Question

Predict the sign of \(\Delta S\) for the following: (a) precipitating solid AgCl from a solution containing \(\mathrm{Ag}^{+}\) and \(\mathrm{Cl}^{-}\) ions (b) dissolving sugar in hot coffee (c) glass turning into sand

Short answer

Question: Predict the sign of the change in entropy (ΔS) for the following processes: (a) precipitation of solid AgCl from a solution containing Ag+ and Cl- ions, (b) dissolving sugar in hot coffee, (c) glass turning into sand. Answer: (a) ΔS < 0, (b) ΔS > 0, (c) ΔS > 0.

Step-by-step solution

Analyze the precipitation of AgCl from a solution

In this case, the process involves the formation of a solid from a solution. When the ions in the solution combine to form a solid, the number of particles in the system decreases, and the system becomes more ordered. Therefore, the change in entropy (ΔS) for this process should be negative.

Analyze dissolving sugar in hot coffee

Dissolving sugar in hot coffee involves the mixing of sugar molecules with the liquid coffee molecules. This increases the number of particles in the system, leading to increased randomness and disorder. Therefore, the change in entropy (ΔS) for this process should be positive.

Analyze glass turning into sand

When glass turns into sand, the large solid structure of glass is broken down into smaller pieces, resulting in an increase in the number of particles in the system. With more particles present, the system becomes more disordered and random. Thus, the change in entropy (ΔS) for this process should be positive. So, to summarize the results: (a) ΔS < 0 (negative change in entropy for precipitation of AgCl) (b) ΔS > 0 (positive change in entropy for dissolving sugar in hot coffee) (c) ΔS > 0 (positive change in entropy for glass turning into sand)

Key concepts

Entropy (ΔS)

Entropy is a measure of the randomness or disorder within a system. In thermodynamics, it's a central concept that helps us understand the spontaneous flow of energy and the likelihood of a process occurring. Entropy can be represented by the symbol ΔS when referring to the change in entropy during a process.

When particles move from a more ordered state to a less ordered state, the entropy increases, which is represented by a positive ΔS. Conversely, when a system becomes more ordered – for example, when a gas condenses into a liquid – the entropy decreases, indicated by a negative ΔS. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. Thus, it's essential to consider entropy changes when predicting whether a chemical reaction or physical process is spontaneous.

Precipitation Reactions

Precipitation reactions are chemical processes where soluble ions in a solution react to form an insoluble compound, which settles out of the solution as a solid, known as a precipitate. From an entropy perspective, these reactions are fascinating because they often result in a decrease in entropy.

The process of precipitating solid AgCl from a solution containing Ag⁺ and Cl⁻ ions exemplifies this concept. As ions in the solution form a solid precipitate, they transition from a more disordered state (freely moving in solution) to a more ordered state (locked in a solid lattice). Thus, the number of possible microstates and the level of disorder in the system decrease, which corresponds to a negative change in entropy (ΔS < 0).

Dissolution Process

The dissolution process involves dissolving a substance, such as sugar, in a solvent like water or coffee. This process can significantly affect the entropy of the system. When sugar dissolves, its molecules become dispersed among the solvent molecules, which increases the level of disorder in the system because the dissolved particles can move more freely.

The act of dissolving sugar in hot coffee is an excellent example: The heat provides energy that allows the sugar molecules to separate and interact more dynamically with the coffee molecules. As a result, the entropy of the system increases due to the higher randomness and greater number of possible microstates (ΔS > 0). This demonstrates how temperature and solute-solvent interactions play crucial roles in dissolution and entropy changes.

Physical State Changes

Physical state changes, such as melting, freezing, evaporation, or sublimation, are all about transitions from one phase of matter to another. These changes are typically accompanied by entropy changes since the degree of order and the freedom of particles to move are different in various phases.

For instance, when glass turns into sand, a process that mimics the transition from a solid to a more disordered state, the original structured arrangement of the glass is disrupted. As it breaks down into smaller particles of sand, the system's entropy increases due to the enhanced disorder and randomness (ΔS > 0). This principle is a key topic in understanding thermodynamics and can be extended to all changes of phase, relating the physical state of a substance to entropy.