Predict the sign of \(\Delta S\) for each of the following and explain. a. the evaporation of alcohol b. the freezing of water c. compressing an ideal gas at constant temperature d. dissolving \(\mathrm{NaCl}\) in water

When alcohol evaporates, the molecules transform from a liquid state to a gaseous state. In liquid form, alcohol molecules are fairly close together and move with limited freedom. However, once they evaporate and become a gas, they spread out and move more freely. The measure of randomness or disorder in a system is known as entropy, and whenever a substance undergoes a phase change from liquid to gas, entropy increases.

This increase in entropy happens because, in the gaseous state, the molecules have higher kinetic energy and there are more possible positions and velocities for each molecule.

Therefore, during the evaporation of alcohol, the entropy change, denoted as \( \Delta S \), is positive, signifying an increase in disorder and energy dispersal within the system.

Conversely, freezing is the process where water changes from its liquid form to its solid form, ice. Liquid water has molecules that are constantly moving in a fluid, random manner. As the temperature is lowered and water begins to freeze, these molecules start to arrange themselves into a fixed, crystalline structure.

This structured arrangement represents a decrease in randomness and an increase in order, meaning that the entropy of the system decreases. In thermodynamics, a decrease in entropy is represented by a negative \( \Delta S \).

When water freezes, energy is released from the water as heat, because the molecules in the solid form vibrate less and, thus, have less kinetic energy compared to the liquid form. The overall result is a negative entropy change, indicating a less disordered system.

When we compress an ideal gas, we are reducing its volume without changing its temperature, a process commonly achieved by increasing the external pressure on the gas. As the volume decreases, the gas molecules have less space to move around, which limits their possible positions.

Entropy, a measure of disorder and the number of ways particles can be arranged, decreases when the particles are confined to a smaller volume. This constraint restricts the randomness, leading to a negative entropy change \( \Delta S \).

Since temperature remains constant during this compression (as per the ideal gas assumption), the decrease in volume directly translates to a decrease in entropy. This process is a clear demonstration of entropy change being heavily influenced by volume and confinement of gas particles.

Dissolution is an important physical process in chemistry, involving a solute (NaCl in this case) being dispersed in a solvent (water), resulting in a solution. Salt (NaCl) is made up of sodium (Na⁺) and chloride (Cl⁻) ions, which are arranged in a crystalline lattice with a very low entropy due to its highly ordered structure.

When NaCl is added to water, the polar water molecules surround and stabilize the Na⁺ and Cl⁻ ions, allowing them to separate and move freely, which creates more disorder and possibilities for their arrangement. This process increases the overall entropy of the system, yielding a positive \( \Delta S \).

The solvation process, therefore, results in the increase of randomness as ions are released from a structured lattice into a more disordered state, helping us conclude that dissolving NaCl in water leads to a positive change in entropy.