Crystallization of sodium acetate from a supersaturated solution occurs spontaneously (see Section 12.1). What can you deduce about the signs of \(\Delta S\) and \(\Delta H ?\)

Entropy, symbolized as ΔS, is a core concept in thermodynamics associated with the level of disorder or randomness in a system. A positive change in entropy (ΔS > 0) suggests that the disorder within the system has increased. Conversely, a negative change in entropy (ΔS < 0) implies that the system has become more ordered.

When sodium acetate crystallizes, it transitions from a disordered, supersaturated liquid state to a highly ordered, solid crystalline structure. This ordering process results in a decrease in entropy, indicating a negative ΔS. Understanding entropy is crucial as it has a direct impact on the spontaneity of chemical processes and helps predict how substances will respond under varying conditions.

Enthalpy, represented by ΔH, reflects the total heat content of a system under constant pressure. When a chemical reaction or physical change occurs, ΔH measures the heat absorbed or released. A negative change in enthalpy (ΔH < 0) signifies that the system has released heat, making the process exothermic. In contrast, a positive change in enthalpy (ΔH > 0) means heat is absorbed by the system, indicating an endothermic process.

For the crystallization of sodium acetate, the process is exothermic because the formation of a solid from a liquid releases heat into the surroundings. This heat release is an important factor that contributes to the spontaneous nature of crystallization, as the reduction in the system's enthalpy helps to drive the process forward.

Gibbs free energy, denoted by ΔG, is a thermodynamic quantity used to predict whether a process will occur spontaneously at a constant temperature and pressure. To ensure spontaneity, the change in Gibbs free energy should be negative (ΔG < 0). The Gibbs free energy equation is given by ΔG = ΔH - TΔS, where T represents the absolute temperature in Kelvin.

The sign of ΔG is influenced by both ΔH and ΔS. For the crystallization of sodium acetate, having both a negative change in entropy (ΔS < 0) and a negative change in enthalpy (ΔH < 0) aligns with the spontaneity observed. However, the temperature at which the process occurs also plays a crucial role. If the temperature is not too high, the negative value of ΔH will be dominant, thus ensuring a negative ΔG and allowing the sodium acetate crystallization to proceed spontaneously.