturated solution, the solvent can still dissolve more solute. Therefore, adding NaNO3 to water will dissolve spontaneously because the system is not at equilibrium and can increase entropy.

Analyzing Supersaturated Solution (c)

In a supersaturated solution, the solution holds more solute than it can normally hold at that temperature. Any disturbance or addition can lead to the solute precipitating out, so the dissolution is nonspontaneous and instead may cause crystallization.

Key concepts

Entropy and Enthalpy

In the realm of chemistry, understanding the terms **entropy** and **enthalpy** is crucial for predicting whether a reaction is spontaneous. **Entropy**, symbolized as \( S \), measures the degree of disorder or randomness in a system. When the entropy of a system increases, the system becomes more disordered, which is often favored in spontaneous processes. **Enthalpy**, represented as \( H \), is the total heat content of a system. A reaction often proceeds spontaneously if it leads to a decrease in enthalpy, resulting in the release of energy into the surroundings.

Spontaneity, however, is not solely dependent on either increased entropy or decreased enthalpy — it is the interplay between the two. This is quantified by the Gibbs free energy change \( \Delta G \), where the formula \( \Delta G = \Delta H - T \Delta S \) (with \( T \) being the absolute temperature) helps in predicting spontaneity. A negative \( \Delta G \) typically indicates a spontaneous process, emphasizing that a reaction can be driven by an increase in entropy, a decrease in enthalpy, or a combination of both.

Saturated Solutions

A **saturated solution** is one where the solvent has absorbed the maximum amount of solute it can hold at a given temperature. At this point, the solution is in a state of dynamic equilibrium, meaning the rate at which the solute dissolves is equal to the rate at which it precipitates back out.

In a saturated solution, if additional solute is introduced, it will not dissolve because the capacity of the solvent is already fully utilized. Thus, no further increase in entropy occurs, and the solution remains unchanged in terms of solute concentration. As such, the addition of more solute beyond the saturation point is non-spontaneous because it does not lead to further mixing or increased disorder. Understanding this concept through enthalpy also shows that without additional energy, the solution process is at a halt.

Unsaturated Solutions

An **unsaturated solution** is one in which the solvent can still dissolve more solute. This occurs when the current solute concentration is less than the maximum capacity of the solvent at a given temperature. Because there is room for more solute, the system is not in equilibrium, and any solute added will dissolve spontaneously.

In this scenario, the dissolution of solute increases the system's entropy because it introduces more disorder. This is why processes in unsaturated solutions are often spontaneous — the addition of more solute does make the system more disordered. Additionally, enthalpy aspects can favor the spontaneous dissolution if the heat is absorbed or released efficiently without adverse barriers. In the case of unsaturated solutions, both entropy and available energy play roles that tilt the occasion in favor of spontaneity.

Supersaturated Solutions

A **supersaturated solution** is a precarious state where the solution holds more solute than it usually can at a specific temperature. Achieving a supersaturated solution typically involves dissolving solute at an elevated temperature and then slowly cooling it. Here, the solution is beyond its equilibrium state, teetering on instability.

In this delicate balance, any disturbance — such as the introduction of a tiny crystal or even a scratch on the container's surface — can trigger rapid crystallization of the excess solute. This crystallization event is non-spontaneous from an entropy standpoint because it decreases the system's disorder. The system will try to return to a stable, lower-energy state by expelling solute, hence reversing the increased solute's characteristics. As such, without specific conditions or manipulations, supersaturated solutions represent a battleground of non-common physicochemical principles.